%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA128-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 06:33:45 PM UTC 2026
% Result : Unsatisfiable 0.73s 0.93s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRA128-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : run_E %s %d THM
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 22:35:17 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.73/0.93 % SZS status Unsatisfiable
% 0.73/0.93 % SZS output start Proof
% 0.73/0.93 tff(r_type, type, (
% 0.73/0.93 r: ( $i * $i ) > $o)).
% 0.73/0.93 tff(s_type, type, (
% 0.73/0.93 s: $i > $i)).
% 0.73/0.93 tff(elem_1_type, type, (
% 0.73/0.93 elem_1: $i)).
% 0.73/0.93 tff(z_type, type, (
% 0.73/0.93 z: $i)).
% 0.73/0.93 tff(b_type, type, (
% 0.73/0.93 b: ( $i * $i ) > $o)).
% 0.73/0.93 tff(inj_0_type, type, (
% 0.73/0.93 inj_0: $i > $i)).
% 0.73/0.93 tff(1,assumption,(b(s(z), z)), introduced(assumption)).
% 0.73/0.93 tff(2,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 0.73/0.93 tff(3,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.73/0.93 tff(4,assumption,(~(z = elem!1)), introduced(assumption)).
% 0.73/0.93 tff(5,plain,
% 0.73/0.93 ((z = elem!1) <=> (elem!1 = z)),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(6,plain,
% 0.73/0.93 ((elem!1 = z) <=> (z = elem!1)),
% 0.73/0.93 inference(symmetry,[status(thm)],[5])).
% 0.73/0.93 tff(7,assumption,(elem!1 = z), introduced(assumption)).
% 0.73/0.93 tff(8,plain,
% 0.73/0.93 (z = elem!1),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.73/0.93 tff(9,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[4, 8])).
% 0.73/0.93 tff(10,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(11,plain,
% 0.73/0.93 (~(elem!1 = z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[10, 4])).
% 0.73/0.93 tff(12,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 0.73/0.93 tff(13,plain,
% 0.73/0.93 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(14,plain,
% 0.73/0.93 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.73/0.93 inference(symmetry,[status(thm)],[13])).
% 0.73/0.93 tff(15,plain,
% 0.73/0.93 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[14])).
% 0.73/0.93 tff(16,plain,
% 0.73/0.93 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(17,plain,
% 0.73/0.93 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[16])).
% 0.73/0.93 tff(18,plain,
% 0.73/0.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(19,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(20,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(21,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 0.73/0.93 tff(22,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.73/0.93 tff(23,plain,(
% 0.73/0.93 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.93 inference(skolemize,[status(sab)],[22])).
% 0.73/0.93 tff(24,plain,
% 0.73/0.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.73/0.93 tff(25,plain,
% 0.73/0.93 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.73/0.93 tff(26,plain,
% 0.73/0.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(27,plain,
% 0.73/0.93 (inj_0(s(z)) = z),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.73/0.93 tff(28,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.73/0.93 tff(29,plain,
% 0.73/0.93 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[28])).
% 0.73/0.93 tff(30,plain,
% 0.73/0.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(31,plain,
% 0.73/0.93 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[30, 25])).
% 0.73/0.93 tff(32,plain,
% 0.73/0.93 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.73/0.93 inference(symmetry,[status(thm)],[31])).
% 0.73/0.93 tff(33,plain,
% 0.73/0.93 (s(s(z)) = z),
% 0.73/0.93 inference(transitivity,[status(thm)],[32, 29, 27])).
% 0.73/0.93 tff(34,plain,
% 0.73/0.93 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(35,plain,
% 0.73/0.93 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[34])).
% 0.73/0.93 tff(36,plain,
% 0.73/0.93 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(37,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 0.73/0.93 tff(38,plain,
% 0.73/0.93 (![X: $i] : (~(s(X) = z))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.73/0.93 tff(39,plain,(
% 0.73/0.93 ![X: $i] : (~(s(X) = z))),
% 0.73/0.93 inference(skolemize,[status(sab)],[38])).
% 0.73/0.93 tff(40,plain,
% 0.73/0.93 (![X: $i] : (~(s(X) = z))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.73/0.93 tff(41,plain,
% 0.73/0.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(42,plain,
% 0.73/0.93 (~(s(s(z)) = z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.73/0.93 tff(43,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.73/0.93 tff(44,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(45,plain,
% 0.73/0.93 (~(s(z) = s(s(s(z))))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[44, 17])).
% 0.73/0.93 tff(46,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.73/0.93 tff(47,plain,
% 0.73/0.93 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[46])).
% 0.73/0.93 tff(48,plain,
% 0.73/0.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(49,plain,
% 0.73/0.93 (inj_0(s(s(z))) = s(z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[48, 25])).
% 0.73/0.93 tff(50,plain,
% 0.73/0.93 (s(z) = inj_0(s(s(z)))),
% 0.73/0.93 inference(symmetry,[status(thm)],[49])).
% 0.73/0.93 tff(51,plain,
% 0.73/0.93 (s(z) = s(s(s(z)))),
% 0.73/0.93 inference(transitivity,[status(thm)],[50, 47, 31, 46])).
% 0.73/0.93 tff(52,assumption,(~(s(z) = s(s(s(z))))), introduced(assumption)).
% 0.73/0.93 tff(53,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.73/0.93 tff(54,plain,((~(s(s(z)) = s(s(s(z))))) | (s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(55,plain,
% 0.73/0.93 (~(s(s(z)) = s(s(s(z))))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[54, 45])).
% 0.73/0.93 tff(56,plain,
% 0.73/0.93 (~(s(s(s(z))) = s(s(z)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[55, 15])).
% 0.73/0.93 tff(57,plain,
% 0.73/0.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(58,plain,
% 0.73/0.93 (~(s(s(s(z))) = z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[57, 40])).
% 0.73/0.93 tff(59,plain,
% 0.73/0.93 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(60,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[59])).
% 0.73/0.93 tff(61,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(62,plain,
% 0.73/0.93 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(63,plain,
% 0.73/0.93 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[62])).
% 0.73/0.93 tff(64,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 0.73/0.93 tff(65,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.73/0.93 tff(66,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.73/0.93 tff(67,plain,(
% 0.73/0.93 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(skolemize,[status(sab)],[66])).
% 0.73/0.93 tff(68,plain,
% 0.73/0.93 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.73/0.93 tff(69,plain,
% 0.73/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(70,plain,
% 0.73/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(71,plain,
% 0.73/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.73/0.93 tff(72,plain,
% 0.73/0.93 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 0.73/0.93 tff(73,plain,
% 0.73/0.93 (r(s(s(s(z))), z)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[72, 12])).
% 0.73/0.93 tff(74,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 0.73/0.93 tff(75,plain,
% 0.73/0.93 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(76,plain,
% 0.73/0.93 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.73/0.93 inference(symmetry,[status(thm)],[75])).
% 0.73/0.93 tff(77,assumption,(b(z, s(z))), introduced(assumption)).
% 0.73/0.93 tff(78,assumption,(elem!1 = s(z)), introduced(assumption)).
% 0.73/0.93 tff(79,plain,
% 0.73/0.93 (s(elem!1) = s(s(z))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[78])).
% 0.73/0.93 tff(80,plain,
% 0.73/0.93 (s(s(elem!1)) = s(s(s(z)))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[79])).
% 0.73/0.93 tff(81,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[2, 80])).
% 0.73/0.93 tff(82,plain,((~(elem!1 = s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(83,plain,
% 0.73/0.93 (~(elem!1 = s(z))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[82, 2])).
% 0.73/0.93 tff(84,plain,
% 0.73/0.93 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(85,plain,
% 0.73/0.93 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 0.73/0.93 inference(symmetry,[status(thm)],[84])).
% 0.73/0.93 tff(86,assumption,(s(z) = elem!1), introduced(assumption)).
% 0.73/0.93 tff(87,plain,
% 0.73/0.93 (elem!1 = s(z)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.73/0.93 tff(88,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 0.73/0.93 tff(89,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.73/0.93 tff(90,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(91,plain,
% 0.73/0.93 (~(s(z) = elem!1)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[90, 83])).
% 0.73/0.93 tff(92,plain,
% 0.73/0.93 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 0.73/0.93 inference(commutativity,[status(thm)],[])).
% 0.73/0.93 tff(93,plain,
% 0.73/0.93 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 0.73/0.93 inference(symmetry,[status(thm)],[92])).
% 0.73/0.93 tff(94,plain,
% 0.73/0.93 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[93])).
% 0.73/0.93 tff(95,plain,
% 0.73/0.93 (~(z = s(s(s(z))))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[58, 94])).
% 0.73/0.93 tff(96,plain,
% 0.73/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(97,plain,
% 0.73/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(98,plain,
% 0.73/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.73/0.93 tff(99,plain,
% 0.73/0.93 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[98, 68])).
% 0.73/0.93 tff(100,plain,
% 0.73/0.93 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.73/0.93 tff(101,plain,
% 0.73/0.93 (r(z, s(s(s(z))))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[100, 74])).
% 0.73/0.93 tff(102,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 0.73/0.93 tff(103,plain,
% 0.73/0.93 (^[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))))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(104,plain,
% 0.73/0.93 (![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)))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[103])).
% 0.73/0.93 tff(105,plain,
% 0.73/0.93 (![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)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(106,plain,
% 0.73/0.93 (^[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)))))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(107,plain,
% 0.73/0.93 (![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)))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[106])).
% 0.73/0.93 tff(108,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 0.73/0.93 tff(109,plain,
% 0.73/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.73/0.93 tff(110,plain,
% 0.73/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.73/0.93 tff(111,plain,(
% 0.73/0.93 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.93 inference(skolemize,[status(sab)],[110])).
% 0.73/0.93 tff(112,plain,
% 0.73/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.73/0.93 tff(113,plain,
% 0.73/0.93 (((~![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)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(114,plain,
% 0.73/0.93 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(115,plain,
% 0.73/0.93 (((~![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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[114])).
% 0.73/0.93 tff(116,plain,
% 0.73/0.93 (((~![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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 0.73/0.93 inference(transitivity,[status(thm)],[115, 113])).
% 0.73/0.93 tff(117,plain,
% 0.73/0.93 ((~![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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(118,plain,
% 0.73/0.93 ((~![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)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.73/0.93 tff(119,plain,
% 0.73/0.93 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[118, 112, 102, 73])).
% 0.73/0.93 tff(120,plain,
% 0.73/0.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(121,plain,
% 0.73/0.93 (inj_0(s(elem!1)) = elem!1),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[120, 25])).
% 0.73/0.93 tff(122,plain,
% 0.73/0.93 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(123,plain,
% 0.73/0.93 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[122, 25])).
% 0.73/0.93 tff(124,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 0.73/0.93 tff(125,plain,
% 0.73/0.93 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[124])).
% 0.73/0.93 tff(126,plain,
% 0.73/0.93 (s(s(z)) = s(elem!1)),
% 0.73/0.93 inference(transitivity,[status(thm)],[32, 125, 123])).
% 0.73/0.93 tff(127,plain,
% 0.73/0.93 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[126])).
% 0.73/0.93 tff(128,plain,
% 0.73/0.93 (s(z) = elem!1),
% 0.73/0.93 inference(transitivity,[status(thm)],[50, 127, 121])).
% 0.73/0.93 tff(129,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 0.73/0.93 tff(130,plain,
% 0.73/0.93 ($false),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.73/0.93 tff(131,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.93 tff(132,plain,
% 0.73/0.93 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[131, 91])).
% 0.73/0.93 tff(133,plain,
% 0.73/0.93 (((~![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))))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(134,plain,
% 0.73/0.93 ((~![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))))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(135,plain,
% 0.73/0.93 ((~![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)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.73/0.93 tff(136,plain,
% 0.73/0.93 (b(s(s(s(z))), s(s(elem!1)))),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[135, 68, 132, 119])).
% 0.73/0.93 tff(137,plain,
% 0.73/0.93 (((~![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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(138,plain,
% 0.73/0.93 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(139,plain,
% 0.73/0.93 (((~![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))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[138])).
% 0.73/0.93 tff(140,plain,
% 0.73/0.93 (((~![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))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.93 inference(transitivity,[status(thm)],[139, 137])).
% 0.73/0.93 tff(141,plain,
% 0.73/0.93 ((~![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))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(142,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.73/0.94 tff(143,plain,
% 0.73/0.94 (~r(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[142, 112, 102, 73])).
% 0.73/0.94 tff(144,plain,
% 0.73/0.94 (((~![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)))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(145,plain,
% 0.73/0.94 ((~![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)))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(146,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.73/0.94 tff(147,plain,
% 0.73/0.94 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[146, 68])).
% 0.73/0.94 tff(148,plain,
% 0.73/0.94 (b(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[147, 143, 2])).
% 0.73/0.94 tff(149,plain,
% 0.73/0.94 (~(s(z) = elem!1)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[90, 88])).
% 0.73/0.94 tff(150,plain,
% 0.73/0.94 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[131, 149])).
% 0.73/0.94 tff(151,plain,
% 0.73/0.94 (b(s(s(s(z))), s(s(elem!1)))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[135, 68, 150, 119])).
% 0.73/0.94 tff(152,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 0.73/0.94 tff(153,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 0.73/0.94 tff(154,plain,
% 0.73/0.94 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[153])).
% 0.73/0.94 tff(155,plain,
% 0.73/0.94 (elem!1 = inj_0(s(elem!1))),
% 0.73/0.94 inference(symmetry,[status(thm)],[121])).
% 0.73/0.94 tff(156,plain,
% 0.73/0.94 (elem!1 = z),
% 0.73/0.94 inference(transitivity,[status(thm)],[155, 154, 27])).
% 0.73/0.94 tff(157,assumption,(~(elem!1 = z)), introduced(assumption)).
% 0.73/0.94 tff(158,plain,
% 0.73/0.94 ($false),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.73/0.94 tff(159,plain,((~(s(elem!1) = s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.94 tff(160,plain,
% 0.73/0.94 (~(s(elem!1) = s(z))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[159, 11])).
% 0.73/0.94 tff(161,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 0.73/0.94 tff(162,plain,
% 0.73/0.94 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[161])).
% 0.73/0.94 tff(163,plain,
% 0.73/0.94 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.73/0.94 inference(symmetry,[status(thm)],[162])).
% 0.73/0.94 tff(164,plain,
% 0.73/0.94 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.73/0.94 inference(symmetry,[status(thm)],[123])).
% 0.73/0.94 tff(165,plain,
% 0.73/0.94 (s(elem!1) = s(z)),
% 0.73/0.94 inference(transitivity,[status(thm)],[164, 163, 49])).
% 0.73/0.94 tff(166,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 0.73/0.94 tff(167,plain,
% 0.73/0.94 ($false),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.73/0.94 tff(168,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.94 tff(169,plain,
% 0.73/0.94 (~(s(s(z)) = s(s(elem!1)))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[168, 160])).
% 0.73/0.94 tff(170,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.94 tff(171,plain,
% 0.73/0.94 (((~![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)))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(172,plain,
% 0.73/0.94 ((~![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)))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(173,plain,
% 0.73/0.94 ((~![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))))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.73/0.94 tff(174,plain,
% 0.73/0.94 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[173, 68])).
% 0.73/0.94 tff(175,plain,
% 0.73/0.94 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[174, 45])).
% 0.73/0.94 tff(176,plain,
% 0.73/0.94 (r(s(z), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[175, 170])).
% 0.73/0.94 tff(177,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.73/0.94 tff(178,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.94 tff(179,assumption,(r(s(z), z)), introduced(assumption)).
% 0.73/0.94 tff(180,plain,
% 0.73/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(181,plain,
% 0.73/0.94 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(182,plain,
% 0.73/0.94 (((~![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))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[181])).
% 0.73/0.94 tff(183,plain,
% 0.73/0.94 (((~![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))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.73/0.94 inference(transitivity,[status(thm)],[182, 180])).
% 0.73/0.94 tff(184,plain,
% 0.73/0.94 ((~![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))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(185,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.73/0.94 tff(186,plain,
% 0.73/0.94 ($false),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[185, 112, 179, 178, 177])).
% 0.73/0.94 tff(187,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.94 tff(188,plain,
% 0.73/0.94 (~r(s(z), z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[187, 176, 73])).
% 0.73/0.94 tff(189,plain,
% 0.73/0.94 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(190,plain,
% 0.73/0.94 (~(s(z) = z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[189, 40])).
% 0.73/0.94 tff(191,plain,
% 0.73/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(192,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(193,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.73/0.94 tff(194,plain,
% 0.73/0.94 (b(s(z), z) | r(s(z), z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[193, 68, 190])).
% 0.73/0.94 tff(195,plain,
% 0.73/0.94 (b(s(z), z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[194, 188])).
% 0.73/0.94 tff(196,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.73/0.94 tff(197,plain,
% 0.73/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(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(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(198,plain,
% 0.73/0.94 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(199,plain,
% 0.73/0.94 (((~![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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[198])).
% 0.73/0.94 tff(200,plain,
% 0.73/0.94 (((~![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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.73/0.94 inference(transitivity,[status(thm)],[199, 197])).
% 0.73/0.94 tff(201,plain,
% 0.73/0.94 ((~![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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(202,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.73/0.94 tff(203,plain,
% 0.73/0.94 (~r(s(s(z)), s(z))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[202, 112, 196, 178])).
% 0.73/0.94 tff(204,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 0.73/0.94 tff(205,plain,
% 0.73/0.94 (s(z) = s(s(z))),
% 0.73/0.94 inference(symmetry,[status(thm)],[204])).
% 0.73/0.94 tff(206,plain,
% 0.73/0.94 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[205])).
% 0.73/0.94 tff(207,plain,
% 0.73/0.94 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.73/0.94 inference(symmetry,[status(thm)],[206])).
% 0.73/0.94 tff(208,plain,
% 0.73/0.94 (s(z) = z),
% 0.73/0.94 inference(transitivity,[status(thm)],[50, 207, 27])).
% 0.73/0.94 tff(209,plain,
% 0.73/0.94 ($false),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[190, 208])).
% 0.73/0.94 tff(210,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.94 tff(211,plain,
% 0.73/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(212,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(213,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.73/0.94 tff(214,plain,
% 0.73/0.94 (b(s(s(z)), s(z))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[213, 68, 210, 203])).
% 0.73/0.94 tff(215,plain,
% 0.73/0.94 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.73/0.94 inference(bind,[status(th)],[])).
% 0.73/0.94 tff(216,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(quant_intro,[status(thm)],[215])).
% 0.73/0.94 tff(217,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(218,plain,
% 0.73/0.94 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.73/0.94 inference(bind,[status(th)],[])).
% 0.73/0.94 tff(219,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(quant_intro,[status(thm)],[218])).
% 0.73/0.94 tff(220,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 0.73/0.94 tff(221,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.73/0.94 tff(222,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.73/0.94 tff(223,plain,(
% 0.73/0.94 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(skolemize,[status(sab)],[222])).
% 0.73/0.94 tff(224,plain,
% 0.73/0.94 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.73/0.94 tff(225,plain,
% 0.73/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(226,plain,
% 0.73/0.94 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(227,plain,
% 0.73/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[226])).
% 0.73/0.94 tff(228,plain,
% 0.73/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.73/0.94 inference(transitivity,[status(thm)],[227, 225])).
% 0.73/0.94 tff(229,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(230,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.73/0.94 tff(231,plain,
% 0.73/0.94 (~b(s(s(z)), z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[230, 224, 77, 1, 214])).
% 0.73/0.94 tff(232,plain,
% 0.73/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(233,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(234,plain,
% 0.73/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.73/0.94 tff(235,plain,
% 0.73/0.94 (r(s(s(z)), z)),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[234, 68, 42, 231])).
% 0.73/0.94 tff(236,plain,
% 0.73/0.94 (((~![X0: $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(z))), z)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(237,plain,
% 0.73/0.94 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))),
% 0.73/0.94 inference(rewrite,[status(thm)],[])).
% 0.73/0.94 tff(238,plain,
% 0.73/0.94 (((~![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))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))))),
% 0.73/0.94 inference(monotonicity,[status(thm)],[237])).
% 0.73/0.94 tff(239,plain,
% 0.73/0.94 (((~![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))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))),
% 0.73/0.94 inference(transitivity,[status(thm)],[238, 236])).
% 0.73/0.94 tff(240,plain,
% 0.73/0.94 ((~![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))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 0.73/0.94 inference(quant_inst,[status(thm)],[])).
% 0.73/0.94 tff(241,plain,
% 0.73/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))),
% 0.73/0.94 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.73/0.94 tff(242,plain,
% 0.73/0.94 ($false),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[241, 112, 196, 177, 235])).
% 0.73/0.94 tff(243,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.94 tff(244,plain,
% 0.73/0.94 (~r(s(s(z)), s(s(s(z))))),
% 0.73/0.94 inference(unit_resolution,[status(thm)],[243, 195, 77, 176, 73])).
% 0.73/0.94 tff(245,plain,
% 0.73/0.94 (((~![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)))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(246,plain,
% 0.73/0.95 ((~![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)))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(247,plain,
% 0.73/0.95 ((~![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))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.73/0.95 tff(248,plain,
% 0.73/0.95 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[247, 68])).
% 0.73/0.95 tff(249,plain,
% 0.73/0.95 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[248, 55])).
% 0.73/0.95 tff(250,plain,
% 0.73/0.95 (b(s(s(z)), s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[249, 244])).
% 0.73/0.95 tff(251,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(252,plain,
% 0.73/0.95 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(253,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[252])).
% 0.73/0.95 tff(254,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.73/0.95 inference(transitivity,[status(thm)],[253, 251])).
% 0.73/0.95 tff(255,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(256,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.73/0.95 tff(257,plain,
% 0.73/0.95 (~b(s(s(z)), s(s(elem!1)))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[256, 224, 250, 152, 151])).
% 0.73/0.95 tff(258,assumption,(~b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(259,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(260,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(261,plain,
% 0.73/0.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(262,plain,
% 0.73/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(263,plain,
% 0.73/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.73/0.95 tff(264,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[263, 68, 260, 259, 258])).
% 0.73/0.95 tff(265,plain,(b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(266,plain,
% 0.73/0.95 (r(s(s(z)), s(s(elem!1)))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[265, 257, 169])).
% 0.73/0.95 tff(267,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(268,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.73/0.95 tff(269,plain,
% 0.73/0.95 (((~![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)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(270,plain,
% 0.73/0.95 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(271,plain,
% 0.73/0.95 (((~![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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[270])).
% 0.73/0.95 tff(272,plain,
% 0.73/0.95 (((~![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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 0.73/0.95 inference(transitivity,[status(thm)],[271, 269])).
% 0.73/0.95 tff(273,plain,
% 0.73/0.95 ((~![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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(274,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.73/0.95 tff(275,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[274, 112, 102, 268, 267])).
% 0.73/0.95 tff(276,plain,((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(277,plain,
% 0.73/0.95 (~r(s(s(z)), z)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[276, 266, 102])).
% 0.73/0.95 tff(278,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 0.73/0.95 tff(279,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 0.73/0.95 tff(280,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[234, 68, 42, 279, 278])).
% 0.73/0.95 tff(281,plain,(b(s(s(z)), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(282,plain,
% 0.73/0.95 (b(s(s(z)), z)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[281, 277])).
% 0.73/0.95 tff(283,plain,
% 0.73/0.95 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 0.73/0.95 inference(commutativity,[status(thm)],[])).
% 0.73/0.95 tff(284,plain,
% 0.73/0.95 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 0.73/0.95 inference(symmetry,[status(thm)],[283])).
% 0.73/0.95 tff(285,assumption,(~r(z, elem!1)), introduced(assumption)).
% 0.73/0.95 tff(286,plain,
% 0.73/0.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(287,plain,
% 0.73/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(288,plain,
% 0.73/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.73/0.95 tff(289,plain,
% 0.73/0.95 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[288, 68])).
% 0.73/0.95 tff(290,plain,
% 0.73/0.95 (b(z, elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[289, 285, 4])).
% 0.73/0.95 tff(291,plain,
% 0.73/0.95 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(292,plain,
% 0.73/0.95 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[291, 25])).
% 0.73/0.95 tff(293,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(294,plain,
% 0.73/0.95 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[118, 112, 102, 177])).
% 0.73/0.95 tff(295,plain,
% 0.73/0.95 (b(s(s(s(z))), s(s(elem!1)))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[135, 68, 150, 294])).
% 0.73/0.95 tff(296,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 0.73/0.95 tff(297,plain,
% 0.73/0.95 (s(s(elem!1)) = s(elem!1)),
% 0.73/0.95 inference(monotonicity,[status(thm)],[296])).
% 0.73/0.95 tff(298,plain,
% 0.73/0.95 (s(elem!1) = s(s(elem!1))),
% 0.73/0.95 inference(symmetry,[status(thm)],[297])).
% 0.73/0.95 tff(299,plain,
% 0.73/0.95 (elem!1 = s(elem!1)),
% 0.73/0.95 inference(symmetry,[status(thm)],[296])).
% 0.73/0.95 tff(300,plain,
% 0.73/0.95 (elem!1 = s(s(elem!1))),
% 0.73/0.95 inference(transitivity,[status(thm)],[299, 298])).
% 0.73/0.95 tff(301,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[3, 300])).
% 0.73/0.95 tff(302,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(303,plain,
% 0.73/0.95 (~(s(elem!1) = elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[302, 3])).
% 0.73/0.95 tff(304,plain,
% 0.73/0.95 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 0.73/0.95 inference(commutativity,[status(thm)],[])).
% 0.73/0.95 tff(305,plain,
% 0.73/0.95 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 0.73/0.95 inference(symmetry,[status(thm)],[304])).
% 0.73/0.95 tff(306,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 0.73/0.95 tff(307,plain,
% 0.73/0.95 (s(s(s(z))) = s(s(elem!1))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.73/0.95 tff(308,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 0.73/0.95 tff(309,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[308, 307])).
% 0.73/0.95 tff(310,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(311,plain,
% 0.73/0.95 (~(s(s(elem!1)) = s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[310, 150])).
% 0.73/0.95 tff(312,plain,
% 0.73/0.95 (~r(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[142, 112, 102, 177])).
% 0.73/0.95 tff(313,plain,
% 0.73/0.95 (b(s(s(elem!1)), s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[147, 312, 311])).
% 0.73/0.95 tff(314,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 0.73/0.95 tff(315,plain,
% 0.73/0.95 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[314])).
% 0.73/0.95 tff(316,plain,
% 0.73/0.95 (elem!1 = s(s(elem!1))),
% 0.73/0.95 inference(transitivity,[status(thm)],[155, 315, 123, 314])).
% 0.73/0.95 tff(317,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[3, 316])).
% 0.73/0.95 tff(318,plain,((~(s(elem!1) = s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(319,plain,
% 0.73/0.95 (~(s(elem!1) = s(s(elem!1)))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[318, 3])).
% 0.73/0.95 tff(320,plain,
% 0.73/0.95 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.73/0.95 inference(commutativity,[status(thm)],[])).
% 0.73/0.95 tff(321,plain,
% 0.73/0.95 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 0.73/0.95 inference(symmetry,[status(thm)],[320])).
% 0.73/0.95 tff(322,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 0.73/0.95 tff(323,plain,
% 0.73/0.95 (s(elem!1) = elem!1),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.73/0.95 tff(324,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 0.73/0.95 tff(325,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.73/0.95 tff(326,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(327,plain,
% 0.73/0.95 (~(elem!1 = s(elem!1))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[326, 303])).
% 0.73/0.95 tff(328,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.73/0.95 tff(329,plain,
% 0.73/0.95 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 0.73/0.95 inference(monotonicity,[status(thm)],[7])).
% 0.73/0.95 tff(330,plain,
% 0.73/0.95 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.73/0.95 inference(symmetry,[status(thm)],[329])).
% 0.73/0.95 tff(331,plain,
% 0.73/0.95 (r(s(s(elem!1)), elem!1)),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[102, 330])).
% 0.73/0.95 tff(332,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[328, 331])).
% 0.73/0.95 tff(333,plain,((~(elem!1 = z)) | r(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(334,plain,
% 0.73/0.95 (~(elem!1 = z)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[333, 328, 102])).
% 0.73/0.95 tff(335,assumption,(z = elem!1), introduced(assumption)).
% 0.73/0.95 tff(336,plain,
% 0.73/0.95 (elem!1 = z),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[335, 5])).
% 0.73/0.95 tff(337,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[157, 336])).
% 0.73/0.95 tff(338,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(339,plain,
% 0.73/0.95 (~(z = elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[338, 334])).
% 0.73/0.95 tff(340,plain,
% 0.73/0.95 (b(z, elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[289, 339, 285])).
% 0.73/0.95 tff(341,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 0.73/0.95 tff(342,plain,
% 0.73/0.95 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 0.73/0.95 inference(monotonicity,[status(thm)],[341])).
% 0.73/0.95 tff(343,plain,
% 0.73/0.95 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 0.73/0.95 inference(symmetry,[status(thm)],[342])).
% 0.73/0.95 tff(344,assumption,(b(z, elem!1)), introduced(assumption)).
% 0.73/0.95 tff(345,plain,
% 0.73/0.95 (b(z, s(s(s(z))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.73/0.95 tff(346,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[74, 345])).
% 0.73/0.95 tff(347,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(348,plain,
% 0.73/0.95 (~(s(s(s(z))) = elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[347, 340, 74])).
% 0.73/0.95 tff(349,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 0.73/0.95 tff(350,plain,
% 0.73/0.95 (elem!1 = s(s(elem!1))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[349, 75])).
% 0.73/0.95 tff(351,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[3, 350])).
% 0.73/0.95 tff(352,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(353,plain,
% 0.73/0.95 (~(s(s(elem!1)) = elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[352, 3])).
% 0.73/0.95 tff(354,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.73/0.95 tff(355,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 0.73/0.95 tff(356,plain,
% 0.73/0.95 (((~![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))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(357,plain,
% 0.73/0.95 ((~![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))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(358,plain,
% 0.73/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.73/0.95 tff(359,plain,
% 0.73/0.95 ($false),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[358, 68, 328, 355, 354])).
% 0.73/0.95 tff(360,plain,(r(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.95 tff(361,plain,
% 0.73/0.95 (b(s(s(elem!1)), elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[360, 328, 353])).
% 0.73/0.95 tff(362,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 0.73/0.95 tff(363,assumption,(r(elem!1, z)), introduced(assumption)).
% 0.73/0.95 tff(364,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(365,plain,
% 0.73/0.95 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(366,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[365])).
% 0.73/0.95 tff(367,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.95 inference(transitivity,[status(thm)],[366, 364])).
% 0.73/0.95 tff(368,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(369,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.73/0.95 tff(370,plain,
% 0.73/0.95 (~r(s(s(s(z))), elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[369, 112, 363, 177])).
% 0.73/0.95 tff(371,plain,
% 0.73/0.95 (((~![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))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(372,plain,
% 0.73/0.95 ((~![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))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(373,plain,
% 0.73/0.95 ((~![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)),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.73/0.95 tff(374,plain,
% 0.73/0.95 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[373, 68])).
% 0.73/0.95 tff(375,plain,
% 0.73/0.95 (b(s(s(s(z))), elem!1)),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[374, 370, 362])).
% 0.73/0.95 tff(376,plain,
% 0.73/0.95 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[283])).
% 0.73/0.95 tff(377,plain,
% 0.73/0.95 (~(elem!1 = s(s(s(z))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[362, 376])).
% 0.73/0.95 tff(378,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(379,plain,
% 0.73/0.95 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(380,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[379])).
% 0.73/0.95 tff(381,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 0.73/0.95 inference(transitivity,[status(thm)],[380, 378])).
% 0.73/0.95 tff(382,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(383,plain,
% 0.73/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.73/0.95 tff(384,plain,
% 0.73/0.95 (~r(elem!1, s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[383, 112, 363, 177])).
% 0.73/0.95 tff(385,plain,
% 0.73/0.95 (((~![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)))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(386,plain,
% 0.73/0.95 ((~![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)))))),
% 0.73/0.95 inference(quant_inst,[status(thm)],[])).
% 0.73/0.95 tff(387,plain,
% 0.73/0.95 ((~![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))))),
% 0.73/0.95 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.73/0.95 tff(388,plain,
% 0.73/0.95 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[387, 68])).
% 0.73/0.95 tff(389,plain,
% 0.73/0.95 (b(elem!1, s(s(s(z))))),
% 0.73/0.95 inference(unit_resolution,[status(thm)],[388, 384, 377])).
% 0.73/0.95 tff(390,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.73/0.95 tff(391,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(392,plain,
% 0.73/0.95 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), 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)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.95 inference(rewrite,[status(thm)],[])).
% 0.73/0.95 tff(393,plain,
% 0.73/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/0.95 inference(monotonicity,[status(thm)],[392])).
% 0.73/0.96 tff(394,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.96 inference(transitivity,[status(thm)],[393, 391])).
% 0.73/0.96 tff(395,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(396,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.73/0.96 tff(397,plain,
% 0.73/0.96 ($false),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[396, 224, 390, 389, 375, 152])).
% 0.73/0.96 tff(398,plain,((~r(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.96 tff(399,plain,
% 0.73/0.96 (~r(elem!1, z)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[398, 361, 313, 348, 177])).
% 0.73/0.96 tff(400,plain,
% 0.73/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(401,plain,
% 0.73/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(402,plain,
% 0.73/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.73/0.96 tff(403,plain,
% 0.73/0.96 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[402, 68])).
% 0.73/0.96 tff(404,plain,
% 0.73/0.96 (b(elem!1, z)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[403, 399, 334])).
% 0.73/0.96 tff(405,assumption,(b(elem!1, z)), introduced(assumption)).
% 0.73/0.96 tff(406,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.73/0.96 tff(407,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 0.73/0.96 tff(408,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.73/0.96 tff(409,plain,
% 0.73/0.96 (~(s(elem!1) = s(z))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[159, 157])).
% 0.73/0.96 tff(410,plain,
% 0.73/0.96 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 0.73/0.96 inference(commutativity,[status(thm)],[])).
% 0.73/0.96 tff(411,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 0.73/0.96 tff(412,plain,
% 0.73/0.96 (s(elem!1) = s(z)),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.73/0.96 tff(413,plain,
% 0.73/0.96 ($false),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[166, 412])).
% 0.73/0.96 tff(414,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.96 tff(415,plain,
% 0.73/0.96 (~(s(z) = s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[414, 166])).
% 0.73/0.96 tff(416,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 0.73/0.96 tff(417,plain,
% 0.73/0.96 (((~![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(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), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(418,plain,
% 0.73/0.96 (((~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), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(419,plain,
% 0.73/0.96 (((~![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), elem!1)) | (~r(s(z), s(elem!1)))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[418])).
% 0.73/0.96 tff(420,plain,
% 0.73/0.96 (((~![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), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(transitivity,[status(thm)],[419, 417])).
% 0.73/0.96 tff(421,plain,
% 0.73/0.96 ((~![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))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(422,plain,
% 0.73/0.96 ((~![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(z), s(elem!1)))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.73/0.96 tff(423,plain,
% 0.73/0.96 (~r(s(z), s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[422, 112, 408, 416])).
% 0.73/0.96 tff(424,plain,
% 0.73/0.96 (((~![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)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(425,plain,
% 0.73/0.96 ((~![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)))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(426,plain,
% 0.73/0.96 ((~![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))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.73/0.96 tff(427,plain,
% 0.73/0.96 (b(s(z), s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[426, 68, 423, 415])).
% 0.73/0.96 tff(428,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 0.73/0.96 tff(429,plain,
% 0.73/0.96 (((~![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(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(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(430,plain,
% 0.73/0.96 (((~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), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(431,plain,
% 0.73/0.96 (((~![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), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[430])).
% 0.73/0.96 tff(432,plain,
% 0.73/0.96 (((~![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), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 0.73/0.96 inference(transitivity,[status(thm)],[431, 429])).
% 0.73/0.96 tff(433,plain,
% 0.73/0.96 ((~![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))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(434,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.73/0.96 tff(435,plain,
% 0.73/0.96 ($false),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[434, 112, 408, 416, 428])).
% 0.73/0.96 tff(436,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.96 tff(437,plain,
% 0.73/0.96 (~r(s(elem!1), s(z))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[436, 416, 408])).
% 0.73/0.96 tff(438,plain,
% 0.73/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(439,plain,
% 0.73/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(440,plain,
% 0.73/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.73/0.96 tff(441,plain,
% 0.73/0.96 (b(s(elem!1), s(z))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[440, 68, 166, 437])).
% 0.73/0.96 tff(442,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(443,plain,
% 0.73/0.96 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(444,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1)))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[443])).
% 0.73/0.96 tff(445,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))),
% 0.73/0.96 inference(transitivity,[status(thm)],[444, 442])).
% 0.73/0.96 tff(446,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(447,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1)))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.73/0.96 tff(448,plain,
% 0.73/0.96 ($false),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[447, 224, 77, 407, 441, 427])).
% 0.73/0.96 tff(449,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.96 tff(450,plain,
% 0.73/0.96 (~r(s(z), elem!1)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[449, 408, 409, 407, 77])).
% 0.73/0.96 tff(451,plain,
% 0.73/0.96 (((~![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))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(452,plain,
% 0.73/0.96 ((~![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))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(453,plain,
% 0.73/0.96 ((~![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)),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.73/0.96 tff(454,plain,
% 0.73/0.96 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[453, 68])).
% 0.73/0.96 tff(455,plain,
% 0.73/0.96 (b(s(z), elem!1)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[454, 450, 129])).
% 0.73/0.96 tff(456,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(457,plain,
% 0.73/0.96 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(458,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[457])).
% 0.73/0.96 tff(459,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.73/0.96 inference(transitivity,[status(thm)],[458, 456])).
% 0.73/0.96 tff(460,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(461,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.73/0.96 tff(462,plain,
% 0.73/0.96 (~b(s(z), z)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[461, 224, 405, 455, 344])).
% 0.73/0.96 tff(463,plain,
% 0.73/0.96 (r(s(z), z)),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[194, 462])).
% 0.73/0.96 tff(464,plain,
% 0.73/0.96 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 0.73/0.96 inference(symmetry,[status(thm)],[410])).
% 0.73/0.96 tff(465,plain,
% 0.73/0.96 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[464])).
% 0.73/0.96 tff(466,plain,
% 0.73/0.96 (~(s(z) = s(elem!1))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[166, 465])).
% 0.73/0.96 tff(467,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 0.73/0.96 tff(468,plain,
% 0.73/0.96 (((~![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), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(469,plain,
% 0.73/0.96 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(470,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), 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), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[469])).
% 0.73/0.96 tff(471,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), 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), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(transitivity,[status(thm)],[470, 468])).
% 0.73/0.96 tff(472,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(473,plain,
% 0.73/0.96 ((~![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), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.73/0.96 tff(474,plain,
% 0.73/0.96 (~r(s(z), s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[473, 112, 408, 179, 467])).
% 0.73/0.96 tff(475,plain,
% 0.73/0.96 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[426, 68, 474])).
% 0.73/0.96 tff(476,plain,
% 0.73/0.96 (b(s(z), s(elem!1))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[475, 466])).
% 0.73/0.96 tff(477,plain,
% 0.73/0.96 (((~![X0: $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), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(478,plain,
% 0.73/0.96 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)))),
% 0.73/0.96 inference(rewrite,[status(thm)],[])).
% 0.73/0.96 tff(479,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z))))),
% 0.73/0.96 inference(monotonicity,[status(thm)],[478])).
% 0.73/0.96 tff(480,plain,
% 0.73/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)))),
% 0.73/0.96 inference(transitivity,[status(thm)],[479, 477])).
% 0.73/0.96 tff(481,plain,
% 0.73/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 0.73/0.96 inference(quant_inst,[status(thm)],[])).
% 0.73/0.96 tff(482,plain,
% 0.73/0.96 ((~![X0: $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), z)) | (~r(s(elem!1), z))),
% 0.73/0.96 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.73/0.96 tff(483,plain,
% 0.73/0.96 (~r(s(elem!1), s(z))),
% 0.73/0.96 inference(unit_resolution,[status(thm)],[482, 112, 179, 467])).
% 0.73/0.96 tff(484,plain,
% 0.73/0.97 (b(s(elem!1), s(z))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[440, 68, 166, 483])).
% 0.73/0.97 tff(485,plain,
% 0.73/0.97 (((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(486,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1)))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[485])).
% 0.73/0.97 tff(487,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))))),
% 0.73/0.97 inference(transitivity,[status(thm)],[486, 442])).
% 0.73/0.97 tff(488,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(489,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.73/0.97 tff(490,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[489, 224, 77, 407, 484, 476])).
% 0.73/0.97 tff(491,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(492,plain,
% 0.73/0.97 (~r(s(elem!1), z)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[491, 463, 77, 409, 407, 408])).
% 0.73/0.97 tff(493,plain,
% 0.73/0.97 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(494,plain,
% 0.73/0.97 (~(s(elem!1) = z)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[493, 40])).
% 0.73/0.97 tff(495,plain,
% 0.73/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(496,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(497,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.73/0.97 tff(498,plain,
% 0.73/0.97 (b(s(elem!1), z) | r(s(elem!1), z)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[497, 68, 494])).
% 0.73/0.97 tff(499,plain,
% 0.73/0.97 (b(s(elem!1), z)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[498, 492])).
% 0.73/0.97 tff(500,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 0.73/0.97 tff(501,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 0.73/0.97 tff(502,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(503,plain,
% 0.73/0.97 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(504,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[503])).
% 0.73/0.97 tff(505,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.73/0.97 inference(transitivity,[status(thm)],[504, 502])).
% 0.73/0.97 tff(506,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(507,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.73/0.97 tff(508,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[507, 224, 501, 405, 500, 407])).
% 0.73/0.97 tff(509,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(510,plain,
% 0.73/0.97 (~b(elem!1, s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[509, 499, 405, 407])).
% 0.73/0.97 tff(511,plain,
% 0.73/0.97 (~(z = elem!1)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[338, 157])).
% 0.73/0.97 tff(512,plain,
% 0.73/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(513,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(514,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.73/0.97 tff(515,plain,
% 0.73/0.97 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[514, 68])).
% 0.73/0.97 tff(516,plain,
% 0.73/0.97 (r(elem!1, s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[515, 510, 327])).
% 0.73/0.97 tff(517,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 0.73/0.97 tff(518,plain,
% 0.73/0.97 (r(s(s(elem!1)), elem!1)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[360, 353, 354])).
% 0.73/0.97 tff(519,plain,
% 0.73/0.97 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 0.73/0.97 inference(commutativity,[status(thm)],[])).
% 0.73/0.97 tff(520,plain,
% 0.73/0.97 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 0.73/0.97 inference(symmetry,[status(thm)],[519])).
% 0.73/0.97 tff(521,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 0.73/0.97 tff(522,plain,
% 0.73/0.97 (s(elem!1) = s(s(elem!1))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.73/0.97 tff(523,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 0.73/0.97 tff(524,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[523, 522])).
% 0.73/0.97 tff(525,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(526,plain,
% 0.73/0.97 (~(s(s(elem!1)) = s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[525, 319])).
% 0.73/0.97 tff(527,plain,
% 0.73/0.97 (((~![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)))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(528,plain,
% 0.73/0.97 ((~![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)))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(529,plain,
% 0.73/0.97 ((~![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))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.73/0.97 tff(530,plain,
% 0.73/0.97 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[529, 68])).
% 0.73/0.97 tff(531,plain,
% 0.73/0.97 (r(s(s(elem!1)), s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[530, 526, 406])).
% 0.73/0.97 tff(532,plain,
% 0.73/0.97 (r(elem!1, s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[515, 327, 517])).
% 0.73/0.97 tff(533,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), 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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(534,plain,
% 0.73/0.97 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(535,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[534])).
% 0.73/0.97 tff(536,plain,
% 0.73/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.73/0.97 inference(transitivity,[status(thm)],[535, 533])).
% 0.73/0.97 tff(537,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(538,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.73/0.97 tff(539,plain,
% 0.73/0.97 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[538, 112])).
% 0.73/0.97 tff(540,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[539, 532, 531, 518])).
% 0.73/0.97 tff(541,plain,((elem!1 = s(s(elem!1))) | b(elem!1, s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(542,plain,
% 0.73/0.97 (b(s(s(elem!1)), elem!1)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[541, 3, 406, 517])).
% 0.73/0.97 tff(543,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 0.73/0.97 tff(544,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.73/0.97 tff(545,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.73/0.97 tff(546,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(547,plain,
% 0.73/0.97 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(548,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[547])).
% 0.73/0.97 tff(549,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.73/0.97 inference(transitivity,[status(thm)],[548, 546])).
% 0.73/0.97 tff(550,plain,
% 0.73/0.97 ((~![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(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(551,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.73/0.97 tff(552,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[551, 112, 543, 545, 544])).
% 0.73/0.97 tff(553,plain,((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(554,plain,
% 0.73/0.97 (~r(elem!1, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[553, 531, 543])).
% 0.73/0.97 tff(555,plain,
% 0.73/0.97 (((~![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))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(556,plain,
% 0.73/0.97 ((~![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))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(557,plain,
% 0.73/0.97 ((~![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)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.73/0.97 tff(558,plain,
% 0.73/0.97 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[557, 68])).
% 0.73/0.97 tff(559,plain,
% 0.73/0.97 (b(elem!1, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[558, 554, 3])).
% 0.73/0.97 tff(560,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.73/0.97 tff(561,plain,
% 0.73/0.97 (~(s(z) = s(elem!1))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[414, 409])).
% 0.73/0.97 tff(562,plain,
% 0.73/0.97 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 0.73/0.97 inference(commutativity,[status(thm)],[])).
% 0.73/0.97 tff(563,plain,
% 0.73/0.97 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 0.73/0.97 inference(symmetry,[status(thm)],[562])).
% 0.73/0.97 tff(564,plain,
% 0.73/0.97 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[563])).
% 0.73/0.97 tff(565,plain,
% 0.73/0.97 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(566,plain,
% 0.73/0.97 (~(s(s(elem!1)) = z)),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[565, 40])).
% 0.73/0.97 tff(567,plain,
% 0.73/0.97 (~(z = s(s(elem!1)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[566, 564])).
% 0.73/0.97 tff(568,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 0.73/0.97 tff(569,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(570,plain,
% 0.73/0.97 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(571,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 0.73/0.97 inference(monotonicity,[status(thm)],[570])).
% 0.73/0.97 tff(572,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 0.73/0.97 inference(transitivity,[status(thm)],[571, 569])).
% 0.73/0.97 tff(573,plain,
% 0.73/0.97 ((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(574,plain,
% 0.73/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.73/0.97 tff(575,plain,
% 0.73/0.97 ($false),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[574, 112, 544, 568, 293])).
% 0.73/0.97 tff(576,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.97 tff(577,plain,
% 0.73/0.97 (~r(z, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[576, 544, 568])).
% 0.73/0.97 tff(578,plain,
% 0.73/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(579,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(580,plain,
% 0.73/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.73/0.97 tff(581,plain,
% 0.73/0.97 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[580, 68, 577])).
% 0.73/0.97 tff(582,plain,
% 0.73/0.97 (b(z, s(s(elem!1)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[581, 567])).
% 0.73/0.97 tff(583,plain,
% 0.73/0.97 (((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(584,plain,
% 0.73/0.98 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(585,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[584])).
% 0.73/0.98 tff(586,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[585, 583])).
% 0.73/0.98 tff(587,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(588,plain,
% 0.73/0.98 ((~![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(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.73/0.98 tff(589,plain,
% 0.73/0.98 (~r(s(s(elem!1)), z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[588, 112, 544, 568])).
% 0.73/0.98 tff(590,plain,
% 0.73/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(591,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(592,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.73/0.98 tff(593,plain,
% 0.73/0.98 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[592, 68, 566])).
% 0.73/0.98 tff(594,plain,
% 0.73/0.98 (b(s(s(elem!1)), z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[593, 589])).
% 0.73/0.98 tff(595,plain,
% 0.73/0.98 (~r(elem!1, s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[553, 543, 544])).
% 0.73/0.98 tff(596,plain,
% 0.73/0.98 (b(elem!1, s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[558, 595, 3])).
% 0.73/0.98 tff(597,plain,
% 0.73/0.98 (((~![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, z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(598,plain,
% 0.73/0.98 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(599,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[598])).
% 0.73/0.98 tff(600,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[599, 597])).
% 0.73/0.98 tff(601,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(602,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.73/0.98 tff(603,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[602, 112, 543, 363, 568])).
% 0.73/0.98 tff(604,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(605,plain,
% 0.73/0.98 (~r(elem!1, z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[604, 543, 568])).
% 0.73/0.98 tff(606,plain,
% 0.73/0.98 (b(elem!1, z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[403, 605, 157])).
% 0.73/0.98 tff(607,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(608,plain,
% 0.73/0.98 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(609,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[608])).
% 0.73/0.98 tff(610,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.73/0.98 inference(transitivity,[status(thm)],[609, 607])).
% 0.73/0.98 tff(611,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(612,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.73/0.98 tff(613,plain,
% 0.73/0.98 ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[612, 224])).
% 0.73/0.98 tff(614,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[613, 606, 596, 594, 582])).
% 0.73/0.98 tff(615,plain,((~r(elem!1, s(elem!1))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(616,plain,
% 0.73/0.98 (~r(z, s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[615, 531, 543, 157, 3])).
% 0.73/0.98 tff(617,plain,
% 0.73/0.98 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 0.73/0.98 inference(commutativity,[status(thm)],[])).
% 0.73/0.98 tff(618,plain,
% 0.73/0.98 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 0.73/0.98 inference(symmetry,[status(thm)],[617])).
% 0.73/0.98 tff(619,plain,
% 0.73/0.98 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[618])).
% 0.73/0.98 tff(620,plain,
% 0.73/0.98 (~(z = s(elem!1))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[494, 619])).
% 0.73/0.98 tff(621,plain,
% 0.73/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(622,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(623,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.73/0.98 tff(624,plain,
% 0.73/0.98 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[623, 68])).
% 0.73/0.98 tff(625,plain,
% 0.73/0.98 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[624, 620])).
% 0.73/0.98 tff(626,plain,
% 0.73/0.98 (b(z, s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[625, 616])).
% 0.73/0.98 tff(627,plain,
% 0.73/0.98 (~r(s(z), elem!1)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[449, 626, 408, 409, 77])).
% 0.73/0.98 tff(628,plain,
% 0.73/0.98 (b(s(z), elem!1)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[454, 627, 129])).
% 0.73/0.98 tff(629,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(630,plain,
% 0.73/0.98 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(631,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[630])).
% 0.73/0.98 tff(632,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 0.73/0.98 inference(transitivity,[status(thm)],[631, 629])).
% 0.73/0.98 tff(633,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(634,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.73/0.98 tff(635,plain,
% 0.73/0.98 (~b(s(z), s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[634, 224, 559, 628, 542])).
% 0.73/0.98 tff(636,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 0.73/0.98 tff(637,plain,
% 0.73/0.98 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[636])).
% 0.73/0.98 tff(638,plain,
% 0.73/0.98 (s(elem!1) = z),
% 0.73/0.98 inference(transitivity,[status(thm)],[164, 637, 27])).
% 0.73/0.98 tff(639,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[494, 638])).
% 0.73/0.98 tff(640,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(641,plain,
% 0.73/0.98 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.73/0.98 inference(commutativity,[status(thm)],[])).
% 0.73/0.98 tff(642,plain,
% 0.73/0.98 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 0.73/0.98 inference(symmetry,[status(thm)],[641])).
% 0.73/0.98 tff(643,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 0.73/0.98 tff(644,plain,
% 0.73/0.98 (s(s(elem!1)) = s(z)),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.73/0.98 tff(645,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 0.73/0.98 tff(646,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[645, 644])).
% 0.73/0.98 tff(647,plain,((~(s(z) = s(s(elem!1)))) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(648,plain,
% 0.73/0.98 (~(s(z) = s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[647, 640])).
% 0.73/0.98 tff(649,plain,
% 0.73/0.98 (((~![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))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(650,plain,
% 0.73/0.98 ((~![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))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(651,plain,
% 0.73/0.98 ((~![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)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.73/0.98 tff(652,plain,
% 0.73/0.98 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[651, 68])).
% 0.73/0.98 tff(653,plain,
% 0.73/0.98 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[652, 648])).
% 0.73/0.98 tff(654,plain,
% 0.73/0.98 (r(s(z), s(s(elem!1)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[653, 635])).
% 0.73/0.98 tff(655,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 0.73/0.98 tff(656,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.73/0.98 tff(657,plain,
% 0.73/0.98 (((~![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(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(658,plain,
% 0.73/0.98 (((~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(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(659,plain,
% 0.73/0.98 (((~![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(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(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[658])).
% 0.73/0.98 tff(660,plain,
% 0.73/0.98 (((~![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(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(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[659, 657])).
% 0.73/0.98 tff(661,plain,
% 0.73/0.98 ((~![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(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(662,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.73/0.98 tff(663,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[662, 112, 544, 656, 655])).
% 0.73/0.98 tff(664,plain,((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(665,plain,
% 0.73/0.98 (~r(s(z), s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[664, 654, 531])).
% 0.73/0.98 tff(666,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 0.73/0.98 tff(667,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 0.73/0.98 tff(668,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 0.73/0.98 tff(669,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[426, 68, 668, 667, 666])).
% 0.73/0.98 tff(670,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(671,plain,
% 0.73/0.98 (b(s(z), s(elem!1))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[670, 665, 561])).
% 0.73/0.98 tff(672,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(673,plain,
% 0.73/0.98 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(674,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[673])).
% 0.73/0.98 tff(675,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[674, 672])).
% 0.73/0.98 tff(676,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(677,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.73/0.99 tff(678,plain,
% 0.73/0.99 (~b(z, s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[677, 224, 77, 626, 671, 560])).
% 0.73/0.99 tff(679,plain,
% 0.73/0.99 (r(z, s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[100, 678])).
% 0.73/0.99 tff(680,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(681,plain,
% 0.73/0.99 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[131, 129])).
% 0.73/0.99 tff(682,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.73/0.99 tff(683,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 0.73/0.99 tff(684,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 0.73/0.99 tff(685,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(686,plain,
% 0.73/0.99 (~b(z, s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[677, 224, 77, 407, 683, 560])).
% 0.73/0.99 tff(687,plain,
% 0.73/0.99 (r(z, s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[100, 686])).
% 0.73/0.99 tff(688,assumption,(r(z, elem!1)), introduced(assumption)).
% 0.73/0.99 tff(689,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(690,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.73/0.99 tff(691,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(692,plain,
% 0.73/0.99 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(693,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[692])).
% 0.73/0.99 tff(694,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.73/0.99 inference(transitivity,[status(thm)],[693, 691])).
% 0.73/0.99 tff(695,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(696,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.73/0.99 tff(697,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[696, 112, 688, 690, 689])).
% 0.73/0.99 tff(698,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(699,plain,
% 0.73/0.99 (~r(s(s(s(z))), elem!1)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[698, 688, 687])).
% 0.73/0.99 tff(700,plain,
% 0.73/0.99 (b(s(s(s(z))), elem!1)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[374, 699, 362])).
% 0.73/0.99 tff(701,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(702,plain,
% 0.73/0.99 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(703,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[702])).
% 0.73/0.99 tff(704,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[703, 701])).
% 0.73/0.99 tff(705,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(706,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.73/0.99 tff(707,plain,
% 0.73/0.99 (~b(s(s(s(z))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[706, 224, 77, 684, 700, 560])).
% 0.73/0.99 tff(708,plain,
% 0.73/0.99 (r(s(s(s(z))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[72, 707])).
% 0.73/0.99 tff(709,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(710,plain,
% 0.73/0.99 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(711,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[710])).
% 0.73/0.99 tff(712,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[711, 709])).
% 0.73/0.99 tff(713,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(714,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.73/0.99 tff(715,plain,
% 0.73/0.99 (~b(s(z), s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[714, 224, 684, 685, 700])).
% 0.73/0.99 tff(716,plain,
% 0.73/0.99 (r(s(z), s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[175, 715])).
% 0.73/0.99 tff(717,plain,
% 0.73/0.99 (((~![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), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(718,plain,
% 0.73/0.99 (((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(719,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[718])).
% 0.73/0.99 tff(720,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.73/0.99 inference(transitivity,[status(thm)],[719, 717])).
% 0.73/0.99 tff(721,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(722,plain,
% 0.73/0.99 ((~![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), z)) | (~r(z, elem!1))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.73/0.99 tff(723,plain,
% 0.73/0.99 (~r(s(elem!1), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[722, 112, 408, 688])).
% 0.73/0.99 tff(724,plain,
% 0.73/0.99 (b(s(elem!1), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[498, 723])).
% 0.73/0.99 tff(725,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(726,plain,
% 0.73/0.99 (((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(727,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[726])).
% 0.73/0.99 tff(728,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.73/0.99 inference(transitivity,[status(thm)],[727, 725])).
% 0.73/0.99 tff(729,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(730,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.73/0.99 tff(731,plain,
% 0.73/0.99 (~b(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[730, 224, 724, 407, 683])).
% 0.73/0.99 tff(732,plain,
% 0.73/0.99 (r(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[194, 731])).
% 0.73/0.99 tff(733,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[185, 112, 732, 716, 708])).
% 0.73/0.99 tff(734,plain,((~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(735,plain,
% 0.73/0.99 (~r(z, elem!1)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[734, 685, 684, 77, 560, 362, 407, 683, 408])).
% 0.73/0.99 tff(736,plain,
% 0.73/0.99 (b(z, elem!1)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[289, 735, 4])).
% 0.73/0.99 tff(737,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(738,plain,
% 0.73/0.99 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(739,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[738])).
% 0.73/0.99 tff(740,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[739, 737])).
% 0.73/0.99 tff(741,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(742,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.73/0.99 tff(743,plain,
% 0.73/0.99 ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[742, 224])).
% 0.73/0.99 tff(744,plain,
% 0.73/0.99 (~b(z, s(s(elem!1)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[743, 736, 682, 390])).
% 0.73/0.99 tff(745,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 0.73/0.99 tff(746,plain,
% 0.73/0.99 (s(s(elem!1)) = z),
% 0.73/0.99 inference(symmetry,[status(thm)],[745])).
% 0.73/0.99 tff(747,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[566, 746])).
% 0.73/0.99 tff(748,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(749,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 0.73/0.99 tff(750,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 0.73/0.99 tff(751,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[580, 68, 750, 749, 748])).
% 0.73/0.99 tff(752,plain,(b(z, s(s(elem!1))) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(753,plain,
% 0.73/0.99 (r(z, s(s(elem!1)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[752, 744])).
% 0.73/0.99 tff(754,plain,
% 0.73/0.99 (~b(s(z), s(s(elem!1)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[634, 224, 682, 684, 390])).
% 0.73/0.99 tff(755,plain,
% 0.73/0.99 (r(s(z), s(s(elem!1)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[653, 754])).
% 0.73/0.99 tff(756,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(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), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(757,plain,
% 0.73/0.99 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(758,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[757])).
% 0.73/0.99 tff(759,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[758, 756])).
% 0.73/0.99 tff(760,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(761,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.73/0.99 tff(762,plain,
% 0.73/0.99 (~r(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[761, 112, 755, 753])).
% 0.73/0.99 tff(763,plain,
% 0.73/0.99 (b(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[194, 762])).
% 0.73/0.99 tff(764,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(765,plain,
% 0.73/1.00 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(766,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[765])).
% 0.73/1.00 tff(767,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[766, 764])).
% 0.73/1.00 tff(768,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(769,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.73/1.00 tff(770,plain,
% 0.73/1.00 (~b(s(s(s(z))), z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[769, 224, 77, 763, 560])).
% 0.73/1.00 tff(771,plain,
% 0.73/1.00 (r(s(s(s(z))), z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[72, 770])).
% 0.73/1.00 tff(772,plain,
% 0.73/1.00 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[304])).
% 0.73/1.00 tff(773,plain,
% 0.73/1.00 (~(s(s(elem!1)) = s(s(s(z))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[308, 772])).
% 0.73/1.00 tff(774,plain,
% 0.73/1.00 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 0.73/1.00 inference(commutativity,[status(thm)],[])).
% 0.73/1.00 tff(775,plain,
% 0.73/1.00 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 0.73/1.00 inference(symmetry,[status(thm)],[774])).
% 0.73/1.00 tff(776,plain,
% 0.73/1.00 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[775])).
% 0.73/1.00 tff(777,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 0.73/1.00 tff(778,plain,
% 0.73/1.00 (s(s(s(z))) = s(elem!1)),
% 0.73/1.00 inference(symmetry,[status(thm)],[777])).
% 0.73/1.00 tff(779,plain,
% 0.73/1.00 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[778])).
% 0.73/1.00 tff(780,plain,
% 0.73/1.00 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 0.73/1.00 inference(symmetry,[status(thm)],[779])).
% 0.73/1.00 tff(781,plain,
% 0.73/1.00 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(z)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[780])).
% 0.73/1.00 tff(782,plain,
% 0.73/1.00 (~b(elem!1, s(s(s(z))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[517, 781])).
% 0.73/1.00 tff(783,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[685, 782])).
% 0.73/1.00 tff(784,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(785,plain,
% 0.73/1.00 (~(s(elem!1) = s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[784, 685, 517])).
% 0.73/1.00 tff(786,plain,
% 0.73/1.00 (~(s(s(s(z))) = s(elem!1))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[785, 776])).
% 0.73/1.00 tff(787,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.73/1.00 tff(788,plain,
% 0.73/1.00 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(789,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[788])).
% 0.73/1.00 tff(790,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[789, 391])).
% 0.73/1.00 tff(791,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(792,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.73/1.00 tff(793,plain,
% 0.73/1.00 (~b(s(s(elem!1)), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[792, 224, 390, 685, 787])).
% 0.73/1.00 tff(794,plain,
% 0.73/1.00 (r(s(s(elem!1)), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[147, 793, 2])).
% 0.73/1.00 tff(795,plain,
% 0.73/1.00 (~b(s(z), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[714, 224, 684, 685, 787])).
% 0.73/1.00 tff(796,plain,
% 0.73/1.00 (r(s(z), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[175, 795])).
% 0.73/1.00 tff(797,plain,
% 0.73/1.00 (((~![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(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(798,plain,
% 0.73/1.00 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(799,plain,
% 0.73/1.00 (((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~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(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[798])).
% 0.73/1.00 tff(800,plain,
% 0.73/1.00 (((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~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(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[799, 797])).
% 0.73/1.00 tff(801,plain,
% 0.73/1.00 ((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(802,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.73/1.00 tff(803,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[802, 112, 544, 656, 796, 794])).
% 0.73/1.00 tff(804,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(805,plain,
% 0.73/1.00 (~b(s(s(s(z))), elem!1)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[804, 685, 755, 773, 390, 544, 684])).
% 0.73/1.00 tff(806,plain,
% 0.73/1.00 (r(s(s(s(z))), elem!1)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[374, 805, 362])).
% 0.73/1.00 tff(807,plain,
% 0.73/1.00 (((~![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(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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(808,plain,
% 0.73/1.00 (((~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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(809,plain,
% 0.73/1.00 (((~![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))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[808])).
% 0.73/1.00 tff(810,plain,
% 0.73/1.00 (((~![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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[809, 807])).
% 0.73/1.00 tff(811,plain,
% 0.73/1.00 ((~![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))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(812,plain,
% 0.73/1.00 ((~![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(s(s(z))), s(elem!1)))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.73/1.00 tff(813,plain,
% 0.73/1.00 (~r(s(s(s(z))), s(elem!1))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[812, 112, 408, 806])).
% 0.73/1.00 tff(814,plain,
% 0.73/1.00 (((~![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)))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(815,plain,
% 0.73/1.00 ((~![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)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(816,plain,
% 0.73/1.00 ((~![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))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.73/1.00 tff(817,plain,
% 0.73/1.00 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[816, 68, 813])).
% 0.73/1.00 tff(818,plain,
% 0.73/1.00 (b(s(s(s(z))), s(elem!1))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[817, 786])).
% 0.73/1.00 tff(819,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(820,plain,
% 0.73/1.00 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(821,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[820])).
% 0.73/1.00 tff(822,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[821, 819])).
% 0.73/1.00 tff(823,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(824,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[823, 822])).
% 0.73/1.00 tff(825,plain,
% 0.73/1.00 (~b(s(z), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[824, 224, 684, 685, 683, 818])).
% 0.73/1.00 tff(826,plain,
% 0.73/1.00 (r(s(z), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[175, 825])).
% 0.73/1.00 tff(827,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 0.73/1.00 tff(828,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(829,plain,
% 0.73/1.00 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(830,plain,
% 0.73/1.00 (((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[829])).
% 0.73/1.00 tff(831,plain,
% 0.73/1.00 (((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[830, 828])).
% 0.73/1.00 tff(832,plain,
% 0.73/1.00 ((~![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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(833,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.73/1.00 tff(834,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[833, 112, 656, 178, 827])).
% 0.73/1.00 tff(835,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(836,plain,
% 0.73/1.00 (~r(s(s(elem!1)), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[835, 826, 755])).
% 0.73/1.00 tff(837,plain,
% 0.73/1.00 (b(s(s(elem!1)), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[147, 836, 773])).
% 0.73/1.00 tff(838,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(839,plain,
% 0.73/1.00 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(840,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[839])).
% 0.73/1.00 tff(841,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[840, 838])).
% 0.73/1.01 tff(842,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(843,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.73/1.01 tff(844,plain,
% 0.73/1.01 (~b(s(s(elem!1)), z)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[843, 224, 736, 390, 685, 837])).
% 0.73/1.01 tff(845,plain,
% 0.73/1.01 (r(s(s(elem!1)), z)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[593, 844])).
% 0.73/1.01 tff(846,plain,
% 0.73/1.01 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[118, 112, 845, 771])).
% 0.73/1.01 tff(847,plain,
% 0.73/1.01 (b(s(s(s(z))), s(s(elem!1)))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[135, 68, 308, 846])).
% 0.73/1.01 tff(848,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(849,plain,
% 0.73/1.01 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(850,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[849])).
% 0.73/1.01 tff(851,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[850, 848])).
% 0.73/1.01 tff(852,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(853,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.73/1.01 tff(854,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[853, 224, 682, 685, 837, 847])).
% 0.73/1.01 tff(855,plain,((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | b(elem!1, s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (z = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(856,plain,
% 0.73/1.01 (~b(elem!1, s(s(s(z))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[855, 559, 681, 542, 628, 671, 517, 408, 362, 531, 77, 560, 4, 626])).
% 0.73/1.01 tff(857,plain,
% 0.73/1.01 (r(elem!1, s(s(s(z))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[388, 856, 680])).
% 0.73/1.01 tff(858,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(859,plain,
% 0.73/1.01 (((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(860,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[859])).
% 0.73/1.01 tff(861,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[860, 858])).
% 0.73/1.01 tff(862,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(863,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.73/1.01 tff(864,plain,
% 0.73/1.01 (~r(z, elem!1)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[863, 112, 857, 679])).
% 0.73/1.01 tff(865,plain,
% 0.73/1.01 (b(z, elem!1)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[289, 864, 4])).
% 0.73/1.01 tff(866,plain,
% 0.73/1.01 (~b(z, s(s(elem!1)))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[743, 865, 559, 542])).
% 0.73/1.01 tff(867,plain,
% 0.73/1.01 (r(z, s(s(elem!1)))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[752, 866])).
% 0.73/1.01 tff(868,plain,
% 0.73/1.01 (~(s(s(elem!1)) = s(s(s(z))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[681, 772])).
% 0.73/1.01 tff(869,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(870,plain,
% 0.73/1.01 (((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(871,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[870])).
% 0.85/1.01 tff(872,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.85/1.01 inference(transitivity,[status(thm)],[871, 869])).
% 0.85/1.01 tff(873,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(874,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.85/1.01 tff(875,plain,
% 0.85/1.01 (~r(elem!1, z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[874, 112, 857, 679])).
% 0.85/1.01 tff(876,plain,
% 0.85/1.01 (b(elem!1, z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[403, 875, 157])).
% 0.85/1.01 tff(877,plain,
% 0.85/1.01 (~b(s(z), z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[461, 224, 876, 628, 865])).
% 0.85/1.01 tff(878,plain,
% 0.85/1.01 (r(s(z), z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[194, 877])).
% 0.85/1.01 tff(879,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(880,plain,
% 0.85/1.01 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(881,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[880])).
% 0.85/1.01 tff(882,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[881, 879])).
% 0.85/1.01 tff(883,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(884,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.85/1.01 tff(885,plain,
% 0.85/1.01 (~b(s(s(elem!1)), z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[884, 224, 876, 865, 542])).
% 0.85/1.01 tff(886,plain,
% 0.85/1.01 (r(s(s(elem!1)), z)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[593, 885])).
% 0.85/1.01 tff(887,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.85/1.01 tff(888,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(889,plain,
% 0.85/1.01 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(890,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[889])).
% 0.85/1.01 tff(891,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[890, 888])).
% 0.85/1.01 tff(892,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(893,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.85/1.01 tff(894,plain,
% 0.85/1.01 ($false),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[893, 112, 102, 179, 887])).
% 0.85/1.01 tff(895,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.01 tff(896,plain,
% 0.85/1.01 (~r(s(s(elem!1)), s(z))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[895, 886, 878])).
% 0.85/1.01 tff(897,plain,
% 0.85/1.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(898,plain,
% 0.85/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(899,plain,
% 0.85/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.85/1.01 tff(900,plain,
% 0.85/1.01 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[899, 68])).
% 0.85/1.01 tff(901,plain,
% 0.85/1.01 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[900, 640])).
% 0.85/1.01 tff(902,plain,
% 0.85/1.01 (b(s(s(elem!1)), s(z))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[901, 896])).
% 0.85/1.01 tff(903,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(904,plain,
% 0.85/1.01 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(905,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[904])).
% 0.85/1.01 tff(906,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(transitivity,[status(thm)],[905, 903])).
% 0.85/1.01 tff(907,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(908,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[907, 906])).
% 0.85/1.01 tff(909,plain,
% 0.85/1.01 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[908, 224, 628, 542, 560])).
% 0.85/1.01 tff(910,plain,
% 0.85/1.01 (~b(s(s(elem!1)), s(s(s(z))))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[909, 902])).
% 0.85/1.01 tff(911,plain,
% 0.85/1.01 (r(s(s(elem!1)), s(s(s(z))))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[147, 910, 868])).
% 0.85/1.01 tff(912,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(913,plain,
% 0.85/1.01 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(914,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[913])).
% 0.85/1.01 tff(915,plain,
% 0.85/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.01 inference(transitivity,[status(thm)],[914, 912])).
% 0.85/1.01 tff(916,plain,
% 0.85/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(917,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.85/1.02 tff(918,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[917, 112, 886, 911, 679, 867])).
% 0.85/1.02 tff(919,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (elem!1 = z) | (z = elem!1) | (elem!1 = s(s(s(z)))) | b(elem!1, s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(elem!1, s(elem!1))) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(920,plain,
% 0.85/1.02 (~b(s(s(s(z))), s(z))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[919, 516, 77, 511, 3, 377, 406, 362, 157, 129, 408, 510])).
% 0.85/1.02 tff(921,plain,
% 0.85/1.02 (((~![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)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(922,plain,
% 0.85/1.02 ((~![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)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(923,plain,
% 0.85/1.02 ((~![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))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.85/1.02 tff(924,plain,
% 0.85/1.02 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[923, 68])).
% 0.85/1.02 tff(925,plain,
% 0.85/1.02 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[924, 44])).
% 0.85/1.02 tff(926,plain,
% 0.85/1.02 (r(s(s(s(z))), s(z))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[925, 920])).
% 0.85/1.02 tff(927,plain,
% 0.85/1.02 (((~![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))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(928,plain,
% 0.85/1.02 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(929,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[928])).
% 0.85/1.02 tff(930,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[929, 927])).
% 0.85/1.02 tff(931,plain,
% 0.85/1.02 ((~![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))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(932,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.85/1.02 tff(933,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[932, 112, 463, 177, 926])).
% 0.85/1.02 tff(934,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), s(elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (s(z) = elem!1) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(935,plain,
% 0.85/1.02 (~r(s(elem!1), elem!1)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[934, 406, 77, 3, 177, 362, 157, 129, 405, 407, 344])).
% 0.85/1.02 tff(936,plain,
% 0.85/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(937,plain,
% 0.85/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(938,plain,
% 0.85/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.85/1.02 tff(939,plain,
% 0.85/1.02 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[938, 68])).
% 0.85/1.02 tff(940,plain,
% 0.85/1.02 (b(s(elem!1), elem!1)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[939, 935, 303])).
% 0.85/1.02 tff(941,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(942,plain,
% 0.85/1.02 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(943,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[942])).
% 0.85/1.02 tff(944,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[943, 941])).
% 0.85/1.02 tff(945,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(946,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.85/1.02 tff(947,plain,
% 0.85/1.02 (~b(s(elem!1), z)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[946, 224, 940, 405, 344])).
% 0.85/1.02 tff(948,plain,
% 0.85/1.02 (r(s(elem!1), z)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[498, 947])).
% 0.85/1.02 tff(949,plain,
% 0.85/1.02 (r(s(s(elem!1)), s(elem!1))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[530, 406, 526])).
% 0.85/1.02 tff(950,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(951,plain,
% 0.85/1.02 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(952,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[951])).
% 0.85/1.02 tff(953,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[952, 950])).
% 0.85/1.02 tff(954,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(955,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.85/1.02 tff(956,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[955, 112, 949, 102, 948])).
% 0.85/1.02 tff(957,plain,(b(s(s(elem!1)), s(elem!1)) | (~r(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (s(z) = elem!1) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(958,plain,
% 0.85/1.02 (~b(z, s(elem!1))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[957, 406, 405, 344, 77, 3, 177, 362, 157, 129, 102])).
% 0.85/1.02 tff(959,plain,
% 0.85/1.02 (~r(z, s(elem!1))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[576, 949, 293])).
% 0.85/1.02 tff(960,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[625, 959, 958])).
% 0.85/1.02 tff(961,plain,(b(s(s(elem!1)), s(elem!1)) | (~r(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (s(z) = elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(962,plain,
% 0.85/1.02 (b(s(s(elem!1)), s(elem!1))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[961, 404, 293, 340, 77, 3, 177, 348, 334, 149, 102])).
% 0.85/1.02 tff(963,plain,
% 0.85/1.02 (~(s(elem!1) = s(z))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[159, 334])).
% 0.85/1.02 tff(964,plain,
% 0.85/1.02 (~b(s(z), z)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[461, 224, 405, 684, 344])).
% 0.85/1.02 tff(965,plain,
% 0.85/1.02 (r(s(z), z)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[194, 964])).
% 0.85/1.02 tff(966,plain,
% 0.85/1.02 (~r(s(z), s(s(s(z))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[187, 965, 177])).
% 0.85/1.02 tff(967,plain,
% 0.85/1.02 (b(s(z), s(s(s(z))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[175, 966])).
% 0.85/1.02 tff(968,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.02 tff(969,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(970,plain,
% 0.85/1.02 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(971,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[970])).
% 0.85/1.02 tff(972,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[971, 969])).
% 0.85/1.02 tff(973,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(974,plain,
% 0.85/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.85/1.02 tff(975,plain,
% 0.85/1.02 ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[974, 224, 684, 390, 968])).
% 0.85/1.02 tff(976,plain,
% 0.85/1.02 (~b(s(z), s(s(elem!1)))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[975, 967])).
% 0.85/1.02 tff(977,plain,
% 0.85/1.02 (r(s(z), s(s(elem!1)))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[653, 976])).
% 0.85/1.02 tff(978,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(979,plain,
% 0.85/1.02 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(980,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[979])).
% 0.85/1.02 tff(981,plain,
% 0.85/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[980, 978])).
% 0.85/1.03 tff(982,plain,
% 0.85/1.03 ((~![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)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(983,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[982, 981])).
% 0.85/1.03 tff(984,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[983, 112, 102, 965, 977])).
% 0.85/1.03 tff(985,plain,((~b(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(986,plain,
% 0.85/1.03 (~b(s(z), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[985, 361, 102, 295, 177, 404, 340])).
% 0.85/1.03 tff(987,plain,
% 0.85/1.03 (r(s(z), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[454, 986, 149])).
% 0.85/1.03 tff(988,plain,
% 0.85/1.03 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(989,plain,
% 0.85/1.03 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[988, 25])).
% 0.85/1.03 tff(990,plain,
% 0.85/1.03 (b(z, elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[289, 511, 285])).
% 0.85/1.03 tff(991,plain,
% 0.85/1.03 (~r(s(z), z)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[895, 887, 102])).
% 0.85/1.03 tff(992,plain,
% 0.85/1.03 (b(s(z), z)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[194, 991])).
% 0.85/1.03 tff(993,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 0.85/1.03 tff(994,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(995,plain,
% 0.85/1.03 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(996,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[995])).
% 0.85/1.03 tff(997,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[996, 994])).
% 0.85/1.03 tff(998,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(999,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.85/1.03 tff(1000,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[999, 112, 545, 887, 993])).
% 0.85/1.03 tff(1001,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1002,plain,
% 0.85/1.03 (~r(elem!1, s(s(elem!1)))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1001, 993, 887])).
% 0.85/1.03 tff(1003,plain,
% 0.85/1.03 (b(elem!1, s(s(elem!1)))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[558, 1002, 3])).
% 0.85/1.03 tff(1004,plain,
% 0.85/1.03 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1005,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1004])).
% 0.85/1.03 tff(1006,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1005, 848])).
% 0.85/1.03 tff(1007,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1008,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.85/1.03 tff(1009,plain,
% 0.85/1.03 (~b(elem!1, s(s(s(z))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1008, 224, 1003, 152, 968])).
% 0.85/1.03 tff(1010,plain,
% 0.85/1.03 (r(elem!1, s(s(s(z))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[388, 1009, 377])).
% 0.85/1.03 tff(1011,plain,
% 0.85/1.03 (~r(elem!1, z)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[874, 112, 1010, 689])).
% 0.85/1.03 tff(1012,plain,
% 0.85/1.03 (b(elem!1, z)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[403, 1011, 157])).
% 0.85/1.03 tff(1013,plain,
% 0.85/1.03 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1014,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1013])).
% 0.85/1.03 tff(1015,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1014, 456])).
% 0.85/1.03 tff(1016,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1017,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.85/1.03 tff(1018,plain,
% 0.85/1.03 (~b(s(z), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1017, 224, 1012, 992, 990])).
% 0.85/1.03 tff(1019,plain,
% 0.85/1.03 (r(s(z), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[454, 1018, 149])).
% 0.85/1.03 tff(1020,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.85/1.03 tff(1021,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1022,plain,
% 0.85/1.03 (((~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))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1023,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(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)))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1022])).
% 0.85/1.03 tff(1024,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(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))))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1023, 1021])).
% 0.85/1.03 tff(1025,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1026,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.85/1.03 tff(1027,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1026, 112, 1020, 178, 993])).
% 0.85/1.03 tff(1028,plain,((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1029,plain,
% 0.85/1.03 (~r(s(z), s(s(s(z))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1028, 1010, 993])).
% 0.85/1.03 tff(1030,plain,
% 0.85/1.03 (b(s(z), s(s(s(z))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[175, 1029])).
% 0.85/1.03 tff(1031,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1032,plain,
% 0.85/1.03 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1033,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1032])).
% 0.85/1.03 tff(1034,plain,
% 0.85/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.85/1.03 tff(1035,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1036,plain,
% 0.85/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.85/1.03 tff(1037,plain,
% 0.85/1.03 (~b(s(s(s(z))), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1036, 224, 1003, 390, 968])).
% 0.85/1.03 tff(1038,plain,
% 0.85/1.03 (r(s(s(s(z))), elem!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[374, 1037, 362])).
% 0.85/1.03 tff(1039,plain,
% 0.85/1.03 (((~![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)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1040,plain,
% 0.85/1.03 (((~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)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1041,plain,
% 0.85/1.03 (((~![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))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1040])).
% 0.85/1.03 tff(1042,plain,
% 0.85/1.03 (((~![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)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.85/1.03 tff(1043,plain,
% 0.85/1.03 ((~![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))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1044,plain,
% 0.85/1.03 ((~![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))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.85/1.03 tff(1045,plain,
% 0.85/1.03 (~r(s(s(s(z))), s(z))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1044, 112, 1019, 1038])).
% 0.85/1.03 tff(1046,plain,
% 0.85/1.03 (b(s(s(s(z))), s(z))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[925, 1045])).
% 0.85/1.03 tff(1047,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 0.85/1.03 tff(1048,plain,
% 0.85/1.03 (((~![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(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)), elem!1)) | (~r(s(s(z)), s(z))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1049,plain,
% 0.85/1.03 (((~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)), elem!1)) | (~r(s(s(z)), s(z))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1050,plain,
% 0.85/1.03 (((~![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)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1049])).
% 0.85/1.03 tff(1051,plain,
% 0.85/1.03 (((~![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)), elem!1)) | (~r(s(s(z)), s(z))))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1050, 1048])).
% 0.85/1.03 tff(1052,plain,
% 0.85/1.03 ((~![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))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1053,plain,
% 0.85/1.03 ((~![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(s(z)), s(z)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.85/1.03 tff(1054,plain,
% 0.85/1.03 (~r(s(s(z)), s(z))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1053, 112, 416, 1047])).
% 0.85/1.03 tff(1055,plain,
% 0.85/1.03 (b(s(s(z)), s(z))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[213, 68, 210, 1054])).
% 0.85/1.03 tff(1056,plain,
% 0.85/1.03 (((~![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)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1057,plain,
% 0.85/1.03 (((~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)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1058,plain,
% 0.85/1.03 (((~![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))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1057])).
% 0.85/1.03 tff(1059,plain,
% 0.85/1.03 (((~![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)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.85/1.04 tff(1060,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1061,plain,
% 0.85/1.04 ((~![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))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.85/1.04 tff(1062,plain,
% 0.85/1.04 (~r(s(z), s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1061, 112, 416, 1047])).
% 0.85/1.04 tff(1063,plain,
% 0.85/1.04 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.85/1.04 inference(commutativity,[status(thm)],[])).
% 0.85/1.04 tff(1064,plain,
% 0.85/1.04 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.85/1.04 inference(symmetry,[status(thm)],[1063])).
% 0.85/1.04 tff(1065,plain,
% 0.85/1.04 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1064])).
% 0.85/1.04 tff(1066,plain,
% 0.85/1.04 (~(s(z) = s(s(z)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[210, 1065])).
% 0.85/1.04 tff(1067,plain,
% 0.85/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1068,plain,
% 0.85/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1069,plain,
% 0.85/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 0.85/1.04 tff(1070,plain,
% 0.85/1.04 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1069, 68])).
% 0.85/1.04 tff(1071,plain,
% 0.85/1.04 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1070, 1066])).
% 0.85/1.04 tff(1072,plain,
% 0.85/1.04 (b(s(z), s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1071, 1062])).
% 0.85/1.04 tff(1073,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1074,plain,
% 0.85/1.04 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1075,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1074])).
% 0.85/1.04 tff(1076,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1075, 1073])).
% 0.85/1.04 tff(1077,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1078,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.85/1.04 tff(1079,plain,
% 0.85/1.04 (~b(z, s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1078, 224, 77, 1072, 1055])).
% 0.85/1.04 tff(1080,plain,
% 0.85/1.04 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 0.85/1.04 inference(commutativity,[status(thm)],[])).
% 0.85/1.04 tff(1081,plain,
% 0.85/1.04 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 0.85/1.04 inference(symmetry,[status(thm)],[1080])).
% 0.85/1.04 tff(1082,plain,
% 0.85/1.04 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1081])).
% 0.85/1.04 tff(1083,plain,
% 0.85/1.04 (~(z = s(s(z)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[42, 1082])).
% 0.85/1.04 tff(1084,plain,
% 0.85/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1085,plain,
% 0.85/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1086,plain,
% 0.85/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.85/1.04 tff(1087,plain,
% 0.85/1.04 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1086, 68])).
% 0.85/1.04 tff(1088,plain,
% 0.85/1.04 (b(z, s(s(z))) | r(z, s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1087, 1083])).
% 0.85/1.04 tff(1089,plain,
% 0.85/1.04 (r(z, s(s(z)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1088, 1079])).
% 0.85/1.04 tff(1090,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.85/1.04 tff(1091,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1092,plain,
% 0.85/1.04 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1093,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1092])).
% 0.85/1.04 tff(1094,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1093, 1091])).
% 0.85/1.04 tff(1095,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1096,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.85/1.04 tff(1097,plain,
% 0.85/1.04 (~b(s(s(z)), s(s(s(z))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1096, 224, 1090, 560, 1055])).
% 0.85/1.04 tff(1098,plain,
% 0.85/1.04 (r(s(s(z)), s(s(s(z))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[249, 1097])).
% 0.85/1.04 tff(1099,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1100,plain,
% 0.85/1.04 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1101,plain,
% 0.85/1.04 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1100])).
% 0.85/1.04 tff(1102,plain,
% 0.85/1.04 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1101, 1099])).
% 0.85/1.04 tff(1103,plain,
% 0.85/1.04 ((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1104,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.85/1.04 tff(1105,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1104, 112, 1098, 689, 1089])).
% 0.85/1.04 tff(1106,plain,((~r(s(s(z)), elem!1)) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1107,plain,
% 0.85/1.04 (~r(s(s(z)), elem!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1106, 1046, 77, 689, 1030, 1019])).
% 0.85/1.04 tff(1108,plain,
% 0.85/1.04 (~(s(s(z)) = s(s(elem!1)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[168, 409])).
% 0.85/1.04 tff(1109,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 0.85/1.04 tff(1110,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1111,plain,
% 0.85/1.04 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1112,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1111])).
% 0.85/1.04 tff(1113,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.85/1.04 tff(1114,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1115,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.85/1.04 tff(1116,plain,
% 0.85/1.04 (~b(s(s(z)), s(s(elem!1)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1115, 224, 682, 390, 1109])).
% 0.85/1.04 tff(1117,plain,
% 0.85/1.04 (r(s(s(z)), s(s(elem!1)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[263, 68, 259, 1116])).
% 0.85/1.04 tff(1118,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.85/1.04 tff(1119,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1120,plain,
% 0.85/1.04 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1121,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1120])).
% 0.85/1.04 tff(1122,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1121, 1119])).
% 0.85/1.04 tff(1123,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1124,plain,
% 0.85/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 0.85/1.04 tff(1125,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1124, 224, 405, 344, 1109, 1118])).
% 0.85/1.04 tff(1126,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1127,plain,
% 0.85/1.04 (~b(s(s(z)), z)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1126, 1109, 405, 344])).
% 0.85/1.04 tff(1128,plain,
% 0.85/1.04 (r(s(s(z)), z)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[281, 1127])).
% 0.85/1.04 tff(1129,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[274, 112, 102, 1128, 1117])).
% 0.85/1.04 tff(1130,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1131,plain,
% 0.85/1.04 (~b(s(s(z)), elem!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1130, 1003, 1108, 102, 390, 1012, 990])).
% 0.85/1.04 tff(1132,plain,
% 0.85/1.04 (((~![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))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1133,plain,
% 0.85/1.04 ((~![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))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1134,plain,
% 0.85/1.04 ((~![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)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 0.85/1.04 tff(1135,plain,
% 0.85/1.04 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1134, 68])).
% 0.85/1.04 tff(1136,plain,
% 0.85/1.04 (s(s(z)) = elem!1),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1135, 1131, 1107])).
% 0.85/1.04 tff(1137,plain,
% 0.85/1.04 (s(s(s(z))) = s(elem!1)),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1136])).
% 0.85/1.04 tff(1138,plain,
% 0.85/1.04 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.04 tff(1139,plain,
% 0.85/1.04 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1138])).
% 0.85/1.04 tff(1140,plain,
% 0.85/1.04 (~b(s(elem!1), elem!1)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1037, 1139])).
% 0.85/1.04 tff(1141,plain,
% 0.85/1.04 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.04 tff(1142,plain,
% 0.85/1.04 (r(z, s(elem!1))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[689, 1141])).
% 0.85/1.04 tff(1143,plain,
% 0.85/1.04 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 0.85/1.04 inference(commutativity,[status(thm)],[])).
% 0.85/1.04 tff(1144,plain,
% 0.85/1.04 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.04 tff(1145,plain,
% 0.85/1.04 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1144, 1143])).
% 0.85/1.04 tff(1146,plain,
% 0.85/1.04 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1145])).
% 0.85/1.04 tff(1147,plain,
% 0.85/1.04 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 0.85/1.04 inference(commutativity,[status(thm)],[])).
% 0.85/1.04 tff(1148,plain,
% 0.85/1.04 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1147])).
% 0.85/1.04 tff(1149,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 0.85/1.04 tff(1150,plain,
% 0.85/1.04 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 0.85/1.04 inference(symmetry,[status(thm)],[1149])).
% 0.85/1.04 tff(1151,plain,
% 0.85/1.04 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1150])).
% 0.85/1.04 tff(1152,plain,
% 0.85/1.04 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 0.85/1.04 inference(symmetry,[status(thm)],[1151])).
% 0.85/1.04 tff(1153,plain,
% 0.85/1.04 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.04 inference(symmetry,[status(thm)],[989])).
% 0.85/1.04 tff(1154,plain,
% 0.85/1.04 (s(s(s(elem!1))) = s(s(z))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1153, 1152, 31])).
% 0.85/1.04 tff(1155,plain,
% 0.85/1.04 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1156,plain,
% 0.85/1.04 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1155, 25])).
% 0.85/1.04 tff(1157,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 0.85/1.04 tff(1158,plain,
% 0.85/1.04 (s(s(z)) = s(s(s(elem!1)))),
% 0.85/1.04 inference(symmetry,[status(thm)],[1157])).
% 0.85/1.04 tff(1159,plain,
% 0.85/1.04 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1158])).
% 0.85/1.04 tff(1160,plain,
% 0.85/1.04 (s(z) = s(s(elem!1))),
% 0.85/1.04 inference(transitivity,[status(thm)],[50, 1159, 1156])).
% 0.85/1.04 tff(1161,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[648, 1160])).
% 0.85/1.04 tff(1162,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1163,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1162, 1154])).
% 0.85/1.04 tff(1164,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1165,plain,
% 0.85/1.04 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1164, 1148])).
% 0.85/1.04 tff(1166,plain,
% 0.85/1.04 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1165, 1146])).
% 0.85/1.04 tff(1167,plain,
% 0.85/1.04 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.04 tff(1168,plain,
% 0.85/1.04 (b(s(elem!1), s(s(elem!1)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[968, 1167])).
% 0.85/1.04 tff(1169,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 0.85/1.04 tff(1170,plain,
% 0.85/1.04 (s(s(s(z))) = s(elem!1)),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1169])).
% 0.85/1.04 tff(1171,plain,
% 0.85/1.04 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1170])).
% 0.85/1.04 tff(1172,plain,
% 0.85/1.04 (r(z, s(elem!1))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[689, 1171])).
% 0.85/1.04 tff(1173,plain,
% 0.85/1.04 (~r(z, s(s(elem!1)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[574, 112, 544, 1172])).
% 0.85/1.04 tff(1174,plain,
% 0.85/1.04 (b(z, s(s(elem!1)))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[752, 1173])).
% 0.85/1.04 tff(1175,plain,
% 0.85/1.04 ((s(s(z)) = z) <=> (elem!1 = z)),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1169])).
% 0.85/1.04 tff(1176,plain,
% 0.85/1.04 ((s(s(z)) = z) <=> (z = elem!1)),
% 0.85/1.04 inference(transitivity,[status(thm)],[1175, 6])).
% 0.85/1.04 tff(1177,plain,
% 0.85/1.04 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1176])).
% 0.85/1.04 tff(1178,plain,
% 0.85/1.04 (~(z = elem!1)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[42, 1177])).
% 0.85/1.04 tff(1179,plain,
% 0.85/1.04 (b(z, elem!1)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[289, 1178, 285])).
% 0.85/1.04 tff(1180,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 0.85/1.04 tff(1181,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.85/1.04 tff(1182,plain,
% 0.85/1.04 (((~![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)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1183,plain,
% 0.85/1.04 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1184,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1183])).
% 0.85/1.04 tff(1185,plain,
% 0.85/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1184, 1182])).
% 0.85/1.05 tff(1186,plain,
% 0.85/1.05 ((~![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))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1187,plain,
% 0.85/1.05 ((~![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)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 0.85/1.05 tff(1188,plain,
% 0.85/1.05 (~r(s(s(elem!1)), s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1187, 112, 1181, 416])).
% 0.85/1.05 tff(1189,plain,
% 0.85/1.05 (b(s(s(elem!1)), s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[901, 1188])).
% 0.85/1.05 tff(1190,plain,
% 0.85/1.05 (((~![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)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1191,plain,
% 0.85/1.05 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1192,plain,
% 0.85/1.05 (((~![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)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1191])).
% 0.85/1.05 tff(1193,plain,
% 0.85/1.05 (((~![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)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1192, 1190])).
% 0.85/1.05 tff(1194,plain,
% 0.85/1.05 ((~![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)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1195,plain,
% 0.85/1.05 ((~![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)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 0.85/1.05 tff(1196,plain,
% 0.85/1.05 (~r(s(z), s(s(elem!1)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1195, 112, 1181, 416])).
% 0.85/1.05 tff(1197,plain,
% 0.85/1.05 (b(s(z), s(s(elem!1)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[653, 1196])).
% 0.85/1.05 tff(1198,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1199,plain,
% 0.85/1.05 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1200,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1199])).
% 0.85/1.05 tff(1201,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1200, 1198])).
% 0.85/1.05 tff(1202,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1203,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.85/1.05 tff(1204,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1203, 224, 77, 1197, 1189, 1180])).
% 0.85/1.05 tff(1205,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1206,plain,
% 0.85/1.05 (~r(s(s(elem!1)), elem!1)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1205, 1174, 77, 416])).
% 0.85/1.05 tff(1207,plain,
% 0.85/1.05 (b(s(s(elem!1)), elem!1)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[360, 1206, 355])).
% 0.85/1.05 tff(1208,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1209,plain,
% 0.85/1.05 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1210,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1209])).
% 0.85/1.05 tff(1211,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.85/1.05 tff(1212,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1213,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.85/1.05 tff(1214,plain,
% 0.85/1.05 ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1213, 224])).
% 0.85/1.05 tff(1215,plain,
% 0.85/1.05 (~b(elem!1, s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1214, 1207, 1179, 77, 1174])).
% 0.85/1.05 tff(1216,plain,
% 0.85/1.05 (s(s(s(s(z)))) = s(s(elem!1))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1170])).
% 0.85/1.05 tff(1217,plain,
% 0.85/1.05 ((s(s(s(s(z)))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1216])).
% 0.85/1.05 tff(1218,plain,
% 0.85/1.05 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1217, 75])).
% 0.85/1.05 tff(1219,plain,
% 0.85/1.05 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1218])).
% 0.85/1.05 tff(1220,plain,
% 0.85/1.05 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1169])).
% 0.85/1.05 tff(1221,plain,
% 0.85/1.05 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1220])).
% 0.85/1.05 tff(1222,plain,
% 0.85/1.05 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1223,plain,
% 0.85/1.05 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1222, 25])).
% 0.85/1.05 tff(1224,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 0.85/1.05 tff(1225,plain,
% 0.85/1.05 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1224])).
% 0.85/1.05 tff(1226,plain,
% 0.85/1.05 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.85/1.05 inference(symmetry,[status(thm)],[1225])).
% 0.85/1.05 tff(1227,plain,
% 0.85/1.05 (s(z) = s(s(s(z)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[50, 1226, 1223])).
% 0.85/1.05 tff(1228,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[45, 1227])).
% 0.85/1.05 tff(1229,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1230,plain,
% 0.85/1.05 (~(s(s(s(s(z)))) = elem!1)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1229, 1221])).
% 0.85/1.05 tff(1231,plain,
% 0.85/1.05 (~(elem!1 = s(s(elem!1)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1230, 1219])).
% 0.85/1.05 tff(1232,plain,
% 0.85/1.05 ((~(s(s(z)) = z)) <=> (~(elem!1 = z))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1175])).
% 0.85/1.05 tff(1233,plain,
% 0.85/1.05 (~(elem!1 = z)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[42, 1232])).
% 0.85/1.05 tff(1234,plain,
% 0.85/1.05 (~r(s(s(elem!1)), z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[588, 112, 544, 1172])).
% 0.85/1.05 tff(1235,plain,
% 0.85/1.05 (b(s(s(elem!1)), z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[593, 1234])).
% 0.85/1.05 tff(1236,plain,
% 0.85/1.05 (~b(elem!1, s(s(elem!1)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[743, 390, 1180, 344])).
% 0.85/1.05 tff(1237,plain,
% 0.85/1.05 (r(elem!1, s(s(elem!1)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[558, 1236, 3])).
% 0.85/1.05 tff(1238,plain,
% 0.85/1.05 (~r(s(s(elem!1)), s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1001, 1237, 993])).
% 0.85/1.05 tff(1239,plain,
% 0.85/1.05 (b(s(s(elem!1)), s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[901, 1238])).
% 0.85/1.05 tff(1240,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 0.85/1.05 tff(1241,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.85/1.05 tff(1242,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1243,plain,
% 0.85/1.05 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1244,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1243])).
% 0.85/1.05 tff(1245,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1244, 1242])).
% 0.85/1.05 tff(1246,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1247,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 0.85/1.05 tff(1248,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1247, 224, 77, 1240, 1, 1241])).
% 0.85/1.05 tff(1249,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1250,plain,
% 0.85/1.05 (~b(s(z), z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1249, 1239, 77, 1240])).
% 0.85/1.05 tff(1251,plain,
% 0.85/1.05 (r(s(z), z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[194, 1250])).
% 0.85/1.05 tff(1252,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1253,plain,
% 0.85/1.05 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1254,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1253])).
% 0.85/1.05 tff(1255,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.85/1.05 tff(1256,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1257,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.85/1.05 tff(1258,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1257, 112, 363, 179, 993])).
% 0.85/1.05 tff(1259,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1260,plain,
% 0.85/1.05 (~r(elem!1, z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1259, 1251, 993])).
% 0.85/1.05 tff(1261,plain,
% 0.85/1.05 (b(elem!1, z)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[403, 1260, 157])).
% 0.85/1.05 tff(1262,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1263,plain,
% 0.85/1.05 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1264,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z)))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1263])).
% 0.85/1.05 tff(1265,plain,
% 0.85/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.85/1.05 tff(1266,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1267,plain,
% 0.85/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.85/1.05 tff(1268,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1267, 224, 77, 1261, 1240, 1239, 390])).
% 0.85/1.05 tff(1269,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1270,plain,
% 0.85/1.05 (~r(elem!1, s(z))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1269, 1207, 1235, 1233, 77, 1231, 1174, 1179])).
% 0.85/1.05 tff(1271,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 0.85/1.05 tff(1272,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 0.85/1.05 tff(1273,plain,
% 0.85/1.05 (((~![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)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1274,plain,
% 0.85/1.05 ((~![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)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1275,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.85/1.06 tff(1276,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1275, 68, 1272, 88, 1271])).
% 0.85/1.06 tff(1277,plain,(r(elem!1, s(z)) | b(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1278,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1277, 1270, 1215, 88])).
% 0.85/1.06 tff(1279,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(z)) | (~b(z, s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(z), elem!1)) | r(z, elem!1) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1280,plain,
% 0.85/1.06 (~r(s(s(elem!1)), s(elem!1))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1279, 1136, 77, 353, 1019, 285, 88, 689])).
% 0.85/1.06 tff(1281,plain,
% 0.85/1.06 (b(s(s(elem!1)), s(elem!1))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[530, 1280, 526])).
% 0.85/1.06 tff(1282,plain,
% 0.85/1.06 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.06 tff(1283,plain,
% 0.85/1.06 (b(s(z), s(elem!1))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1030, 1282])).
% 0.85/1.06 tff(1284,plain,
% 0.85/1.06 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1137])).
% 0.85/1.06 tff(1285,plain,
% 0.85/1.06 (b(s(elem!1), s(z))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1046, 1284])).
% 0.85/1.06 tff(1286,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 0.85/1.06 tff(1287,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 0.85/1.06 tff(1288,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 0.85/1.06 tff(1289,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.85/1.06 tff(1290,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 0.85/1.06 tff(1291,plain,
% 0.85/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1292,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1293,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.85/1.06 tff(1294,plain,
% 0.85/1.06 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1293, 68])).
% 0.85/1.06 tff(1295,plain,
% 0.85/1.06 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1294, 1288, 1290])).
% 0.85/1.06 tff(1296,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 0.85/1.06 tff(1297,plain,
% 0.85/1.06 (s(elem!1) = s(s(s(elem!1)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1296])).
% 0.85/1.06 tff(1298,plain,
% 0.85/1.06 (s(s(s(elem!1))) = s(elem!1)),
% 0.85/1.06 inference(symmetry,[status(thm)],[1297])).
% 0.85/1.06 tff(1299,plain,
% 0.85/1.06 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1298])).
% 0.85/1.06 tff(1300,plain,
% 0.85/1.06 (s(s(elem!1)) = elem!1),
% 0.85/1.06 inference(symmetry,[status(thm)],[1296])).
% 0.85/1.06 tff(1301,plain,
% 0.85/1.06 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1300])).
% 0.85/1.06 tff(1302,plain,
% 0.85/1.06 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1301])).
% 0.85/1.06 tff(1303,plain,
% 0.85/1.06 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1302])).
% 0.85/1.06 tff(1304,plain,
% 0.85/1.06 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1288, 1303])).
% 0.85/1.06 tff(1305,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1304, 1299])).
% 0.85/1.06 tff(1306,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1307,plain,
% 0.85/1.06 (~(elem!1 = s(s(elem!1)))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1306, 1288])).
% 0.85/1.06 tff(1308,plain,
% 0.85/1.06 (~(s(elem!1) = elem!1)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[302, 1307])).
% 0.85/1.06 tff(1309,plain,
% 0.85/1.06 (r(s(elem!1), elem!1)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[939, 1308, 1287])).
% 0.85/1.06 tff(1310,plain,
% 0.85/1.06 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1311,plain,
% 0.85/1.06 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1312,plain,
% 0.85/1.06 (((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1311])).
% 0.85/1.06 tff(1313,plain,
% 0.85/1.06 (((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.85/1.06 tff(1314,plain,
% 0.85/1.06 ((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1315,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.85/1.06 tff(1316,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1315, 112, 1309, 1295, 1289])).
% 0.85/1.06 tff(1317,plain,((s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | b(s(elem!1), elem!1) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1318,plain,
% 0.85/1.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1317, 1289, 1288, 1287])).
% 0.85/1.06 tff(1319,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1320,plain,
% 0.85/1.06 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1321,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1320])).
% 0.85/1.06 tff(1322,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1321, 1319])).
% 0.85/1.06 tff(1323,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1324,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 0.85/1.06 tff(1325,plain,
% 0.85/1.06 (~b(s(s(s(s(elem!1)))), z)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1324, 224, 1318, 405, 344])).
% 0.85/1.06 tff(1326,plain,
% 0.85/1.06 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1327,plain,
% 0.85/1.06 (((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1328,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1327])).
% 0.85/1.06 tff(1329,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1328, 1326])).
% 0.85/1.06 tff(1330,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1331,plain,
% 0.85/1.06 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.85/1.06 tff(1332,plain,
% 0.85/1.06 (~r(s(s(s(s(elem!1)))), z)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1331, 112, 568, 1289])).
% 0.85/1.06 tff(1333,plain,
% 0.85/1.06 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1334,plain,
% 0.85/1.06 (~(s(s(s(s(elem!1)))) = z)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1333, 40])).
% 0.85/1.06 tff(1335,plain,
% 0.85/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1336,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1337,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.85/1.06 tff(1338,plain,
% 0.85/1.06 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1337, 68, 1334])).
% 0.85/1.06 tff(1339,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1338, 1332, 1325])).
% 0.85/1.06 tff(1340,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1341,plain,
% 0.85/1.06 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1340, 1288, 405, 344, 568, 1287])).
% 0.85/1.06 tff(1342,plain,
% 0.85/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1343,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1344,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.85/1.06 tff(1345,plain,
% 0.85/1.06 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1344, 68])).
% 0.85/1.06 tff(1346,plain,
% 0.85/1.06 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1345, 1341, 1286])).
% 0.85/1.06 tff(1347,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 0.85/1.06 tff(1348,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1349,plain,
% 0.85/1.06 (((~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1350,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1349])).
% 0.85/1.06 tff(1351,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1350, 1348])).
% 0.85/1.06 tff(1352,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1353,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 0.85/1.06 tff(1354,plain,
% 0.85/1.06 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1353, 224, 1347, 683, 1346])).
% 0.85/1.06 tff(1355,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 0.85/1.06 tff(1356,plain,
% 0.85/1.06 (s(z) = s(s(s(s(elem!1))))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1355])).
% 0.85/1.06 tff(1357,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.06 tff(1358,plain,
% 0.85/1.06 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1357])).
% 0.85/1.06 tff(1359,plain,
% 0.85/1.06 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1358])).
% 0.85/1.06 tff(1360,plain,
% 0.85/1.06 (s(s(s(elem!1))) = z),
% 0.85/1.06 inference(transitivity,[status(thm)],[1153, 1359, 27])).
% 0.85/1.06 tff(1361,plain,
% 0.85/1.06 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1362,plain,
% 0.85/1.06 (~(s(s(s(elem!1))) = z)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1361, 40])).
% 0.85/1.06 tff(1363,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1362, 1360])).
% 0.85/1.06 tff(1364,plain,(~(s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1365,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1364, 1356])).
% 0.85/1.06 tff(1366,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1367,plain,
% 0.85/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1368,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1369,plain,
% 0.85/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.85/1.06 tff(1370,plain,
% 0.85/1.06 (r(s(s(s(s(elem!1)))), s(z))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 1354])).
% 0.85/1.06 tff(1371,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.06 tff(1372,plain,
% 0.85/1.06 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1371])).
% 0.85/1.06 tff(1373,plain,
% 0.85/1.06 (s(elem!1) = s(s(s(elem!1)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[164, 1372, 989])).
% 0.85/1.06 tff(1374,plain,
% 0.85/1.06 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1373])).
% 0.85/1.06 tff(1375,plain,
% 0.85/1.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1374])).
% 0.85/1.06 tff(1376,plain,
% 0.85/1.06 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1156])).
% 0.85/1.06 tff(1377,plain,
% 0.85/1.06 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1371])).
% 0.85/1.06 tff(1378,plain,
% 0.85/1.06 (s(s(s(s(elem!1)))) = elem!1),
% 0.85/1.06 inference(transitivity,[status(thm)],[1377, 1376, 1375, 121])).
% 0.85/1.06 tff(1379,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1288, 1378])).
% 0.85/1.06 tff(1380,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1381,plain,
% 0.85/1.06 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1380, 1288])).
% 0.85/1.06 tff(1382,plain,
% 0.85/1.06 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.06 inference(commutativity,[status(thm)],[])).
% 0.85/1.06 tff(1383,plain,
% 0.85/1.06 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 0.85/1.06 inference(symmetry,[status(thm)],[1382])).
% 0.85/1.06 tff(1384,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 0.85/1.06 tff(1385,plain,
% 0.85/1.06 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.85/1.06 tff(1386,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.85/1.06 tff(1387,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1386, 1385])).
% 0.85/1.06 tff(1388,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1389,plain,
% 0.85/1.06 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1388, 1381])).
% 0.85/1.06 tff(1390,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.06 tff(1391,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.85/1.06 tff(1392,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1393,plain,
% 0.85/1.06 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1394,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1393])).
% 0.85/1.06 tff(1395,plain,
% 0.85/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.85/1.06 tff(1396,plain,
% 0.85/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1397,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.85/1.07 tff(1398,plain,
% 0.85/1.07 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 1390, 1346])).
% 0.85/1.07 tff(1399,plain,
% 0.85/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1400,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1401,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 0.85/1.07 tff(1402,plain,
% 0.85/1.07 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1401, 68, 1398, 1389])).
% 0.85/1.07 tff(1403,plain,
% 0.85/1.07 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.85/1.07 inference(commutativity,[status(thm)],[])).
% 0.85/1.07 tff(1404,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.07 tff(1405,plain,
% 0.85/1.07 (s(s(s(s(elem!1)))) = elem!1),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.85/1.07 tff(1406,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1288, 1405])).
% 0.85/1.07 tff(1407,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1408,plain,
% 0.85/1.07 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1407, 1288])).
% 0.85/1.07 tff(1409,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.85/1.07 tff(1410,plain,
% 0.85/1.07 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1353, 224, 1347, 683, 1409])).
% 0.85/1.07 tff(1411,plain,
% 0.85/1.07 (r(s(s(s(s(elem!1)))), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 1410])).
% 0.85/1.07 tff(1412,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.85/1.07 tff(1413,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1414,plain,
% 0.85/1.07 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1415,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1414])).
% 0.85/1.07 tff(1416,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1415, 1413])).
% 0.85/1.07 tff(1417,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1418,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 0.85/1.07 tff(1419,plain,
% 0.85/1.07 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1418, 224, 1391, 390, 1409, 1412])).
% 0.85/1.07 tff(1420,plain,
% 0.85/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1421,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1422,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.85/1.07 tff(1423,plain,
% 0.85/1.07 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1422, 68, 1386, 1419])).
% 0.85/1.07 tff(1424,plain,
% 0.85/1.07 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1388, 1386])).
% 0.85/1.07 tff(1425,plain,
% 0.85/1.07 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 1390, 1409])).
% 0.85/1.07 tff(1426,plain,
% 0.85/1.07 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1401, 68, 1425, 1424])).
% 0.85/1.07 tff(1427,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1428,plain,
% 0.85/1.07 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1429,plain,
% 0.85/1.07 (((~![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(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1428])).
% 0.85/1.07 tff(1430,plain,
% 0.85/1.07 (((~![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(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1429, 1427])).
% 0.85/1.07 tff(1431,plain,
% 0.85/1.07 ((~![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(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1432,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.85/1.07 tff(1433,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1432, 112, 887, 1426, 1423, 1411])).
% 0.85/1.07 tff(1434,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1435,plain,
% 0.85/1.07 (~b(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1434, 1346, 1381, 1391, 390, 887, 1347, 683, 1390])).
% 0.85/1.07 tff(1436,plain,
% 0.85/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1437,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1438,plain,
% 0.85/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.85/1.07 tff(1439,plain,
% 0.85/1.07 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1438, 68])).
% 0.85/1.07 tff(1440,plain,
% 0.85/1.07 (r(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1439, 1435, 1408])).
% 0.85/1.07 tff(1441,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1442,plain,
% 0.85/1.07 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1443,plain,
% 0.85/1.07 (((~![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(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1442])).
% 0.85/1.07 tff(1444,plain,
% 0.85/1.07 (((~![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(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1443, 1441])).
% 0.85/1.07 tff(1445,plain,
% 0.85/1.07 ((~![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(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1446,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 0.85/1.07 tff(1447,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1446, 112, 993, 1440, 1402, 1370])).
% 0.85/1.07 tff(1448,plain,((s(s(s(s(elem!1)))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(elem!1))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1449,plain,
% 0.85/1.07 (s(s(s(s(elem!1)))) = elem!1),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1448, 993, 1285, 1283, 1281, 1168, 390, 887, 1166, 1012, 990, 1142, 1140])).
% 0.85/1.07 tff(1450,plain,
% 0.85/1.07 (elem!1 = s(s(s(s(elem!1))))),
% 0.85/1.07 inference(symmetry,[status(thm)],[1449])).
% 0.85/1.07 tff(1451,plain,
% 0.85/1.07 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1136, 1450])).
% 0.85/1.07 tff(1452,plain,
% 0.85/1.07 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1451])).
% 0.85/1.07 tff(1453,plain,
% 0.85/1.07 (s(z) = s(s(s(elem!1)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[50, 1452, 989])).
% 0.85/1.07 tff(1454,plain,
% 0.85/1.07 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1453])).
% 0.85/1.07 tff(1455,plain,
% 0.85/1.07 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.85/1.07 inference(symmetry,[status(thm)],[1454])).
% 0.85/1.07 tff(1456,plain,
% 0.85/1.07 (s(s(elem!1)) = z),
% 0.85/1.07 inference(transitivity,[status(thm)],[1376, 1455, 27])).
% 0.85/1.07 tff(1457,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[566, 1456])).
% 0.85/1.07 tff(1458,plain,((~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | r(z, elem!1) | (elem!1 = s(z)) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1459,plain,
% 0.85/1.07 (~r(elem!1, s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1458, 887, 390, 968, 689, 77, 285, 88, 102, 157, 362, 152, 3])).
% 0.85/1.07 tff(1460,plain,
% 0.85/1.07 (b(elem!1, s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1277, 1459, 88])).
% 0.85/1.07 tff(1461,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1462,plain,
% 0.85/1.07 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1463,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1462])).
% 0.85/1.07 tff(1464,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1463, 1461])).
% 0.85/1.07 tff(1465,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1466,plain,
% 0.85/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 0.85/1.07 tff(1467,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1466, 224, 77, 405, 992, 1460])).
% 0.85/1.07 tff(1468,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | r(z, elem!1) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1469,plain,
% 0.85/1.07 (~r(s(s(elem!1)), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1468, 404, 77, 88, 361, 295, 101, 285, 102, 334, 348, 313, 3])).
% 0.85/1.07 tff(1470,plain,
% 0.85/1.07 (b(s(s(elem!1)), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[901, 1469])).
% 0.85/1.07 tff(1471,plain,
% 0.85/1.07 (b(s(z), s(elem!1))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[670, 423, 415])).
% 0.85/1.07 tff(1472,plain,
% 0.85/1.07 (~r(s(elem!1), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[436, 408, 416])).
% 0.85/1.07 tff(1473,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 0.85/1.07 tff(1474,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 0.85/1.07 tff(1475,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[440, 68, 166, 1474, 1473])).
% 0.85/1.07 tff(1476,plain,(b(s(elem!1), s(z)) | (s(elem!1) = s(z)) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1477,plain,
% 0.85/1.07 (b(s(elem!1), s(z))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1476, 1472, 166])).
% 0.85/1.07 tff(1478,plain,
% 0.85/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1479,plain,
% 0.85/1.08 (((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1480,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1479])).
% 0.85/1.08 tff(1481,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1480, 1478])).
% 0.85/1.08 tff(1482,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1483,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.85/1.08 tff(1484,plain,
% 0.85/1.08 ($false),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1483, 224, 1391, 1241, 1477, 1471])).
% 0.85/1.08 tff(1485,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.08 tff(1486,plain,
% 0.85/1.08 (~r(s(elem!1), elem!1)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1485, 962, 1470, 987, 963])).
% 0.85/1.08 tff(1487,plain,
% 0.85/1.08 (b(s(elem!1), elem!1)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[939, 1486, 303])).
% 0.85/1.08 tff(1488,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 0.85/1.08 tff(1489,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1490,plain,
% 0.85/1.08 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1491,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1490])).
% 0.85/1.08 tff(1492,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.85/1.08 tff(1493,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1494,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.85/1.08 tff(1495,plain,
% 0.85/1.08 ($false),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1494, 224, 501, 1488, 1391, 390])).
% 0.85/1.08 tff(1496,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.08 tff(1497,plain,
% 0.85/1.08 (~b(elem!1, s(elem!1))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1496, 1487, 361, 962])).
% 0.85/1.08 tff(1498,plain,
% 0.85/1.08 (r(elem!1, s(elem!1))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[515, 1497, 327])).
% 0.85/1.08 tff(1499,plain,
% 0.85/1.08 (~b(s(elem!1), z)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[946, 224, 1487, 404, 340])).
% 0.85/1.08 tff(1500,plain,
% 0.85/1.08 (r(s(elem!1), z)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[498, 1499])).
% 0.85/1.08 tff(1501,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1502,plain,
% 0.85/1.08 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1503,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), 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), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1502])).
% 0.85/1.08 tff(1504,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), 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), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1503, 1501])).
% 0.85/1.08 tff(1505,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1506,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 0.85/1.08 tff(1507,plain,
% 0.85/1.08 (~r(s(elem!1), s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1506, 112, 1500, 177])).
% 0.85/1.08 tff(1508,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1509,plain,
% 0.85/1.08 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1510,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1509])).
% 0.85/1.08 tff(1511,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1510, 1508])).
% 0.85/1.08 tff(1512,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1513,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.85/1.08 tff(1514,plain,
% 0.85/1.08 (~r(s(elem!1), s(s(elem!1)))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1513, 112, 102, 1500])).
% 0.85/1.08 tff(1515,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.08 tff(1516,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.08 tff(1517,plain,
% 0.85/1.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1518,plain,
% 0.85/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1519,plain,
% 0.85/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 0.85/1.08 tff(1520,plain,
% 0.85/1.08 ($false),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1519, 68, 1516, 1515, 523])).
% 0.85/1.08 tff(1521,plain,(b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.08 tff(1522,plain,
% 0.85/1.08 (b(s(elem!1), s(s(elem!1)))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1521, 1514, 319])).
% 0.85/1.08 tff(1523,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1524,plain,
% 0.85/1.08 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1525,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1524])).
% 0.85/1.08 tff(1526,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1525, 1523])).
% 0.85/1.08 tff(1527,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1528,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.85/1.08 tff(1529,plain,
% 0.85/1.08 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1528, 224, 1487, 361, 295])).
% 0.85/1.08 tff(1530,plain,
% 0.85/1.08 (~b(s(elem!1), s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1529, 1522])).
% 0.85/1.08 tff(1531,plain,
% 0.85/1.08 (((~![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)))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1532,plain,
% 0.85/1.08 ((~![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)))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1533,plain,
% 0.85/1.08 ((~![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))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 0.85/1.08 tff(1534,plain,
% 0.85/1.08 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1533, 68])).
% 0.85/1.08 tff(1535,plain,
% 0.85/1.08 (s(elem!1) = s(s(s(z)))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1534, 1530, 1507])).
% 0.85/1.08 tff(1536,plain,
% 0.85/1.08 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1535])).
% 0.85/1.08 tff(1537,plain,
% 0.85/1.08 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 0.85/1.08 inference(symmetry,[status(thm)],[1536])).
% 0.85/1.08 tff(1538,plain,
% 0.85/1.08 (s(s(elem!1)) = s(s(s(s(z))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1535])).
% 0.85/1.08 tff(1539,plain,
% 0.85/1.08 (s(s(s(s(z)))) = s(s(elem!1))),
% 0.85/1.08 inference(symmetry,[status(thm)],[1538])).
% 0.85/1.08 tff(1540,plain,
% 0.85/1.08 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1539])).
% 0.85/1.08 tff(1541,plain,
% 0.85/1.08 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.85/1.08 inference(symmetry,[status(thm)],[1540])).
% 0.85/1.08 tff(1542,plain,
% 0.85/1.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[313, 1541])).
% 0.85/1.08 tff(1543,plain,
% 0.85/1.08 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1538])).
% 0.85/1.08 tff(1544,plain,
% 0.85/1.08 (b(s(s(s(s(z)))), s(z))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1470, 1543])).
% 0.85/1.08 tff(1545,plain,
% 0.85/1.08 (~r(s(s(elem!1)), s(z))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[895, 179, 102])).
% 0.85/1.08 tff(1546,plain,
% 0.85/1.08 (b(s(s(elem!1)), s(z))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[901, 1545])).
% 0.85/1.08 tff(1547,plain,
% 0.85/1.08 (~r(s(z), s(s(elem!1)))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[983, 112, 102, 179])).
% 0.85/1.08 tff(1548,plain,
% 0.85/1.08 (b(s(z), s(s(elem!1)))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[653, 1547])).
% 0.85/1.08 tff(1549,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1550,plain,
% 0.85/1.08 (((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1551,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1550])).
% 0.85/1.08 tff(1552,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1551, 1549])).
% 0.85/1.08 tff(1553,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1554,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 0.85/1.08 tff(1555,plain,
% 0.85/1.08 ($false),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1554, 224, 1390, 1548, 1546, 484])).
% 0.85/1.08 tff(1556,plain,((~r(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.08 tff(1557,plain,
% 0.85/1.08 (~r(s(z), z)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1556, 1522, 102, 963, 1500])).
% 0.85/1.08 tff(1558,plain,
% 0.85/1.08 (b(s(z), z)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[194, 1557])).
% 0.85/1.08 tff(1559,plain,
% 0.85/1.08 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1535])).
% 0.85/1.08 tff(1560,plain,
% 0.85/1.08 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 0.85/1.08 inference(symmetry,[status(thm)],[1559])).
% 0.85/1.08 tff(1561,plain,
% 0.85/1.08 (s(s(z)) = elem!1),
% 0.85/1.08 inference(transitivity,[status(thm)],[32, 1560, 121])).
% 0.85/1.08 tff(1562,plain,
% 0.85/1.08 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1561])).
% 0.85/1.08 tff(1563,plain,
% 0.85/1.08 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 0.85/1.08 inference(symmetry,[status(thm)],[1562])).
% 0.85/1.08 tff(1564,plain,
% 0.85/1.08 (~(elem!1 = s(s(s(z))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[348, 376])).
% 0.85/1.08 tff(1565,plain,
% 0.85/1.08 (~b(elem!1, s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[784, 1535, 1497])).
% 0.85/1.08 tff(1566,plain,
% 0.85/1.08 (r(elem!1, s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[388, 1565, 1564])).
% 0.85/1.08 tff(1567,plain,
% 0.85/1.08 (r(s(s(z)), s(s(s(z))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1566, 1563])).
% 0.85/1.08 tff(1568,plain,
% 0.85/1.08 (~r(s(z), s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[243, 1567, 77, 1558, 177])).
% 0.85/1.08 tff(1569,plain,
% 0.85/1.08 (b(s(z), s(s(s(z))))),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[175, 1568])).
% 0.85/1.08 tff(1570,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.85/1.08 tff(1571,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.85/1.08 tff(1572,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1573,plain,
% 0.85/1.08 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1574,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1573])).
% 0.85/1.08 tff(1575,plain,
% 0.85/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1574, 1572])).
% 0.85/1.08 tff(1576,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1577,plain,
% 0.85/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 0.85/1.09 tff(1578,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1577, 224, 1090, 560, 1571, 1570])).
% 0.85/1.09 tff(1579,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1580,plain,
% 0.85/1.09 (~b(s(s(s(z))), s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1579, 1569, 1544, 1542])).
% 0.85/1.09 tff(1581,plain,
% 0.85/1.09 (r(s(s(s(z))), s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[925, 1580])).
% 0.85/1.09 tff(1582,plain,
% 0.85/1.09 (r(s(elem!1), s(z))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1581, 1537])).
% 0.85/1.09 tff(1583,plain,
% 0.85/1.09 (elem!1 = s(s(z))),
% 0.85/1.09 inference(transitivity,[status(thm)],[155, 1559, 31])).
% 0.85/1.09 tff(1584,plain,
% 0.85/1.09 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1583])).
% 0.85/1.09 tff(1585,plain,
% 0.85/1.09 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1584])).
% 0.85/1.09 tff(1586,plain,
% 0.85/1.09 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1585])).
% 0.85/1.09 tff(1587,plain,
% 0.85/1.09 (b(elem!1, z) <=> b(s(s(z)), z)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1583])).
% 0.85/1.09 tff(1588,plain,
% 0.85/1.09 (b(s(s(z)), z)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[404, 1587])).
% 0.85/1.09 tff(1589,plain,
% 0.85/1.09 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1590,plain,
% 0.85/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1589])).
% 0.85/1.09 tff(1591,plain,
% 0.85/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1590, 225])).
% 0.85/1.09 tff(1592,plain,
% 0.85/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1593,plain,
% 0.85/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 0.85/1.09 tff(1594,plain,
% 0.85/1.09 (~b(s(s(z)), s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1593, 224, 77, 1558, 1588])).
% 0.85/1.09 tff(1595,plain,
% 0.85/1.09 (~b(elem!1, s(z))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1594, 1586])).
% 0.85/1.09 tff(1596,plain,
% 0.85/1.09 (r(elem!1, s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1277, 1595, 88])).
% 0.85/1.09 tff(1597,plain,
% 0.85/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1598,plain,
% 0.85/1.09 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1599,plain,
% 0.85/1.09 (((~![X0: $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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1598])).
% 0.85/1.09 tff(1600,plain,
% 0.85/1.09 (((~![X0: $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(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1599, 1597])).
% 0.85/1.09 tff(1601,plain,
% 0.85/1.09 ((~![X0: $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))))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1602,plain,
% 0.85/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.85/1.09 tff(1603,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1602, 112, 543, 993, 428])).
% 0.85/1.09 tff(1604,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1605,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1604, 1596, 1582, 1498])).
% 0.85/1.09 tff(1606,plain,(r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | r(z, elem!1) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1607,plain,
% 0.85/1.09 (r(s(s(elem!1)), elem!1)),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1606, 102, 77, 177, 88, 285, 3, 293, 74])).
% 0.85/1.09 tff(1608,plain,
% 0.85/1.09 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 0.85/1.09 inference(commutativity,[status(thm)],[])).
% 0.85/1.09 tff(1609,plain,
% 0.85/1.09 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1608])).
% 0.85/1.09 tff(1610,plain,
% 0.85/1.09 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1609])).
% 0.85/1.09 tff(1611,plain,
% 0.85/1.09 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1612,plain,
% 0.85/1.09 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1611])).
% 0.85/1.09 tff(1613,plain,
% 0.85/1.09 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1614,plain,
% 0.85/1.09 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1613, 40])).
% 0.85/1.09 tff(1615,plain,
% 0.85/1.09 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1614, 1612])).
% 0.85/1.09 tff(1616,plain,
% 0.85/1.09 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1615, 1610])).
% 0.85/1.09 tff(1617,plain,
% 0.85/1.09 (s(z) = s(elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1618,plain,
% 0.85/1.09 (s(elem!1) = s(z)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1617])).
% 0.85/1.09 tff(1619,plain,
% 0.85/1.09 (s(s(z)) = s(s(elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1617])).
% 0.85/1.09 tff(1620,plain,
% 0.85/1.09 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1619])).
% 0.85/1.09 tff(1621,plain,
% 0.85/1.09 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1620])).
% 0.85/1.09 tff(1622,plain,
% 0.85/1.09 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1621, 1618])).
% 0.85/1.09 tff(1623,plain,
% 0.85/1.09 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1622])).
% 0.85/1.09 tff(1624,plain,
% 0.85/1.09 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1620, 1617])).
% 0.85/1.09 tff(1625,plain,
% 0.85/1.09 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1624])).
% 0.85/1.09 tff(1626,plain,
% 0.85/1.09 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1625])).
% 0.85/1.09 tff(1627,plain,
% 0.85/1.09 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1620])).
% 0.85/1.09 tff(1628,plain,
% 0.85/1.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[968, 1627])).
% 0.85/1.09 tff(1629,plain,
% 0.85/1.09 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1630,plain,
% 0.85/1.09 (r(elem!1, s(s(s(z))))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[689, 1629])).
% 0.85/1.09 tff(1631,plain,
% 0.85/1.09 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1632,plain,
% 0.85/1.09 (r(s(s(s(z))), elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[177, 1631])).
% 0.85/1.09 tff(1633,plain,
% 0.85/1.09 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1617])).
% 0.85/1.09 tff(1634,plain,
% 0.85/1.09 (b(z, s(z)) <=> b(elem!1, s(z))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1635,plain,
% 0.85/1.09 (b(elem!1, s(z))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[77, 1634])).
% 0.85/1.09 tff(1636,plain,
% 0.85/1.09 (b(elem!1, s(elem!1))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1635, 1633])).
% 0.85/1.09 tff(1637,plain,
% 0.85/1.09 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1638,plain,
% 0.85/1.09 (r(elem!1, s(s(elem!1)))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[293, 1637])).
% 0.85/1.09 tff(1639,plain,
% 0.85/1.09 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1619])).
% 0.85/1.09 tff(1640,plain,
% 0.85/1.09 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1639])).
% 0.85/1.09 tff(1641,plain,
% 0.85/1.09 (r(s(s(z)), elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1181, 1640])).
% 0.85/1.09 tff(1642,plain,
% 0.85/1.09 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1617])).
% 0.85/1.09 tff(1643,plain,
% 0.85/1.09 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1642])).
% 0.85/1.09 tff(1644,plain,
% 0.85/1.09 (r(s(z), elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[408, 1643])).
% 0.85/1.09 tff(1645,plain,
% 0.85/1.09 (r(s(z), z) <=> r(s(z), elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1646,plain,
% 0.85/1.09 (r(s(z), elem!1) <=> r(s(z), z)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1645])).
% 0.85/1.09 tff(1647,plain,
% 0.85/1.09 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 0.85/1.09 inference(transitivity,[status(thm)],[1643, 1646])).
% 0.85/1.09 tff(1648,plain,
% 0.85/1.09 (r(s(z), z)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[408, 1647])).
% 0.85/1.09 tff(1649,plain,
% 0.85/1.09 (~r(s(z), s(s(s(z))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[187, 1648, 177])).
% 0.85/1.09 tff(1650,plain,
% 0.85/1.09 (b(s(z), s(s(s(z))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[175, 1649])).
% 0.85/1.09 tff(1651,plain,
% 0.85/1.09 (~b(s(s(s(z))), s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1106, 1650, 77, 689, 1047, 1644])).
% 0.85/1.09 tff(1652,plain,
% 0.85/1.09 (r(s(s(s(z))), s(z))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[925, 1651])).
% 0.85/1.09 tff(1653,plain,
% 0.85/1.09 (r(s(s(s(elem!1))), s(elem!1))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1652, 1623])).
% 0.85/1.09 tff(1654,plain,
% 0.85/1.09 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1621])).
% 0.85/1.09 tff(1655,plain,
% 0.85/1.09 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1654])).
% 0.85/1.09 tff(1656,plain,
% 0.85/1.09 (r(s(s(s(elem!1))), elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1632, 1655])).
% 0.85/1.09 tff(1657,plain,
% 0.85/1.09 (((~![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(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1658,plain,
% 0.85/1.09 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1659,plain,
% 0.85/1.09 (((~![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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1658])).
% 0.85/1.09 tff(1660,plain,
% 0.85/1.09 (((~![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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.85/1.09 tff(1661,plain,
% 0.85/1.09 ((~![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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1662,plain,
% 0.85/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.85/1.09 tff(1663,plain,
% 0.85/1.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1662, 112, 408, 1656])).
% 0.85/1.09 tff(1664,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1663, 1653])).
% 0.85/1.09 tff(1665,plain,((~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1666,plain,
% 0.85/1.09 (~r(s(elem!1), elem!1)),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1665, 335, 77, 689, 1641, 177])).
% 0.85/1.09 tff(1667,plain,
% 0.85/1.09 (b(s(elem!1), elem!1)),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[939, 1666, 324])).
% 0.85/1.09 tff(1668,plain,
% 0.85/1.09 (elem!1 = z),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[338, 335])).
% 0.85/1.09 tff(1669,plain,
% 0.85/1.09 (z = elem!1),
% 0.85/1.09 inference(symmetry,[status(thm)],[7])).
% 0.85/1.09 tff(1670,plain,
% 0.85/1.09 (s(z) = s(elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1669])).
% 0.85/1.09 tff(1671,plain,
% 0.85/1.09 (s(elem!1) = s(z)),
% 0.85/1.09 inference(symmetry,[status(thm)],[1670])).
% 0.85/1.09 tff(1672,plain,
% 0.85/1.09 (s(s(elem!1)) = s(s(z))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1671])).
% 0.85/1.09 tff(1673,plain,
% 0.85/1.09 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1672])).
% 0.85/1.09 tff(1674,plain,
% 0.85/1.09 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1673])).
% 0.85/1.09 tff(1675,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.09 tff(1676,plain,
% 0.85/1.09 (s(z) = s(s(s(s(z))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1670, 1675, 1674])).
% 0.85/1.09 tff(1677,plain,
% 0.85/1.09 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1676])).
% 0.85/1.09 tff(1678,plain,
% 0.85/1.09 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1677])).
% 0.85/1.09 tff(1679,plain,
% 0.85/1.09 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1223])).
% 0.85/1.09 tff(1680,plain,
% 0.85/1.09 (s(s(s(z))) = z),
% 0.85/1.09 inference(transitivity,[status(thm)],[1679, 1678, 27])).
% 0.85/1.09 tff(1681,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[58, 1680])).
% 0.85/1.09 tff(1682,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1683,plain,
% 0.85/1.09 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1682, 1668])).
% 0.85/1.09 tff(1684,plain,
% 0.85/1.09 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1384])).
% 0.85/1.09 tff(1685,plain,
% 0.85/1.09 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1619, 1684])).
% 0.85/1.09 tff(1686,plain,
% 0.85/1.09 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(commutativity,[status(thm)],[])).
% 0.85/1.09 tff(1687,plain,
% 0.85/1.09 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1620])).
% 0.85/1.09 tff(1688,plain,
% 0.85/1.09 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1687])).
% 0.85/1.09 tff(1689,plain,
% 0.85/1.09 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1688, 1686])).
% 0.85/1.09 tff(1690,plain,
% 0.85/1.09 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(elem!1))))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1689])).
% 0.85/1.09 tff(1691,plain,
% 0.85/1.09 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1229, 1690])).
% 0.85/1.09 tff(1692,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1691, 1685])).
% 0.85/1.09 tff(1693,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1694,plain,
% 0.85/1.09 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1693, 335])).
% 0.85/1.09 tff(1695,plain,
% 0.85/1.09 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1621])).
% 0.85/1.09 tff(1696,plain,
% 0.85/1.09 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1695])).
% 0.85/1.09 tff(1697,plain,
% 0.85/1.09 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[152, 1696])).
% 0.85/1.09 tff(1698,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.09 tff(1699,plain,
% 0.85/1.09 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1620])).
% 0.85/1.09 tff(1700,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.85/1.09 tff(1701,plain,
% 0.85/1.09 (elem!1 = z),
% 0.85/1.09 inference(symmetry,[status(thm)],[335])).
% 0.85/1.09 tff(1702,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))), introduced(assumption)).
% 0.85/1.09 tff(1703,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1702])).
% 0.85/1.09 tff(1704,plain,
% 0.85/1.09 ((~![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)))))))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1705,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1704, 25])).
% 0.85/1.09 tff(1706,plain,
% 0.85/1.09 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1705])).
% 0.85/1.09 tff(1707,plain,
% 0.85/1.09 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 0.85/1.09 inference(transitivity,[status(thm)],[1706, 1703, 123])).
% 0.85/1.09 tff(1708,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1707])).
% 0.85/1.09 tff(1709,plain,
% 0.85/1.09 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[292])).
% 0.85/1.09 tff(1710,plain,
% 0.85/1.09 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1687])).
% 0.85/1.09 tff(1711,plain,
% 0.85/1.09 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1710])).
% 0.85/1.09 tff(1712,plain,
% 0.85/1.09 (s(s(s(s(s(elem!1))))) = z),
% 0.85/1.09 inference(transitivity,[status(thm)],[1711, 1709, 1708, 121, 1701])).
% 0.85/1.09 tff(1713,plain,
% 0.85/1.09 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1714,plain,
% 0.85/1.09 (~(s(s(s(s(s(elem!1))))) = z)),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1713, 40])).
% 0.85/1.09 tff(1715,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1714, 1712])).
% 0.85/1.09 tff(1716,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1717,plain,
% 0.85/1.09 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1716, 335])).
% 0.85/1.09 tff(1718,plain,
% 0.85/1.09 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1711])).
% 0.85/1.09 tff(1719,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.85/1.09 tff(1720,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(elem!1))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1719])).
% 0.85/1.09 tff(1721,plain,
% 0.85/1.09 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 0.85/1.09 inference(transitivity,[status(thm)],[1706, 1720, 1156])).
% 0.85/1.09 tff(1722,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1721])).
% 0.85/1.09 tff(1723,plain,
% 0.85/1.09 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1722])).
% 0.85/1.09 tff(1724,plain,
% 0.85/1.09 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(transitivity,[status(thm)],[164, 1723, 292, 1718])).
% 0.85/1.09 tff(1725,plain,
% 0.85/1.09 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1724])).
% 0.85/1.09 tff(1726,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1725])).
% 0.85/1.09 tff(1727,plain,
% 0.85/1.09 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.85/1.09 inference(quant_inst,[status(thm)],[])).
% 0.85/1.09 tff(1728,plain,
% 0.85/1.09 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1727, 25])).
% 0.85/1.09 tff(1729,plain,
% 0.85/1.09 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.85/1.09 inference(symmetry,[status(thm)],[1728])).
% 0.85/1.09 tff(1730,plain,
% 0.85/1.09 (s(s(s(s(elem!1)))) = elem!1),
% 0.85/1.09 inference(transitivity,[status(thm)],[1729, 1726, 121])).
% 0.85/1.09 tff(1731,plain,
% 0.85/1.09 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.85/1.09 inference(monotonicity,[status(thm)],[335])).
% 0.85/1.09 tff(1732,plain,
% 0.85/1.09 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1731])).
% 0.85/1.09 tff(1733,plain,
% 0.85/1.09 (~(s(s(s(s(elem!1)))) = elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[1334, 1732])).
% 0.85/1.09 tff(1734,plain,
% 0.85/1.09 ($false),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1733, 1730])).
% 0.85/1.09 tff(1735,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.09 tff(1736,plain,
% 0.85/1.09 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 0.85/1.09 inference(unit_resolution,[status(thm)],[1735, 335])).
% 0.85/1.09 tff(1737,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.09 tff(1738,plain,
% 0.85/1.09 (r(s(s(s(elem!1))), elem!1)),
% 0.85/1.09 inference(modus_ponens,[status(thm)],[690, 1655])).
% 0.85/1.09 tff(1739,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.85/1.09 tff(1740,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 0.85/1.09 tff(1741,plain,
% 0.85/1.09 (((~![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(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~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(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1742,plain,
% 0.85/1.09 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.09 inference(rewrite,[status(thm)],[])).
% 0.85/1.09 tff(1743,plain,
% 0.85/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(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(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 0.85/1.09 inference(monotonicity,[status(thm)],[1742])).
% 0.85/1.09 tff(1744,plain,
% 0.85/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(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(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1743, 1741])).
% 0.85/1.10 tff(1745,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1746,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 0.85/1.10 tff(1747,plain,
% 0.85/1.10 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1746, 112, 1740, 1739])).
% 0.85/1.10 tff(1748,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.10 tff(1749,plain,
% 0.85/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1750,plain,
% 0.85/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1751,plain,
% 0.85/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 0.85/1.10 tff(1752,plain,
% 0.85/1.10 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1751, 68, 1748, 1747])).
% 0.85/1.10 tff(1753,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(s(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(s(elem!1)))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1754,plain,
% 0.85/1.10 (((~r(s(s(elem!1)), elem!1)) | (~r(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(z))))))), s(s(elem!1))))) <=> ((~r(s(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(s(elem!1)))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1755,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(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(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(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1754])).
% 0.85/1.10 tff(1756,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(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(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(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1755, 1753])).
% 0.85/1.10 tff(1757,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(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(z))))))), s(s(elem!1)))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1758,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 0.85/1.10 tff(1759,plain,
% 0.85/1.10 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1758, 112, 1181, 1740])).
% 0.85/1.10 tff(1760,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), introduced(assumption)).
% 0.85/1.10 tff(1761,plain,
% 0.85/1.10 (((~![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))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1762,plain,
% 0.85/1.10 ((~![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))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1763,plain,
% 0.85/1.10 ((~![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)))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.85/1.10 tff(1764,plain,
% 0.85/1.10 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1763, 68, 1760, 1759])).
% 0.85/1.10 tff(1765,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1766,plain,
% 0.85/1.10 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1767,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1766])).
% 0.85/1.10 tff(1768,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1767, 1765])).
% 0.85/1.10 tff(1769,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1770,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 0.85/1.10 tff(1771,plain,
% 0.85/1.10 ($false),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1770, 224, 1698, 1737, 1764, 1752])).
% 0.85/1.10 tff(1772,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.10 tff(1773,plain,
% 0.85/1.10 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1772, 1738, 1737, 1736, 1717, 1698, 1181])).
% 0.85/1.10 tff(1774,plain,
% 0.85/1.10 (((~![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))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1775,plain,
% 0.85/1.10 ((~![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))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1776,plain,
% 0.85/1.10 ((~![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)),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 0.85/1.10 tff(1777,plain,
% 0.85/1.10 ((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)),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1776, 68])).
% 0.85/1.10 tff(1778,plain,
% 0.85/1.10 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1777, 1773, 1615])).
% 0.85/1.10 tff(1779,plain,
% 0.85/1.10 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(symmetry,[status(thm)],[1403])).
% 0.85/1.10 tff(1780,plain,
% 0.85/1.10 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1731, 1779])).
% 0.85/1.10 tff(1781,plain,
% 0.85/1.10 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1780])).
% 0.85/1.10 tff(1782,plain,
% 0.85/1.10 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1334, 1781])).
% 0.85/1.10 tff(1783,plain,
% 0.85/1.10 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1621])).
% 0.85/1.10 tff(1784,plain,
% 0.85/1.10 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.85/1.10 inference(symmetry,[status(thm)],[1783])).
% 0.85/1.10 tff(1785,plain,
% 0.85/1.10 (r(elem!1, s(s(s(elem!1))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1020, 1784])).
% 0.85/1.10 tff(1786,plain,
% 0.85/1.10 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1620])).
% 0.85/1.10 tff(1787,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 0.85/1.10 tff(1788,plain,
% 0.85/1.10 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 0.85/1.10 tff(1789,plain,
% 0.85/1.10 (((~![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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1790,plain,
% 0.85/1.10 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1791,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1790])).
% 0.85/1.10 tff(1792,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1791, 1789])).
% 0.85/1.10 tff(1793,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1794,plain,
% 0.85/1.10 ((~![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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 0.85/1.10 tff(1795,plain,
% 0.85/1.10 ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1794, 112, 1788])).
% 0.85/1.10 tff(1796,plain,
% 0.85/1.10 (~r(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1795, 1785])).
% 0.85/1.10 tff(1797,plain,
% 0.85/1.10 (b(elem!1, s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1439, 1796, 1782])).
% 0.85/1.10 tff(1798,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 0.85/1.10 tff(1799,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1800,plain,
% 0.85/1.10 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1801,plain,
% 0.85/1.10 (((~![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(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1800])).
% 0.85/1.10 tff(1802,plain,
% 0.85/1.10 (((~![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(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1801, 1799])).
% 0.85/1.10 tff(1803,plain,
% 0.85/1.10 ((~![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(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1804,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 0.85/1.10 tff(1805,plain,
% 0.85/1.10 ($false),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1804, 112, 1798, 1020, 1787])).
% 0.85/1.10 tff(1806,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.10 tff(1807,plain,
% 0.85/1.10 (~r(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1806, 1787, 1020])).
% 0.85/1.10 tff(1808,plain,
% 0.85/1.10 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1294, 1807, 1733])).
% 0.85/1.10 tff(1809,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1810,plain,
% 0.85/1.10 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1811,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1810])).
% 0.85/1.10 tff(1812,plain,
% 0.85/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1811, 1809])).
% 0.85/1.10 tff(1813,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1814,plain,
% 0.85/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 0.85/1.10 tff(1815,plain,
% 0.85/1.10 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1814, 224, 1808, 1797, 1778])).
% 0.85/1.10 tff(1816,plain,
% 0.85/1.10 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1687])).
% 0.85/1.10 tff(1817,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.85/1.10 tff(1818,plain,
% 0.85/1.10 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1817])).
% 0.85/1.10 tff(1819,plain,
% 0.85/1.10 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.85/1.10 inference(symmetry,[status(thm)],[1818])).
% 0.85/1.10 tff(1820,plain,
% 0.85/1.10 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1153, 1819, 1705])).
% 0.85/1.10 tff(1821,plain,
% 0.85/1.10 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1820])).
% 0.85/1.10 tff(1822,plain,
% 0.85/1.10 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(transitivity,[status(thm)],[1376, 1821, 292, 1816])).
% 0.85/1.10 tff(1823,plain,
% 0.85/1.10 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.85/1.10 inference(monotonicity,[status(thm)],[1822])).
% 0.85/1.10 tff(1824,plain,
% 0.85/1.10 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 0.85/1.10 inference(symmetry,[status(thm)],[1823])).
% 0.85/1.10 tff(1825,plain,
% 0.85/1.10 (s(s(s(s(elem!1)))) = s(elem!1)),
% 0.85/1.10 inference(transitivity,[status(thm)],[1729, 1824, 123])).
% 0.85/1.10 tff(1826,plain,
% 0.85/1.10 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(symmetry,[status(thm)],[1143])).
% 0.85/1.10 tff(1827,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 0.85/1.10 tff(1828,plain,
% 0.85/1.10 (s(elem!1) = s(s(s(s(elem!1))))),
% 0.85/1.10 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 0.85/1.10 tff(1829,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.85/1.10 tff(1830,plain,
% 0.85/1.10 ($false),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1829, 1828])).
% 0.85/1.10 tff(1831,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.10 tff(1832,plain,
% 0.85/1.10 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1831, 1683])).
% 0.85/1.10 tff(1833,plain,
% 0.85/1.10 ($false),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1832, 1825])).
% 0.85/1.10 tff(1834,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.10 tff(1835,plain,
% 0.85/1.10 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))),
% 0.85/1.10 inference(unit_resolution,[status(thm)],[1834, 335])).
% 0.85/1.10 tff(1836,plain,
% 0.85/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 0.85/1.10 inference(rewrite,[status(thm)],[])).
% 0.85/1.10 tff(1837,plain,
% 0.85/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 0.85/1.10 inference(quant_inst,[status(thm)],[])).
% 0.85/1.10 tff(1838,plain,
% 0.85/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 0.85/1.11 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 0.85/1.11 tff(1839,plain,
% 0.85/1.11 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 1815])).
% 0.85/1.11 tff(1840,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.11 inference(rewrite,[status(thm)],[])).
% 0.85/1.11 tff(1841,plain,
% 0.85/1.11 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(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(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.11 inference(rewrite,[status(thm)],[])).
% 0.85/1.11 tff(1842,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 0.85/1.11 inference(monotonicity,[status(thm)],[1841])).
% 0.85/1.11 tff(1843,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.11 inference(transitivity,[status(thm)],[1842, 1840])).
% 0.85/1.11 tff(1844,plain,
% 0.85/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 0.85/1.11 inference(quant_inst,[status(thm)],[])).
% 0.85/1.11 tff(1845,plain,
% 0.85/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 0.85/1.11 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 0.85/1.11 tff(1846,plain,
% 0.85/1.11 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1845, 224, 501, 1488, 1778])).
% 0.85/1.11 tff(1847,assumption,(s(s(s(s(s(s(s(z))))))) = s(elem!1)), introduced(assumption)).
% 0.85/1.11 tff(1848,plain,
% 0.85/1.11 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 0.85/1.11 inference(monotonicity,[status(thm)],[1847])).
% 0.85/1.11 tff(1849,plain,
% 0.85/1.11 (s(s(s(s(s(s(z)))))) = z),
% 0.85/1.11 inference(transitivity,[status(thm)],[1706, 1848, 121, 1701])).
% 0.85/1.11 tff(1850,plain,
% 0.85/1.11 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.85/1.11 inference(quant_inst,[status(thm)],[])).
% 0.85/1.11 tff(1851,plain,
% 0.85/1.11 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1850, 40])).
% 0.85/1.11 tff(1852,plain,
% 0.85/1.11 ($false),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1851, 1849])).
% 0.85/1.11 tff(1853,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.11 tff(1854,plain,
% 0.85/1.11 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1853, 335])).
% 0.85/1.11 tff(1855,plain,
% 0.85/1.11 (((~![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)))),
% 0.85/1.11 inference(rewrite,[status(thm)],[])).
% 0.85/1.11 tff(1856,plain,
% 0.85/1.11 ((~![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)))),
% 0.85/1.11 inference(quant_inst,[status(thm)],[])).
% 0.85/1.11 tff(1857,plain,
% 0.85/1.11 ((~![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))),
% 0.85/1.11 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 0.85/1.11 tff(1858,plain,
% 0.85/1.11 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1857, 68, 1854, 1846])).
% 0.85/1.11 tff(1859,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.11 inference(rewrite,[status(thm)],[])).
% 0.85/1.11 tff(1860,plain,
% 0.85/1.11 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.11 inference(rewrite,[status(thm)],[])).
% 0.85/1.11 tff(1861,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 0.85/1.11 inference(monotonicity,[status(thm)],[1860])).
% 0.85/1.11 tff(1862,plain,
% 0.85/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.85/1.11 inference(transitivity,[status(thm)],[1861, 1859])).
% 0.85/1.11 tff(1863,plain,
% 0.85/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 0.85/1.11 inference(quant_inst,[status(thm)],[])).
% 0.85/1.11 tff(1864,plain,
% 0.85/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 0.85/1.11 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 0.85/1.11 tff(1865,plain,
% 0.85/1.11 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 0.85/1.11 inference(unit_resolution,[status(thm)],[1864, 224, 1488, 1808, 1797])).
% 0.85/1.11 tff(1866,plain,
% 0.85/1.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1867,plain,
% 0.95/1.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 0.95/1.11 inference(quant_inst,[status(thm)],[])).
% 0.95/1.11 tff(1868,plain,
% 0.95/1.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 0.95/1.11 tff(1869,plain,
% 0.95/1.11 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1868, 68])).
% 0.95/1.11 tff(1870,plain,
% 0.95/1.11 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1869, 1865, 1683])).
% 0.95/1.11 tff(1871,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1872,plain,
% 0.95/1.11 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1873,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 0.95/1.11 inference(monotonicity,[status(thm)],[1872])).
% 0.95/1.11 tff(1874,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.11 inference(transitivity,[status(thm)],[1873, 1871])).
% 0.95/1.11 tff(1875,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.11 inference(quant_inst,[status(thm)],[])).
% 0.95/1.11 tff(1876,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 0.95/1.11 tff(1877,plain,
% 0.95/1.11 ($false),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1876, 112, 1700, 1870, 1858, 1839])).
% 0.95/1.11 tff(1878,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.11 tff(1879,plain,
% 0.95/1.11 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1878, 1697, 501, 1488, 1700, 1698, 1181, 690, 335, 1020])).
% 0.95/1.11 tff(1880,plain,
% 0.95/1.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1881,plain,
% 0.95/1.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 0.95/1.11 inference(quant_inst,[status(thm)],[])).
% 0.95/1.11 tff(1882,plain,
% 0.95/1.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 0.95/1.11 tff(1883,plain,
% 0.95/1.11 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1882, 68])).
% 0.95/1.11 tff(1884,plain,
% 0.95/1.11 (b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1883, 1164])).
% 0.95/1.11 tff(1885,plain,
% 0.95/1.11 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1884, 1879])).
% 0.95/1.11 tff(1886,plain,
% 0.95/1.11 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1885, 1699])).
% 0.95/1.11 tff(1887,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1888,plain,
% 0.95/1.11 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1889,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.95/1.11 inference(monotonicity,[status(thm)],[1888])).
% 0.95/1.11 tff(1890,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.11 inference(transitivity,[status(thm)],[1889, 1887])).
% 0.95/1.11 tff(1891,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.95/1.11 inference(quant_inst,[status(thm)],[])).
% 0.95/1.11 tff(1892,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.95/1.11 tff(1893,plain,
% 0.95/1.11 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1892, 224, 1886, 1698, 1697])).
% 0.95/1.11 tff(1894,plain,
% 0.95/1.11 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1401, 68, 1893, 1694])).
% 0.95/1.11 tff(1895,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1896,plain,
% 0.95/1.11 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.11 inference(rewrite,[status(thm)],[])).
% 0.95/1.11 tff(1897,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.95/1.11 inference(monotonicity,[status(thm)],[1896])).
% 0.95/1.11 tff(1898,plain,
% 0.95/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.11 inference(transitivity,[status(thm)],[1897, 1895])).
% 0.95/1.11 tff(1899,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 0.95/1.11 inference(quant_inst,[status(thm)],[])).
% 0.95/1.11 tff(1900,plain,
% 0.95/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.95/1.11 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 0.95/1.11 tff(1901,plain,
% 0.95/1.11 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1900, 112, 1700, 1894])).
% 0.95/1.11 tff(1902,plain,
% 0.95/1.11 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 0.95/1.11 inference(unit_resolution,[status(thm)],[1869, 1901, 1683])).
% 0.95/1.11 tff(1903,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, 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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1904,plain,
% 0.95/1.12 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1905,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1904])).
% 0.95/1.12 tff(1906,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.95/1.12 tff(1907,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1908,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.95/1.12 tff(1909,plain,
% 0.95/1.12 (~r(elem!1, s(s(s(s(elem!1)))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1908, 112, 545, 1894])).
% 0.95/1.12 tff(1910,plain,
% 0.95/1.12 (b(elem!1, s(s(s(s(elem!1)))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1439, 1909, 1782])).
% 0.95/1.12 tff(1911,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1912,plain,
% 0.95/1.12 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1913,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1912])).
% 0.95/1.12 tff(1914,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1913, 1911])).
% 0.95/1.12 tff(1915,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1916,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 0.95/1.12 tff(1917,plain,
% 0.95/1.12 (~r(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1916, 112, 545, 1894])).
% 0.95/1.12 tff(1918,plain,
% 0.95/1.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1294, 1917, 1733])).
% 0.95/1.12 tff(1919,plain,
% 0.95/1.12 ($false),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1864, 224, 1488, 1918, 1910, 1902])).
% 0.95/1.12 tff(1920,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.12 tff(1921,plain,
% 0.95/1.12 (~r(s(elem!1), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1920, 1667, 1638, 1628, 335, 1636, 1181, 1632, 1630, 152])).
% 0.95/1.12 tff(1922,plain,
% 0.95/1.12 (b(s(elem!1), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1521, 1921, 523])).
% 0.95/1.12 tff(1923,plain,
% 0.95/1.12 (~(s(s(elem!1)) = s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[525, 523])).
% 0.95/1.12 tff(1924,plain,
% 0.95/1.12 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1772, 1738, 1697, 1736, 1717, 1698, 1181])).
% 0.95/1.12 tff(1925,plain,
% 0.95/1.12 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1777, 1924, 1615])).
% 0.95/1.12 tff(1926,plain,
% 0.95/1.12 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1617])).
% 0.95/1.12 tff(1927,plain,
% 0.95/1.12 (b(s(z), z) <=> b(s(z), elem!1)),
% 0.95/1.12 inference(monotonicity,[status(thm)],[335])).
% 0.95/1.12 tff(1928,plain,
% 0.95/1.12 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 0.95/1.12 inference(transitivity,[status(thm)],[1927, 1926])).
% 0.95/1.12 tff(1929,plain,
% 0.95/1.12 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1617])).
% 0.95/1.12 tff(1930,plain,
% 0.95/1.12 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 0.95/1.12 inference(symmetry,[status(thm)],[1929])).
% 0.95/1.12 tff(1931,plain,
% 0.95/1.12 (r(s(s(elem!1)), s(z))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[544, 1930])).
% 0.95/1.12 tff(1932,plain,
% 0.95/1.12 (~r(s(z), z)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[895, 1931, 102])).
% 0.95/1.12 tff(1933,plain,
% 0.95/1.12 (b(s(z), z)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[194, 1932])).
% 0.95/1.12 tff(1934,plain,
% 0.95/1.12 (b(s(elem!1), elem!1)),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1933, 1928])).
% 0.95/1.12 tff(1935,plain,
% 0.95/1.12 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1845, 224, 501, 1934, 1925])).
% 0.95/1.12 tff(1936,plain,
% 0.95/1.12 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1857, 68, 1854, 1935])).
% 0.95/1.12 tff(1937,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1938,plain,
% 0.95/1.12 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1939,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1938])).
% 0.95/1.12 tff(1940,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1939, 1937])).
% 0.95/1.12 tff(1941,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1942,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 0.95/1.12 tff(1943,plain,
% 0.95/1.12 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1942, 112, 1181, 544, 1936])).
% 0.95/1.12 tff(1944,plain,
% 0.95/1.12 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 1943])).
% 0.95/1.12 tff(1945,plain,
% 0.95/1.12 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1770, 224, 1698, 1697, 1944])).
% 0.95/1.12 tff(1946,plain,
% 0.95/1.12 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 1945])).
% 0.95/1.12 tff(1947,plain,
% 0.95/1.12 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1621])).
% 0.95/1.12 tff(1948,plain,
% 0.95/1.12 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 0.95/1.12 inference(symmetry,[status(thm)],[1947])).
% 0.95/1.12 tff(1949,plain,
% 0.95/1.12 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1617])).
% 0.95/1.12 tff(1950,plain,
% 0.95/1.12 ((~(s(z) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1949])).
% 0.95/1.12 tff(1951,plain,
% 0.95/1.12 (~(s(elem!1) = s(s(s(z))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[45, 1950])).
% 0.95/1.12 tff(1952,plain,
% 0.95/1.12 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1621])).
% 0.95/1.12 tff(1953,plain,
% 0.95/1.12 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1952])).
% 0.95/1.12 tff(1954,plain,
% 0.95/1.12 (~r(s(elem!1), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1920, 1934, 545, 1698, 335, 501, 1181, 690, 1020, 152])).
% 0.95/1.12 tff(1955,plain,
% 0.95/1.12 (b(s(elem!1), s(s(elem!1)))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1521, 1954, 523])).
% 0.95/1.12 tff(1956,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1957,plain,
% 0.95/1.12 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1958,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1957])).
% 0.95/1.12 tff(1959,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1958, 1956])).
% 0.95/1.12 tff(1960,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1961,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 0.95/1.12 tff(1962,plain,
% 0.95/1.12 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1961, 224, 1955, 1698, 1697])).
% 0.95/1.12 tff(1963,plain,
% 0.95/1.12 (~b(s(elem!1), s(s(s(z))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1962, 1953])).
% 0.95/1.12 tff(1964,plain,
% 0.95/1.12 (r(s(elem!1), s(s(s(z))))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1534, 1963, 1951])).
% 0.95/1.12 tff(1965,plain,
% 0.95/1.12 (r(s(elem!1), s(s(s(elem!1))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1964, 1948])).
% 0.95/1.12 tff(1966,plain,
% 0.95/1.12 (((~![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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1967,plain,
% 0.95/1.12 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1968,plain,
% 0.95/1.12 (((~![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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(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), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1967])).
% 0.95/1.12 tff(1969,plain,
% 0.95/1.12 (((~![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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(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), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1968, 1966])).
% 0.95/1.12 tff(1970,plain,
% 0.95/1.12 ((~![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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1971,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 0.95/1.12 tff(1972,plain,
% 0.95/1.12 ($false),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1971, 112, 1936, 1965, 1946])).
% 0.95/1.12 tff(1973,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.12 tff(1974,plain,
% 0.95/1.12 (~r(s(s(elem!1)), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1973, 1628, 335, 1181, 1636, 1632, 152, 523, 1638, 1630, 102])).
% 0.95/1.12 tff(1975,plain,
% 0.95/1.12 (b(s(s(elem!1)), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[530, 1974, 1923])).
% 0.95/1.12 tff(1976,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1977,plain,
% 0.95/1.12 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1978,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1977])).
% 0.95/1.12 tff(1979,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.12 inference(transitivity,[status(thm)],[1978, 1976])).
% 0.95/1.12 tff(1980,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.95/1.12 inference(quant_inst,[status(thm)],[])).
% 0.95/1.12 tff(1981,plain,
% 0.95/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 0.95/1.12 tff(1982,plain,
% 0.95/1.12 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1981, 224, 1975, 1922, 1628])).
% 0.95/1.12 tff(1983,plain,
% 0.95/1.12 (~b(s(s(s(z))), s(z))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1982, 1626])).
% 0.95/1.12 tff(1984,plain,
% 0.95/1.12 (r(s(s(s(z))), s(z))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[925, 1983])).
% 0.95/1.12 tff(1985,plain,
% 0.95/1.12 (r(s(s(s(elem!1))), s(elem!1))),
% 0.95/1.12 inference(modus_ponens,[status(thm)],[1984, 1623])).
% 0.95/1.12 tff(1986,plain,
% 0.95/1.12 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1772, 1656, 1697, 1736, 1717, 1628, 1181])).
% 0.95/1.12 tff(1987,plain,
% 0.95/1.12 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1777, 1986, 1615])).
% 0.95/1.12 tff(1988,plain,
% 0.95/1.12 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1845, 224, 1636, 1667, 1987])).
% 0.95/1.12 tff(1989,plain,
% 0.95/1.12 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 0.95/1.12 inference(unit_resolution,[status(thm)],[1857, 68, 1854, 1988])).
% 0.95/1.12 tff(1990,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1991,plain,
% 0.95/1.12 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.12 inference(rewrite,[status(thm)],[])).
% 0.95/1.12 tff(1992,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 0.95/1.12 inference(monotonicity,[status(thm)],[1991])).
% 0.95/1.12 tff(1993,plain,
% 0.95/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[1992, 1990])).
% 0.95/1.13 tff(1994,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(1995,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 0.95/1.13 tff(1996,plain,
% 0.95/1.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1995, 112, 1989, 1985])).
% 0.95/1.13 tff(1997,plain,
% 0.95/1.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 1996])).
% 0.95/1.13 tff(1998,plain,
% 0.95/1.13 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(1999,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[1998])).
% 0.95/1.13 tff(2000,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[1999, 1765])).
% 0.95/1.13 tff(2001,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(elem!1))))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2002,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 0.95/1.13 tff(2003,plain,
% 0.95/1.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2002, 224, 1628, 1697, 1997])).
% 0.95/1.13 tff(2004,plain,
% 0.95/1.13 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 2003])).
% 0.95/1.13 tff(2005,plain,
% 0.95/1.13 (((~![X0: $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(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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2006,plain,
% 0.95/1.13 (((~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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2007,plain,
% 0.95/1.13 (((~![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(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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[2006])).
% 0.95/1.13 tff(2008,plain,
% 0.95/1.13 (((~![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(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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[2007, 2005])).
% 0.95/1.13 tff(2009,plain,
% 0.95/1.13 ((~![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(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))))))))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2010,plain,
% 0.95/1.13 ((~![X0: $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(s(s(s(s(s(s(z)))))))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.95/1.13 tff(2011,plain,
% 0.95/1.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2010, 112, 1638, 2004])).
% 0.95/1.13 tff(2012,plain,
% 0.95/1.13 (((~![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)))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2013,plain,
% 0.95/1.13 ((~![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)))))))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2014,plain,
% 0.95/1.13 ((~![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))))))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.95/1.13 tff(2015,plain,
% 0.95/1.13 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2014, 68, 2011])).
% 0.95/1.13 tff(2016,plain,
% 0.95/1.13 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2015, 1616])).
% 0.95/1.13 tff(2017,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2018,plain,
% 0.95/1.13 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2019,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[2018])).
% 0.95/1.13 tff(2020,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[2019, 2017])).
% 0.95/1.13 tff(2021,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2022,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 0.95/1.13 tff(2023,plain,
% 0.95/1.13 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2022, 112, 1798, 1181])).
% 0.95/1.13 tff(2024,plain,
% 0.95/1.13 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1806, 1798, 1020])).
% 0.95/1.13 tff(2025,plain,
% 0.95/1.13 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1884, 2024])).
% 0.95/1.13 tff(2026,plain,
% 0.95/1.13 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2025, 1699])).
% 0.95/1.13 tff(2027,plain,
% 0.95/1.13 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1892, 224, 2026, 1698, 1737])).
% 0.95/1.13 tff(2028,plain,
% 0.95/1.13 ($false),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1401, 68, 2027, 1694, 2023])).
% 0.95/1.13 tff(2029,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.13 tff(2030,plain,
% 0.95/1.13 (~r(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2029, 1628, 1697, 1181, 335, 1630])).
% 0.95/1.13 tff(2031,plain,
% 0.95/1.13 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1294, 2030, 1733])).
% 0.95/1.13 tff(2032,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2033,plain,
% 0.95/1.13 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2034,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[2033])).
% 0.95/1.13 tff(2035,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[2034, 2032])).
% 0.95/1.13 tff(2036,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2037,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 0.95/1.13 tff(2038,plain,
% 0.95/1.13 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2037, 224, 2031, 1987, 2016])).
% 0.95/1.13 tff(2039,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.95/1.13 tff(2040,plain,
% 0.95/1.13 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 0.95/1.13 inference(symmetry,[status(thm)],[2039])).
% 0.95/1.13 tff(2041,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.95/1.13 tff(2042,plain,
% 0.95/1.13 ($false),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2041, 2040])).
% 0.95/1.13 tff(2043,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.13 tff(2044,plain,
% 0.95/1.13 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2043, 1835])).
% 0.95/1.13 tff(2045,plain,
% 0.95/1.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2046,plain,
% 0.95/1.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2047,plain,
% 0.95/1.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 0.95/1.13 tff(2048,plain,
% 0.95/1.13 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2047, 68, 2044, 2038])).
% 0.95/1.13 tff(2049,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2050,plain,
% 0.95/1.13 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2051,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 0.95/1.13 inference(monotonicity,[status(thm)],[2050])).
% 0.95/1.13 tff(2052,plain,
% 0.95/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.95/1.13 inference(transitivity,[status(thm)],[2051, 2049])).
% 0.95/1.13 tff(2053,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.95/1.13 inference(quant_inst,[status(thm)],[])).
% 0.95/1.13 tff(2054,plain,
% 0.95/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.95/1.13 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 0.95/1.13 tff(2055,plain,
% 0.95/1.13 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[2054, 224, 1636, 1667, 2031])).
% 0.95/1.13 tff(2056,plain,
% 0.95/1.13 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.95/1.13 inference(unit_resolution,[status(thm)],[1345, 2055, 1832])).
% 0.95/1.13 tff(2057,plain,
% 0.95/1.13 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.13 inference(rewrite,[status(thm)],[])).
% 0.95/1.13 tff(2058,plain,
% 0.95/1.13 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2059,plain,
% 0.95/1.14 (((~![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(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2058])).
% 0.95/1.14 tff(2060,plain,
% 0.95/1.14 (((~![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(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2059, 2057])).
% 0.95/1.14 tff(2061,plain,
% 0.95/1.14 ((~![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(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2062,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 0.95/1.14 tff(2063,plain,
% 0.95/1.14 ($false),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2062, 112, 2056, 1989, 2048])).
% 0.95/1.14 tff(2064,plain,((~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (s(elem!1) = elem!1) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.14 tff(2065,plain,
% 0.95/1.14 (~(z = elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2064, 1607, 319, 313, 303, 77, 101, 177, 102, 295, 293])).
% 0.95/1.14 tff(2066,plain,
% 0.95/1.14 (b(z, elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[289, 2065, 285])).
% 0.95/1.14 tff(2067,plain,
% 0.95/1.14 ((~(z = elem!1)) <=> (~(elem!1 = z))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[5])).
% 0.95/1.14 tff(2068,plain,
% 0.95/1.14 (~(elem!1 = z)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2065, 2067])).
% 0.95/1.14 tff(2069,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2070,plain,
% 0.95/1.14 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2071,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2070])).
% 0.95/1.14 tff(2072,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2071, 2069])).
% 0.95/1.14 tff(2073,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2074,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 0.95/1.14 tff(2075,plain,
% 0.95/1.14 ($false),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2074, 112, 1181, 363, 102])).
% 0.95/1.14 tff(2076,plain,((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.14 tff(2077,plain,
% 0.95/1.14 (~r(elem!1, z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2076, 1607, 102])).
% 0.95/1.14 tff(2078,plain,
% 0.95/1.14 (b(elem!1, z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[403, 2077, 2068])).
% 0.95/1.14 tff(2079,plain,
% 0.95/1.14 (~(s(s(s(z))) = elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[347, 2066, 74])).
% 0.95/1.14 tff(2080,plain,
% 0.95/1.14 (b(s(s(elem!1)), s(elem!1))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[961, 2078, 293, 2066, 77, 3, 177, 2079, 2068, 149, 102])).
% 0.95/1.14 tff(2081,plain,
% 0.95/1.14 (~(s(elem!1) = s(z))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[159, 2068])).
% 0.95/1.14 tff(2082,plain,
% 0.95/1.14 (~r(s(z), s(s(s(z))))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[187, 179, 177])).
% 0.95/1.14 tff(2083,plain,
% 0.95/1.14 (b(s(z), s(s(s(z))))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[175, 2082])).
% 0.95/1.14 tff(2084,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2085,plain,
% 0.95/1.14 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2086,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2085])).
% 0.95/1.14 tff(2087,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2086, 2084])).
% 0.95/1.14 tff(2088,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2089,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 0.95/1.14 tff(2090,plain,
% 0.95/1.14 (~b(s(z), s(s(elem!1)))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2089, 224, 2083, 152, 968])).
% 0.95/1.14 tff(2091,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2092,plain,
% 0.95/1.14 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2093,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2092])).
% 0.95/1.14 tff(2094,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2093, 2091])).
% 0.95/1.14 tff(2095,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2096,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 0.95/1.14 tff(2097,plain,
% 0.95/1.14 (~r(s(z), s(s(elem!1)))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2096, 112, 1181, 102, 179])).
% 0.95/1.14 tff(2098,plain,
% 0.95/1.14 ($false),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[653, 2097, 2090])).
% 0.95/1.14 tff(2099,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.14 tff(2100,plain,
% 0.95/1.14 (~r(s(z), z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2099, 1607, 102, 313, 295, 177])).
% 0.95/1.14 tff(2101,plain,
% 0.95/1.14 (b(s(z), z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[194, 2100])).
% 0.95/1.14 tff(2102,plain,
% 0.95/1.14 (~b(s(z), elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1017, 224, 2078, 2101, 2066])).
% 0.95/1.14 tff(2103,plain,
% 0.95/1.14 (r(s(z), elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[454, 2102, 149])).
% 0.95/1.14 tff(2104,plain,
% 0.95/1.14 (~b(s(s(elem!1)), s(z))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1485, 416, 166, 1391, 408])).
% 0.95/1.14 tff(2105,plain,
% 0.95/1.14 (r(s(s(elem!1)), s(z))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[901, 2104])).
% 0.95/1.14 tff(2106,plain,
% 0.95/1.14 ($false),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1187, 112, 1181, 416, 2105])).
% 0.95/1.14 tff(2107,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.14 tff(2108,plain,
% 0.95/1.14 (~r(s(elem!1), elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2107, 2103, 2081, 2080, 1607])).
% 0.95/1.14 tff(2109,plain,
% 0.95/1.14 (b(s(elem!1), elem!1)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[939, 2108, 303])).
% 0.95/1.14 tff(2110,plain,
% 0.95/1.14 (~b(s(elem!1), z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[946, 224, 2109, 2078, 2066])).
% 0.95/1.14 tff(2111,plain,
% 0.95/1.14 (r(s(elem!1), z)),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[498, 2110])).
% 0.95/1.14 tff(2112,plain,
% 0.95/1.14 (~r(s(elem!1), s(s(s(z))))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1506, 112, 2111, 177])).
% 0.95/1.14 tff(2113,plain,
% 0.95/1.14 (((~![X0: $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)), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2114,plain,
% 0.95/1.14 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), 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)), z)) | (~r(s(elem!1), z)))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2115,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(elem!1), z))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2114])).
% 0.95/1.14 tff(2116,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), 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)), z)) | (~r(s(elem!1), z)))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2115, 2113])).
% 0.95/1.14 tff(2117,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2118,plain,
% 0.95/1.14 ((~![X0: $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)), z)) | (~r(s(elem!1), z))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 0.95/1.14 tff(2119,plain,
% 0.95/1.14 (~r(s(elem!1), s(s(elem!1)))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2118, 112, 1607, 102, 2111])).
% 0.95/1.14 tff(2120,plain,
% 0.95/1.14 (b(s(elem!1), s(s(elem!1)))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1521, 2119, 319])).
% 0.95/1.14 tff(2121,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2122,plain,
% 0.95/1.14 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~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(s(z))))))),
% 0.95/1.14 inference(rewrite,[status(thm)],[])).
% 0.95/1.14 tff(2123,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z)))))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2122])).
% 0.95/1.14 tff(2124,plain,
% 0.95/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))))),
% 0.95/1.14 inference(transitivity,[status(thm)],[2123, 2121])).
% 0.95/1.14 tff(2125,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.95/1.14 inference(quant_inst,[status(thm)],[])).
% 0.95/1.14 tff(2126,plain,
% 0.95/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z)))))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 0.95/1.14 tff(2127,plain,
% 0.95/1.14 (~b(s(elem!1), s(s(s(z))))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[2126, 224, 2120, 313, 295])).
% 0.95/1.14 tff(2128,plain,
% 0.95/1.14 (s(elem!1) = s(s(s(z)))),
% 0.95/1.14 inference(unit_resolution,[status(thm)],[1534, 2127, 2112])).
% 0.95/1.14 tff(2129,plain,
% 0.95/1.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2128])).
% 0.95/1.14 tff(2130,plain,
% 0.95/1.14 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2129])).
% 0.95/1.14 tff(2131,plain,
% 0.95/1.14 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 0.95/1.14 inference(symmetry,[status(thm)],[2130])).
% 0.95/1.14 tff(2132,plain,
% 0.95/1.14 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2131])).
% 0.95/1.14 tff(2133,plain,
% 0.95/1.14 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 0.95/1.14 inference(symmetry,[status(thm)],[2132])).
% 0.95/1.14 tff(2134,plain,
% 0.95/1.14 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2128])).
% 0.95/1.14 tff(2135,plain,
% 0.95/1.14 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 0.95/1.14 inference(symmetry,[status(thm)],[2134])).
% 0.95/1.14 tff(2136,plain,
% 0.95/1.14 (s(s(z)) = elem!1),
% 0.95/1.14 inference(transitivity,[status(thm)],[32, 2135, 121])).
% 0.95/1.14 tff(2137,plain,
% 0.95/1.14 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2132, 2136])).
% 0.95/1.14 tff(2138,plain,
% 0.95/1.14 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2137])).
% 0.95/1.14 tff(2139,plain,
% 0.95/1.14 (elem!1 = s(s(z))),
% 0.95/1.14 inference(transitivity,[status(thm)],[155, 2134, 31])).
% 0.95/1.14 tff(2140,plain,
% 0.95/1.14 (b(elem!1, z) <=> b(s(s(z)), z)),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2139])).
% 0.95/1.14 tff(2141,plain,
% 0.95/1.14 (b(s(s(z)), z)),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2078, 2140])).
% 0.95/1.14 tff(2142,plain,
% 0.95/1.14 (b(z, elem!1) <=> b(z, s(s(z)))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2139])).
% 0.95/1.14 tff(2143,plain,
% 0.95/1.14 (b(z, s(s(z)))),
% 0.95/1.14 inference(modus_ponens,[status(thm)],[2066, 2142])).
% 0.95/1.14 tff(2144,plain,
% 0.95/1.14 (s(s(s(z))) = s(elem!1)),
% 0.95/1.14 inference(symmetry,[status(thm)],[2128])).
% 0.95/1.14 tff(2145,plain,
% 0.95/1.14 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 0.95/1.14 inference(monotonicity,[status(thm)],[2144])).
% 0.95/1.14 tff(2146,plain,
% 0.95/1.14 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 0.95/1.14 inference(symmetry,[status(thm)],[2145])).
% 0.95/1.15 tff(2147,plain,
% 0.95/1.15 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2128, 2136])).
% 0.95/1.15 tff(2148,plain,
% 0.95/1.15 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), s(s(z)))),
% 0.95/1.15 inference(symmetry,[status(thm)],[2147])).
% 0.95/1.15 tff(2149,plain,
% 0.95/1.15 (~r(s(s(elem!1)), s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[1187, 112, 1607, 2103])).
% 0.95/1.15 tff(2150,plain,
% 0.95/1.15 (b(s(s(elem!1)), s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[901, 2149])).
% 0.95/1.15 tff(2151,plain,
% 0.95/1.15 (~r(s(z), s(s(elem!1)))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[1195, 112, 1607, 2103])).
% 0.95/1.15 tff(2152,plain,
% 0.95/1.15 (b(s(z), s(s(elem!1)))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[653, 2151])).
% 0.95/1.15 tff(2153,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2154,plain,
% 0.95/1.15 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2155,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2154])).
% 0.95/1.15 tff(2156,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.95/1.15 inference(transitivity,[status(thm)],[2155, 2153])).
% 0.95/1.15 tff(2157,plain,
% 0.95/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(2158,plain,
% 0.95/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 0.95/1.15 tff(2159,plain,
% 0.95/1.15 (~b(s(s(s(z))), s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[2158, 224, 2152, 2150, 295])).
% 0.95/1.15 tff(2160,plain,
% 0.95/1.15 (r(s(s(s(z))), s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[925, 2159])).
% 0.95/1.15 tff(2161,plain,
% 0.95/1.15 (~b(elem!1, s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[1466, 224, 77, 2078, 2101])).
% 0.95/1.15 tff(2162,plain,
% 0.95/1.15 (r(elem!1, s(z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[1277, 2161, 88])).
% 0.95/1.15 tff(2163,plain,
% 0.95/1.15 (((~![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)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2164,plain,
% 0.95/1.15 (((~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)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2165,plain,
% 0.95/1.15 (((~![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))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2164])).
% 0.95/1.15 tff(2166,plain,
% 0.95/1.15 (((~![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)))),
% 0.95/1.15 inference(transitivity,[status(thm)],[2165, 2163])).
% 0.95/1.15 tff(2167,plain,
% 0.95/1.15 ((~![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)))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(2168,plain,
% 0.95/1.15 ((~![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))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 0.95/1.15 tff(2169,plain,
% 0.95/1.15 (~r(s(s(s(z))), elem!1)),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[2168, 112, 2162, 2160])).
% 0.95/1.15 tff(2170,plain,
% 0.95/1.15 (b(s(s(s(z))), elem!1)),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[374, 2169, 2079])).
% 0.95/1.15 tff(2171,plain,
% 0.95/1.15 (b(s(elem!1), s(s(z)))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2170, 2148])).
% 0.95/1.15 tff(2172,plain,
% 0.95/1.15 (b(s(s(s(z))), s(s(z)))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2171, 2146])).
% 0.95/1.15 tff(2173,plain,
% 0.95/1.15 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2174,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2173])).
% 0.95/1.15 tff(2175,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.95/1.15 inference(transitivity,[status(thm)],[2174, 2084])).
% 0.95/1.15 tff(2176,plain,
% 0.95/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(2177,plain,
% 0.95/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 0.95/1.15 tff(2178,plain,
% 0.95/1.15 (~b(s(z), s(s(s(z))))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[2177, 224, 2152, 313, 295])).
% 0.95/1.15 tff(2179,plain,
% 0.95/1.15 (r(s(z), s(s(s(z))))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[175, 2178])).
% 0.95/1.15 tff(2180,plain,
% 0.95/1.15 (~r(s(s(z)), s(s(s(z))))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[243, 2179, 77, 2101, 177])).
% 0.95/1.15 tff(2181,plain,
% 0.95/1.15 (b(s(s(z)), s(s(s(z))))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[249, 2180])).
% 0.95/1.15 tff(2182,plain,
% 0.95/1.15 (s(s(elem!1)) = s(s(s(s(z))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[777])).
% 0.95/1.15 tff(2183,plain,
% 0.95/1.15 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2182])).
% 0.95/1.15 tff(2184,plain,
% 0.95/1.15 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2183])).
% 0.95/1.15 tff(2185,plain,
% 0.95/1.15 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 0.95/1.15 inference(symmetry,[status(thm)],[2184])).
% 0.95/1.15 tff(2186,plain,
% 0.95/1.15 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2185])).
% 0.95/1.15 tff(2187,plain,
% 0.95/1.15 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 0.95/1.15 inference(symmetry,[status(thm)],[2186])).
% 0.95/1.15 tff(2188,plain,
% 0.95/1.15 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2185])).
% 0.95/1.15 tff(2189,plain,
% 0.95/1.15 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2188])).
% 0.95/1.15 tff(2190,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.95/1.15 tff(2191,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 0.95/1.15 tff(2192,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2193,plain,
% 0.95/1.15 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.95/1.15 inference(rewrite,[status(thm)],[])).
% 0.95/1.15 tff(2194,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.95/1.15 inference(monotonicity,[status(thm)],[2193])).
% 0.95/1.15 tff(2195,plain,
% 0.95/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.95/1.15 inference(transitivity,[status(thm)],[2194, 2192])).
% 0.95/1.15 tff(2196,plain,
% 0.95/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.95/1.15 inference(quant_inst,[status(thm)],[])).
% 0.95/1.15 tff(2197,plain,
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% 0.95/1.15 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 0.95/1.15 tff(2198,plain,
% 0.95/1.15 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[2197, 224, 2191, 1118])).
% 0.95/1.15 tff(2199,plain,
% 0.95/1.15 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.95/1.15 inference(unit_resolution,[status(thm)],[2198, 2190])).
% 0.95/1.15 tff(2200,plain,
% 0.95/1.15 (~b(s(s(s(s(elem!1)))), z)),
% 0.95/1.15 inference(modus_ponens,[status(thm)],[2199, 2189])).
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% 0.95/1.16 inference(modus_ponens,[status(thm)],[1364, 2264])).
% 0.95/1.16 tff(2266,plain,
% 0.95/1.16 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[777])).
% 0.95/1.16 tff(2267,plain,
% 0.95/1.16 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2266])).
% 0.95/1.16 tff(2268,plain,
% 0.95/1.16 (s(s(z)) = elem!1),
% 0.95/1.16 inference(transitivity,[status(thm)],[32, 2267, 121])).
% 0.95/1.16 tff(2269,plain,
% 0.95/1.16 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2185, 2268])).
% 0.95/1.16 tff(2270,plain,
% 0.95/1.16 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2269])).
% 0.95/1.16 tff(2271,plain,
% 0.95/1.16 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[1295, 2270])).
% 0.95/1.16 tff(2272,plain,
% 0.95/1.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2268])).
% 0.95/1.16 tff(2273,plain,
% 0.95/1.16 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2272])).
% 0.95/1.16 tff(2274,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.95/1.16 tff(2275,plain,
% 0.95/1.16 (r(s(s(s(s(z)))), s(s(z)))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 0.95/1.16 tff(2276,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.95/1.16 tff(2277,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), 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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), 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(z)))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2278,plain,
% 0.95/1.16 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), 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(z)))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2279,plain,
% 0.95/1.16 (((~![X0: $i, X3: $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(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(z)))), 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(z))))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2278])).
% 0.95/1.16 tff(2280,plain,
% 0.95/1.16 (((~![X0: $i, X3: $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(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(z)))), 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(z)))))),
% 0.95/1.16 inference(transitivity,[status(thm)],[2279, 2277])).
% 0.95/1.16 tff(2281,plain,
% 0.95/1.16 ((~![X0: $i, X3: $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(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2282,plain,
% 0.95/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 0.95/1.16 tff(2283,plain,
% 0.95/1.16 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2282, 112, 2276])).
% 0.95/1.16 tff(2284,plain,
% 0.95/1.16 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2283, 2275, 2271])).
% 0.95/1.16 tff(2285,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 0.95/1.16 tff(2286,plain,
% 0.95/1.16 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.95/1.16 inference(transitivity,[status(thm)],[2184, 2285, 2249])).
% 0.95/1.16 tff(2287,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 0.95/1.16 tff(2288,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2287, 2286])).
% 0.95/1.16 tff(2289,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~(s(elem!1) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2290,plain,
% 0.95/1.16 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2289, 1389, 777])).
% 0.95/1.16 tff(2291,plain,
% 0.95/1.16 (((~![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))))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2292,plain,
% 0.95/1.16 ((~![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))))))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2293,plain,
% 0.95/1.16 ((~![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)))))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 0.95/1.16 tff(2294,plain,
% 0.95/1.16 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2293, 68, 2290, 2284])).
% 0.95/1.16 tff(2295,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.95/1.16 tff(2296,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2297,plain,
% 0.95/1.16 (((~b(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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(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(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2298,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2297])).
% 0.95/1.16 tff(2299,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.95/1.16 inference(transitivity,[status(thm)],[2298, 2296])).
% 0.95/1.16 tff(2300,plain,
% 0.95/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2301,plain,
% 0.95/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.95/1.16 tff(2302,plain,
% 0.95/1.16 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2301, 224, 1570, 2295, 2294])).
% 0.95/1.16 tff(2303,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.95/1.16 tff(2304,plain,
% 0.95/1.16 (((~![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(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(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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2305,plain,
% 0.95/1.16 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), 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(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(z)))))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2306,plain,
% 0.95/1.16 (((~![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(s(s(s(s(z)))))), 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(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(z))))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2305])).
% 0.95/1.16 tff(2307,plain,
% 0.95/1.16 (((~![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(s(s(s(s(z)))))), 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(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(z)))))),
% 0.95/1.16 inference(transitivity,[status(thm)],[2306, 2304])).
% 0.95/1.16 tff(2308,plain,
% 0.95/1.16 ((~![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(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2309,plain,
% 0.95/1.16 ((~![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(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(z))))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 0.95/1.16 tff(2310,plain,
% 0.95/1.16 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2309, 112, 178, 2303])).
% 0.95/1.16 tff(2311,plain,
% 0.95/1.16 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2310, 2271])).
% 0.95/1.16 tff(2312,plain,
% 0.95/1.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2313,plain,
% 0.95/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2314,plain,
% 0.95/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 0.95/1.16 tff(2315,plain,
% 0.95/1.16 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2314, 68, 2311])).
% 0.95/1.16 tff(2316,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2315, 2302, 2265])).
% 0.95/1.16 tff(2317,plain,((s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2318,plain,
% 0.95/1.16 (s(s(s(s(elem!1)))) = elem!1),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2317, 2259, 2257, 2128, 2248, 2179, 2246, 2244, 2242])).
% 0.95/1.16 tff(2319,plain,
% 0.95/1.16 (elem!1 = s(s(s(s(elem!1))))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2318])).
% 0.95/1.16 tff(2320,plain,
% 0.95/1.16 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 0.95/1.16 inference(transitivity,[status(thm)],[32, 2135, 121, 2319, 2133])).
% 0.95/1.16 tff(2321,plain,
% 0.95/1.16 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2320])).
% 0.95/1.16 tff(2322,plain,
% 0.95/1.16 (s(z) = s(s(s(s(s(z)))))),
% 0.95/1.16 inference(transitivity,[status(thm)],[50, 2321, 292])).
% 0.95/1.16 tff(2323,plain,
% 0.95/1.16 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2322])).
% 0.95/1.16 tff(2324,plain,
% 0.95/1.16 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2323])).
% 0.95/1.16 tff(2325,plain,
% 0.95/1.16 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2326,plain,
% 0.95/1.16 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2325, 25])).
% 0.95/1.16 tff(2327,plain,
% 0.95/1.16 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.95/1.16 inference(symmetry,[status(thm)],[2326])).
% 0.95/1.16 tff(2328,plain,
% 0.95/1.16 (s(s(s(s(z)))) = z),
% 0.95/1.16 inference(transitivity,[status(thm)],[2327, 2324, 27])).
% 0.95/1.16 tff(2329,plain,
% 0.95/1.16 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2330,plain,
% 0.95/1.16 (~(s(s(s(s(z)))) = z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2329, 40])).
% 0.95/1.16 tff(2331,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2330, 2328])).
% 0.95/1.16 tff(2332,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | b(z, s(s(s(z)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2333,plain,
% 0.95/1.16 (~r(z, s(s(elem!1)))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2332, 285, 88, 77, 3, 177, 74, 102])).
% 0.95/1.16 tff(2334,plain,
% 0.95/1.16 (b(z, s(s(elem!1)))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[752, 2333])).
% 0.95/1.16 tff(2335,plain,
% 0.95/1.16 (~r(s(z), z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[187, 178, 177])).
% 0.95/1.16 tff(2336,plain,
% 0.95/1.16 (b(s(z), z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[194, 2335])).
% 0.95/1.16 tff(2337,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 0.95/1.16 tff(2338,plain,
% 0.95/1.16 (r(s(z), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[454, 149, 2337])).
% 0.95/1.16 tff(2339,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2340,plain,
% 0.95/1.16 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 0.95/1.16 inference(rewrite,[status(thm)],[])).
% 0.95/1.16 tff(2341,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))))),
% 0.95/1.16 inference(monotonicity,[status(thm)],[2340])).
% 0.95/1.16 tff(2342,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 0.95/1.16 inference(transitivity,[status(thm)],[2341, 2339])).
% 0.95/1.16 tff(2343,plain,
% 0.95/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 0.95/1.16 inference(quant_inst,[status(thm)],[])).
% 0.95/1.16 tff(2344,plain,
% 0.95/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))),
% 0.95/1.16 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 0.95/1.16 tff(2345,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2344, 112, 1181, 102, 688])).
% 0.95/1.16 tff(2346,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2347,plain,
% 0.95/1.16 (~r(z, elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2346, 1181, 102])).
% 0.95/1.16 tff(2348,plain,
% 0.95/1.16 (~r(z, s(s(elem!1)))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2332, 88, 77, 3, 2347, 177, 74, 102])).
% 0.95/1.16 tff(2349,plain,
% 0.95/1.16 (b(z, s(s(elem!1)))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[752, 2348])).
% 0.95/1.16 tff(2350,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[1205, 2349, 2338, 77, 1181])).
% 0.95/1.16 tff(2351,plain,((elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | b(s(z), elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2352,plain,
% 0.95/1.16 (b(s(z), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2351, 1181, 88, 77, 3, 177, 74, 102])).
% 0.95/1.16 tff(2353,plain,
% 0.95/1.16 (~r(elem!1, z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2076, 1181, 102])).
% 0.95/1.16 tff(2354,plain,
% 0.95/1.16 (b(elem!1, z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[403, 2353, 157])).
% 0.95/1.16 tff(2355,plain,
% 0.95/1.16 ($false),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[461, 224, 2354, 1, 2352, 344])).
% 0.95/1.16 tff(2356,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (elem!1 = z) | (elem!1 = s(z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.16 tff(2357,plain,
% 0.95/1.16 (~r(s(s(elem!1)), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[2356, 290, 2336, 11, 88, 77, 3, 177, 74, 102])).
% 0.95/1.16 tff(2358,plain,
% 0.95/1.16 (b(s(s(elem!1)), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[360, 2357, 353])).
% 0.95/1.16 tff(2359,plain,
% 0.95/1.16 (~b(elem!1, s(z))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[1214, 2358, 2334, 77, 290])).
% 0.95/1.16 tff(2360,plain,
% 0.95/1.16 (r(elem!1, s(z))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[1277, 2359, 88])).
% 0.95/1.16 tff(2361,plain,
% 0.95/1.16 (~r(elem!1, s(s(s(z))))),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[1028, 2360, 178])).
% 0.95/1.16 tff(2362,plain,
% 0.95/1.16 (~(s(s(s(z))) = elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[347, 290, 74])).
% 0.95/1.16 tff(2363,plain,
% 0.95/1.16 (~r(elem!1, z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[398, 2358, 152, 2362, 177])).
% 0.95/1.16 tff(2364,plain,
% 0.95/1.16 (b(elem!1, z)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[403, 2363, 11])).
% 0.95/1.16 tff(2365,plain,
% 0.95/1.16 (~b(s(z), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[985, 2364, 290, 295, 177, 2358, 102])).
% 0.95/1.16 tff(2366,plain,
% 0.95/1.16 (r(s(z), elem!1)),
% 0.95/1.16 inference(unit_resolution,[status(thm)],[454, 2365, 149])).
% 0.95/1.16 tff(2367,plain,
% 0.95/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(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)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2368,plain,
% 0.95/1.17 (((~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)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2369,plain,
% 0.95/1.17 (((~![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))), 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))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2368])).
% 0.95/1.17 tff(2370,plain,
% 0.95/1.17 (((~![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))), 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)))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2369, 2367])).
% 0.95/1.17 tff(2371,plain,
% 0.95/1.17 ((~![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))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2372,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 0.95/1.17 tff(2373,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2372, 112, 416, 178, 690])).
% 0.95/1.17 tff(2374,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2375,plain,
% 0.95/1.17 (~r(s(s(s(z))), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2374, 2366, 178])).
% 0.95/1.17 tff(2376,plain,
% 0.95/1.17 (b(s(s(s(z))), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[374, 2375, 2362])).
% 0.95/1.17 tff(2377,plain,
% 0.95/1.17 (~r(s(s(z)), s(s(s(z))))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[243, 2336, 77, 178, 177])).
% 0.95/1.17 tff(2378,plain,
% 0.95/1.17 (b(s(s(z)), s(s(s(z))))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[249, 2377])).
% 0.95/1.17 tff(2379,plain,
% 0.95/1.17 (~b(s(s(z)), s(s(elem!1)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[256, 224, 2378, 152, 295])).
% 0.95/1.17 tff(2380,plain,
% 0.95/1.17 (r(s(s(z)), s(s(elem!1)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[265, 2379, 169])).
% 0.95/1.17 tff(2381,plain,
% 0.95/1.17 (~b(elem!1, s(s(elem!1)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[743, 2358, 2334, 290])).
% 0.95/1.17 tff(2382,plain,
% 0.95/1.17 (r(elem!1, s(s(elem!1)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[558, 2381, 3])).
% 0.95/1.17 tff(2383,plain,
% 0.95/1.17 (((~![X0: $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(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(elem!1, s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2384,plain,
% 0.95/1.17 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2385,plain,
% 0.95/1.17 (((~![X0: $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(z)), s(s(elem!1)))) | (~r(elem!1, s(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(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2384])).
% 0.95/1.17 tff(2386,plain,
% 0.95/1.17 (((~![X0: $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(z)), s(s(elem!1)))) | (~r(elem!1, s(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(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2385, 2383])).
% 0.95/1.17 tff(2387,plain,
% 0.95/1.17 ((~![X0: $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(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2388,plain,
% 0.95/1.17 ((~![X0: $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(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 0.95/1.17 tff(2389,plain,
% 0.95/1.17 (~r(s(s(z)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2388, 112, 2382, 2380])).
% 0.95/1.17 tff(2390,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2391,plain,
% 0.95/1.17 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2392,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2391])).
% 0.95/1.17 tff(2393,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2392, 2390])).
% 0.95/1.17 tff(2394,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2395,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.95/1.17 tff(2396,plain,
% 0.95/1.17 (~b(s(s(elem!1)), s(s(z)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2395, 224, 2378, 2358, 2376, 152])).
% 0.95/1.17 tff(2397,plain,
% 0.95/1.17 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 0.95/1.17 inference(monotonicity,[status(thm)],[1169])).
% 0.95/1.17 tff(2398,plain,
% 0.95/1.17 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 0.95/1.17 inference(symmetry,[status(thm)],[2397])).
% 0.95/1.17 tff(2399,plain,
% 0.95/1.17 (b(s(s(elem!1)), s(s(z)))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[390, 2398])).
% 0.95/1.17 tff(2400,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 0.95/1.17 tff(2401,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2400, 2399])).
% 0.95/1.17 tff(2402,plain,((~(s(s(z)) = elem!1)) | b(s(s(elem!1)), s(s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2403,plain,
% 0.95/1.17 (~(s(s(z)) = elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2402, 2396, 2358])).
% 0.95/1.17 tff(2404,plain,
% 0.95/1.17 (b(s(s(z)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[1135, 2403, 2389])).
% 0.95/1.17 tff(2405,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2406,plain,
% 0.95/1.17 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(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(s(z))))))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2407,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z)))))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2406])).
% 0.95/1.17 tff(2408,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2407, 2405])).
% 0.95/1.17 tff(2409,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2410,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 0.95/1.17 tff(2411,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2410, 224, 2212, 685, 787, 1109])).
% 0.95/1.17 tff(2412,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2413,plain,
% 0.95/1.17 (~b(elem!1, s(s(s(z))))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2412, 2404, 2378, 2376])).
% 0.95/1.17 tff(2414,plain,
% 0.95/1.17 (elem!1 = s(s(s(z)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[388, 2413, 2361])).
% 0.95/1.17 tff(2415,plain,
% 0.95/1.17 (s(s(s(z))) = elem!1),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2414, 284])).
% 0.95/1.17 tff(2416,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2362, 2415])).
% 0.95/1.17 tff(2417,plain,(r(z, elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z)) | (~b(z, s(z))) | b(z, s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2418,plain,
% 0.95/1.17 (r(z, elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2417, 176, 152, 73, 102, 3, 88, 77, 74, 4])).
% 0.95/1.17 tff(2419,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[863, 112, 1020, 688, 689])).
% 0.95/1.17 tff(2420,plain,((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2421,plain,
% 0.95/1.17 (~r(elem!1, s(s(s(z))))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2420, 2418, 101])).
% 0.95/1.17 tff(2422,plain,
% 0.95/1.17 (~r(s(s(elem!1)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2346, 2418, 102])).
% 0.95/1.17 tff(2423,plain,
% 0.95/1.17 (b(s(s(elem!1)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[360, 2422, 353])).
% 0.95/1.17 tff(2424,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2425,plain,
% 0.95/1.17 (((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2426,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2425])).
% 0.95/1.17 tff(2427,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2426, 2424])).
% 0.95/1.17 tff(2428,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2429,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 0.95/1.17 tff(2430,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2429, 112, 688, 690, 177])).
% 0.95/1.17 tff(2431,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2432,plain,
% 0.95/1.17 (~r(s(s(s(z))), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2431, 688, 73])).
% 0.95/1.17 tff(2433,plain,
% 0.95/1.17 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 0.95/1.17 inference(monotonicity,[status(thm)],[341])).
% 0.95/1.17 tff(2434,plain,
% 0.95/1.17 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 0.95/1.17 inference(symmetry,[status(thm)],[2433])).
% 0.95/1.17 tff(2435,plain,
% 0.95/1.17 (b(s(s(s(z))), z)),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[405, 2434])).
% 0.95/1.17 tff(2436,plain,
% 0.95/1.17 ($false),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[12, 2435])).
% 0.95/1.17 tff(2437,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.17 tff(2438,plain,
% 0.95/1.17 (~(s(s(s(z))) = elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2437, 405, 12])).
% 0.95/1.17 tff(2439,plain,
% 0.95/1.17 (b(s(s(s(z))), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[374, 2438, 2432])).
% 0.95/1.17 tff(2440,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.95/1.17 tff(2441,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~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)), z)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2442,plain,
% 0.95/1.17 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~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)), z)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2443,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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)), z))))),
% 0.95/1.17 inference(monotonicity,[status(thm)],[2442])).
% 0.95/1.17 tff(2444,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~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)), z)))),
% 0.95/1.17 inference(transitivity,[status(thm)],[2443, 2441])).
% 0.95/1.17 tff(2445,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.95/1.17 inference(quant_inst,[status(thm)],[])).
% 0.95/1.17 tff(2446,plain,
% 0.95/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~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)), z))),
% 0.95/1.17 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 0.95/1.17 tff(2447,plain,
% 0.95/1.17 (~b(s(s(z)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2446, 224, 405, 250, 2439, 1118])).
% 0.95/1.17 tff(2448,plain,
% 0.95/1.17 (~b(s(s(elem!1)), s(s(z)))),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2395, 224, 250, 390, 2439, 152])).
% 0.95/1.17 tff(2449,plain,
% 0.95/1.17 (~(s(s(z)) = elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[2402, 2448, 390])).
% 0.95/1.17 tff(2450,plain,
% 0.95/1.17 (r(s(s(z)), elem!1)),
% 0.95/1.17 inference(unit_resolution,[status(thm)],[1135, 2449, 2447])).
% 0.95/1.17 tff(2451,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2452,plain,
% 0.95/1.17 (((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 0.95/1.17 inference(rewrite,[status(thm)],[])).
% 0.95/1.17 tff(2453,plain,
% 0.95/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2452])).
% 0.95/1.18 tff(2454,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2453, 2451])).
% 0.95/1.18 tff(2455,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2456,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 0.95/1.18 tff(2457,plain,
% 0.95/1.18 (~r(s(s(z)), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2456, 112, 688, 1047])).
% 0.95/1.18 tff(2458,plain,
% 0.95/1.18 (b(s(s(z)), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[234, 68, 42, 2457])).
% 0.95/1.18 tff(2459,plain,
% 0.95/1.18 (((~![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), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2460,plain,
% 0.95/1.18 (((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2461,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2460])).
% 0.95/1.18 tff(2462,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2461, 2459])).
% 0.95/1.18 tff(2463,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2464,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 0.95/1.18 tff(2465,plain,
% 0.95/1.18 (~r(s(z), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2464, 112, 416, 688])).
% 0.95/1.18 tff(2466,plain,
% 0.95/1.18 (b(s(z), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[194, 2465])).
% 0.95/1.18 tff(2467,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[230, 224, 77, 2466, 1055, 2458])).
% 0.95/1.18 tff(2468,plain,((~r(s(s(z)), elem!1)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2469,plain,
% 0.95/1.18 (~r(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2468, 2450, 77, 688])).
% 0.95/1.18 tff(2470,plain,
% 0.95/1.18 (b(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[454, 2469, 129])).
% 0.95/1.18 tff(2471,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 0.95/1.18 tff(2472,plain,
% 0.95/1.18 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2471])).
% 0.95/1.18 tff(2473,plain,
% 0.95/1.18 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 0.95/1.18 inference(symmetry,[status(thm)],[2472])).
% 0.95/1.18 tff(2474,plain,
% 0.95/1.18 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2473])).
% 0.95/1.18 tff(2475,plain,
% 0.95/1.18 (~b(s(z), elem!1)),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[170, 2474])).
% 0.95/1.18 tff(2476,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[684, 2475])).
% 0.95/1.18 tff(2477,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2478,plain,
% 0.95/1.18 (~(elem!1 = s(s(s(z))))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2477, 2470, 170])).
% 0.95/1.18 tff(2479,plain,
% 0.95/1.18 (b(elem!1, s(s(s(z))))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[388, 2478, 2440])).
% 0.95/1.18 tff(2480,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[792, 224, 390, 2479, 2439, 152])).
% 0.95/1.18 tff(2481,plain,((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | (s(z) = elem!1) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(z)), z)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2482,plain,
% 0.95/1.18 (~b(elem!1, z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2481, 2423, 152, 2421, 170, 149, 77, 2418, 282, 12])).
% 0.95/1.18 tff(2483,plain,
% 0.95/1.18 (r(elem!1, z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[403, 2482, 11])).
% 0.95/1.18 tff(2484,plain,
% 0.95/1.18 (s(s(s(z))) = elem!1),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[398, 2483, 152, 2423, 73])).
% 0.95/1.18 tff(2485,plain,
% 0.95/1.18 (elem!1 = s(s(s(z)))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[341, 283])).
% 0.95/1.18 tff(2486,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[680, 2485])).
% 0.95/1.18 tff(2487,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2488,plain,
% 0.95/1.18 (elem!1 = s(s(s(z)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2487, 2484])).
% 0.95/1.18 tff(2489,plain,
% 0.95/1.18 (~b(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2477, 2488, 170])).
% 0.95/1.18 tff(2490,plain,
% 0.95/1.18 (r(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[454, 2489, 149])).
% 0.95/1.18 tff(2491,plain,
% 0.95/1.18 (~b(z, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[449, 408, 166, 416, 77])).
% 0.95/1.18 tff(2492,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(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(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2493,plain,
% 0.95/1.18 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2494,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2493])).
% 0.95/1.18 tff(2495,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2494, 2492])).
% 0.95/1.18 tff(2496,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2497,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 0.95/1.18 tff(2498,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2497, 112, 408, 688, 568])).
% 0.95/1.18 tff(2499,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2500,plain,
% 0.95/1.18 (~r(z, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2499, 408, 688])).
% 0.95/1.18 tff(2501,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[625, 2500, 2491])).
% 0.95/1.18 tff(2502,plain,((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2503,plain,
% 0.95/1.18 (~r(s(elem!1), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2502, 2490, 160, 2418, 77])).
% 0.95/1.18 tff(2504,plain,
% 0.95/1.18 (b(s(elem!1), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[939, 2503, 303])).
% 0.95/1.18 tff(2505,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 0.95/1.18 tff(2506,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 0.95/1.18 tff(2507,plain,
% 0.95/1.18 (~r(elem!1, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[604, 568, 363])).
% 0.95/1.18 tff(2508,plain,
% 0.95/1.18 (b(elem!1, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[515, 2507, 2506])).
% 0.95/1.18 tff(2509,plain,
% 0.95/1.18 (~b(s(s(elem!1)), s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[1496, 2508, 390, 1488])).
% 0.95/1.18 tff(2510,plain,
% 0.95/1.18 (r(s(s(elem!1)), s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[530, 2509, 2505])).
% 0.95/1.18 tff(2511,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[588, 112, 2510, 102, 568])).
% 0.95/1.18 tff(2512,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2513,plain,
% 0.95/1.18 (~r(z, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2512, 2504, 526, 2423, 102, 327, 2483])).
% 0.95/1.18 tff(2514,plain,
% 0.95/1.18 (b(z, s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[625, 2513])).
% 0.95/1.18 tff(2515,plain,
% 0.95/1.18 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2484])).
% 0.95/1.18 tff(2516,plain,
% 0.95/1.18 (b(s(s(z)), elem!1)),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[250, 2515])).
% 0.95/1.18 tff(2517,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2518,plain,
% 0.95/1.18 (((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2519,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2518])).
% 0.95/1.18 tff(2520,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2519, 2517])).
% 0.95/1.18 tff(2521,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2522,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 0.95/1.18 tff(2523,plain,
% 0.95/1.18 (~b(s(s(z)), s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2522, 224, 2504, 2516, 2514, 282])).
% 0.95/1.18 tff(2524,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 0.95/1.18 tff(2525,plain,
% 0.95/1.18 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2524])).
% 0.95/1.18 tff(2526,plain,
% 0.95/1.18 (s(z) = elem!1),
% 0.95/1.18 inference(transitivity,[status(thm)],[50, 2525, 121])).
% 0.95/1.18 tff(2527,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[129, 2526])).
% 0.95/1.18 tff(2528,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2529,plain,
% 0.95/1.18 (~(s(s(z)) = s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2528, 149])).
% 0.95/1.18 tff(2530,plain,
% 0.95/1.18 (((~![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)))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2531,plain,
% 0.95/1.18 ((~![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)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2532,plain,
% 0.95/1.18 ((~![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))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 0.95/1.18 tff(2533,plain,
% 0.95/1.18 (r(s(s(z)), s(elem!1))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2532, 68, 2529, 2523])).
% 0.95/1.18 tff(2534,plain,
% 0.95/1.18 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2484])).
% 0.95/1.18 tff(2535,plain,
% 0.95/1.18 (b(elem!1, s(s(elem!1)))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[151, 2534])).
% 0.95/1.18 tff(2536,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2537,plain,
% 0.95/1.18 (((~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)))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2538,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2537])).
% 0.95/1.18 tff(2539,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2538, 2536])).
% 0.95/1.18 tff(2540,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2541,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 0.95/1.18 tff(2542,plain,
% 0.95/1.18 (~b(s(elem!1), s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2541, 224, 2504, 2535, 2423])).
% 0.95/1.18 tff(2543,plain,
% 0.95/1.18 (r(s(elem!1), s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[1521, 2542, 319])).
% 0.95/1.18 tff(2544,plain,
% 0.95/1.18 (((~![X0: $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(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(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2545,plain,
% 0.95/1.18 (((~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(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2546,plain,
% 0.95/1.18 (((~![X0: $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(elem!1))) | (~r(s(s(z)), s(s(elem!1))))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2545])).
% 0.95/1.18 tff(2547,plain,
% 0.95/1.18 (((~![X0: $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(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2546, 2544])).
% 0.95/1.18 tff(2548,plain,
% 0.95/1.18 ((~![X0: $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))))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2549,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 0.95/1.18 tff(2550,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2549, 112, 2543, 266, 2533])).
% 0.95/1.18 tff(2551,plain,(b(s(z), s(s(s(z)))) | (~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | b(s(s(s(z))), z) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z)) | b(z, s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2552,plain,
% 0.95/1.18 (b(s(z), s(s(s(z))))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2551, 3, 77, 152, 12, 102, 88, 74, 4])).
% 0.95/1.18 tff(2553,plain,
% 0.95/1.18 (~b(s(z), s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2089, 224, 2552, 152, 151])).
% 0.95/1.18 tff(2554,plain,
% 0.95/1.18 (r(s(z), s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[653, 2553])).
% 0.95/1.18 tff(2555,plain,
% 0.95/1.18 (b(z, elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[289, 2347, 4])).
% 0.95/1.18 tff(2556,plain,
% 0.95/1.18 (~r(s(z), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2099, 1181, 177, 102, 152, 295])).
% 0.95/1.18 tff(2557,plain,
% 0.95/1.18 (b(s(z), z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[194, 2556])).
% 0.95/1.18 tff(2558,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2356, 2557, 2555, 1181, 11, 88, 77, 3, 177, 74, 102])).
% 0.95/1.18 tff(2559,plain,((~r(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.18 tff(2560,plain,
% 0.95/1.18 (~r(s(s(elem!1)), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2559, 3, 77, 88, 177, 74, 102, 4, 152])).
% 0.95/1.18 tff(2561,plain,
% 0.95/1.18 (b(s(s(elem!1)), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[360, 2560, 353])).
% 0.95/1.18 tff(2562,plain,
% 0.95/1.18 (~r(elem!1, z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[398, 2362, 152, 2561, 177])).
% 0.95/1.18 tff(2563,plain,
% 0.95/1.18 (b(elem!1, z)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[403, 2562, 11])).
% 0.95/1.18 tff(2564,plain,
% 0.95/1.18 (~b(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[985, 2563, 2561, 295, 177, 290, 102])).
% 0.95/1.18 tff(2565,plain,
% 0.95/1.18 (r(s(z), elem!1)),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[454, 2564, 149])).
% 0.95/1.18 tff(2566,plain,
% 0.95/1.18 (~b(elem!1, s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[743, 2334, 2561, 290])).
% 0.95/1.18 tff(2567,plain,
% 0.95/1.18 (r(elem!1, s(s(elem!1)))),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[558, 2566, 3])).
% 0.95/1.18 tff(2568,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2569,plain,
% 0.95/1.18 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.18 inference(rewrite,[status(thm)],[])).
% 0.95/1.18 tff(2570,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 0.95/1.18 inference(monotonicity,[status(thm)],[2569])).
% 0.95/1.18 tff(2571,plain,
% 0.95/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.18 inference(transitivity,[status(thm)],[2570, 2568])).
% 0.95/1.18 tff(2572,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 0.95/1.18 inference(quant_inst,[status(thm)],[])).
% 0.95/1.18 tff(2573,plain,
% 0.95/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 0.95/1.18 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 0.95/1.18 tff(2574,plain,
% 0.95/1.18 ($false),
% 0.95/1.18 inference(unit_resolution,[status(thm)],[2573, 112, 2567, 656, 2565])).
% 0.95/1.18 tff(2575,plain,(r(z, elem!1) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | b(z, s(s(s(z)))) | (elem!1 = s(z)) | (~b(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2576,plain,
% 0.95/1.19 (r(z, elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2575, 2554, 73, 102, 3, 152, 74, 88, 77, 4])).
% 0.95/1.19 tff(2577,plain,
% 0.95/1.19 (~r(s(s(s(z))), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2431, 2576, 73])).
% 0.95/1.19 tff(2578,plain,
% 0.95/1.19 (~r(s(s(elem!1)), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2559, 3, 77, 88, 73, 74, 102, 4, 152])).
% 0.95/1.19 tff(2579,plain,
% 0.95/1.19 (~(s(s(z)) = s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[168, 166])).
% 0.95/1.19 tff(2580,plain,
% 0.95/1.19 (s(s(s(z))) = elem!1),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[398, 363, 152, 361, 177])).
% 0.95/1.19 tff(2581,plain,
% 0.95/1.19 (r(s(s(s(z))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2580])).
% 0.95/1.19 tff(2582,plain,
% 0.95/1.19 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2581])).
% 0.95/1.19 tff(2583,plain,
% 0.95/1.19 (~r(elem!1, s(s(elem!1)))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[294, 2582])).
% 0.95/1.19 tff(2584,plain,
% 0.95/1.19 (~r(s(s(z)), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[276, 268, 102])).
% 0.95/1.19 tff(2585,plain,
% 0.95/1.19 (b(s(s(z)), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[265, 2584, 259])).
% 0.95/1.19 tff(2586,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 0.95/1.19 tff(2587,plain,
% 0.95/1.19 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 0.95/1.19 inference(commutativity,[status(thm)],[])).
% 0.95/1.19 tff(2588,plain,
% 0.95/1.19 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 0.95/1.19 inference(symmetry,[status(thm)],[2587])).
% 0.95/1.19 tff(2589,plain,
% 0.95/1.19 (b(s(s(elem!1)), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[360, 353, 328])).
% 0.95/1.19 tff(2590,plain,
% 0.95/1.19 (s(s(s(z))) = elem!1),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[398, 2589, 152, 363, 177])).
% 0.95/1.19 tff(2591,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2590])).
% 0.95/1.19 tff(2592,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2591, 2587])).
% 0.95/1.19 tff(2593,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 0.95/1.19 inference(transitivity,[status(thm)],[2592, 2588])).
% 0.95/1.19 tff(2594,plain,
% 0.95/1.19 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2593])).
% 0.95/1.19 tff(2595,plain,
% 0.95/1.19 (~(s(s(z)) = elem!1)),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[55, 2594])).
% 0.95/1.19 tff(2596,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.95/1.19 tff(2597,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.95/1.19 tff(2598,plain,
% 0.95/1.19 (b(elem!1, s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[558, 3, 2597])).
% 0.95/1.19 tff(2599,plain,
% 0.95/1.19 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2600,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2599])).
% 0.95/1.19 tff(2601,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2600, 1110])).
% 0.95/1.19 tff(2602,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.95/1.19 inference(quant_inst,[status(thm)],[])).
% 0.95/1.19 tff(2603,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 0.95/1.19 tff(2604,plain,
% 0.95/1.19 (~b(s(s(z)), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2603, 224, 2598, 2589, 2596])).
% 0.95/1.19 tff(2605,plain,
% 0.95/1.19 ($false),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[1135, 2604, 2595, 2586])).
% 0.95/1.19 tff(2606,plain,((elem!1 = s(s(elem!1))) | r(s(s(z)), elem!1) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2607,plain,
% 0.95/1.19 (r(s(s(z)), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2606, 2585, 152, 3, 363, 177, 328, 2583])).
% 0.95/1.19 tff(2608,plain,
% 0.95/1.19 ($false),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2456, 112, 688, 2607, 268])).
% 0.95/1.19 tff(2609,plain,((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2610,plain,
% 0.95/1.19 (~r(s(s(z)), z)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2609, 363, 152, 3, 688, 177, 328, 2579, 102])).
% 0.95/1.19 tff(2611,plain,
% 0.95/1.19 (b(s(s(z)), z)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[281, 2610])).
% 0.95/1.19 tff(2612,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2580])).
% 0.95/1.19 tff(2613,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2612, 2587])).
% 0.95/1.19 tff(2614,plain,
% 0.95/1.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 0.95/1.19 inference(transitivity,[status(thm)],[2613, 2588])).
% 0.95/1.19 tff(2615,plain,
% 0.95/1.19 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2614])).
% 0.95/1.19 tff(2616,plain,
% 0.95/1.19 (~(s(s(z)) = elem!1)),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[55, 2615])).
% 0.95/1.19 tff(2617,plain,
% 0.95/1.19 (~r(s(elem!1), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2499, 568, 688])).
% 0.95/1.19 tff(2618,plain,
% 0.95/1.19 (~(elem!1 = s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[326, 324])).
% 0.95/1.19 tff(2619,plain,
% 0.95/1.19 (~b(s(elem!1), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2512, 568, 2505, 390, 102, 2618, 363])).
% 0.95/1.19 tff(2620,plain,
% 0.95/1.19 ($false),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[939, 2619, 2617, 324])).
% 0.95/1.19 tff(2621,plain,((~r(z, s(elem!1))) | (s(elem!1) = elem!1) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2622,plain,
% 0.95/1.19 (~r(z, s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2621, 363, 526, 361, 102, 303, 688])).
% 0.95/1.19 tff(2623,plain,
% 0.95/1.19 (b(z, s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[625, 2622])).
% 0.95/1.19 tff(2624,plain,
% 0.95/1.19 (~(s(s(z)) = s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2528, 129])).
% 0.95/1.19 tff(2625,plain,
% 0.95/1.19 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2580])).
% 0.95/1.19 tff(2626,plain,
% 0.95/1.19 (b(s(s(s(z))), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[135, 68, 681, 294])).
% 0.95/1.19 tff(2627,plain,
% 0.95/1.19 (b(elem!1, s(s(elem!1)))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 0.95/1.19 tff(2628,plain,
% 0.95/1.19 (~b(s(z), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2089, 224, 1090, 152, 2626])).
% 0.95/1.19 tff(2629,plain,
% 0.95/1.19 (r(s(z), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[653, 2628])).
% 0.95/1.19 tff(2630,plain,
% 0.95/1.19 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2580])).
% 0.95/1.19 tff(2631,plain,
% 0.95/1.19 (b(s(z), elem!1)),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[1090, 2630])).
% 0.95/1.19 tff(2632,plain,
% 0.95/1.19 (~b(s(elem!1), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2541, 224, 1488, 682, 390])).
% 0.95/1.19 tff(2633,plain,
% 0.95/1.19 (r(s(elem!1), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[1521, 2632, 523])).
% 0.95/1.19 tff(2634,plain,
% 0.95/1.19 (((~![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), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2635,plain,
% 0.95/1.19 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2636,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2635])).
% 0.95/1.19 tff(2637,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2636, 2634])).
% 0.95/1.19 tff(2638,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 0.95/1.19 inference(quant_inst,[status(thm)],[])).
% 0.95/1.19 tff(2639,plain,
% 0.95/1.19 ((~![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), z)) | (~r(elem!1, z))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 0.95/1.19 tff(2640,plain,
% 0.95/1.19 (~r(s(z), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2639, 112, 363, 179])).
% 0.95/1.19 tff(2641,plain,
% 0.95/1.19 (b(s(z), elem!1)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[454, 2640, 129])).
% 0.95/1.19 tff(2642,plain,
% 0.95/1.19 (~b(s(z), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[634, 224, 682, 2641, 390])).
% 0.95/1.19 tff(2643,plain,
% 0.95/1.19 (r(s(z), s(s(elem!1)))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[653, 2642])).
% 0.95/1.19 tff(2644,plain,
% 0.95/1.19 (((~![X0: $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(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2645,plain,
% 0.95/1.19 (((~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(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2646,plain,
% 0.95/1.19 (((~![X0: $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(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2645])).
% 0.95/1.19 tff(2647,plain,
% 0.95/1.19 (((~![X0: $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(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2646, 2644])).
% 0.95/1.19 tff(2648,plain,
% 0.95/1.19 ((~![X0: $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))))),
% 0.95/1.19 inference(quant_inst,[status(thm)],[])).
% 0.95/1.19 tff(2649,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 0.95/1.19 tff(2650,plain,
% 0.95/1.19 (~r(s(elem!1), s(z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2649, 112, 1700, 2643])).
% 0.95/1.19 tff(2651,plain,
% 0.95/1.19 (~r(elem!1, s(z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[1259, 363, 179])).
% 0.95/1.19 tff(2652,plain,
% 0.95/1.19 (s(z) = elem!1),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[78, 84])).
% 0.95/1.19 tff(2653,plain,
% 0.95/1.19 ($false),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[129, 2652])).
% 0.95/1.19 tff(2654,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2655,plain,
% 0.95/1.19 (~(elem!1 = s(z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2654, 129])).
% 0.95/1.19 tff(2656,plain,
% 0.95/1.19 (b(elem!1, s(z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[1275, 68, 2655, 2651])).
% 0.95/1.19 tff(2657,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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)))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2658,plain,
% 0.95/1.19 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2659,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2658])).
% 0.95/1.19 tff(2660,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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)))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2659, 2657])).
% 0.95/1.19 tff(2661,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 0.95/1.19 inference(quant_inst,[status(thm)],[])).
% 0.95/1.19 tff(2662,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 0.95/1.19 tff(2663,plain,
% 0.95/1.19 (~b(s(elem!1), s(z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2662, 224, 1488, 2641, 2656])).
% 0.95/1.19 tff(2664,plain,
% 0.95/1.19 ($false),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[440, 68, 166, 2663, 2650])).
% 0.95/1.19 tff(2665,plain,((~r(elem!1, z)) | (s(elem!1) = s(z)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.19 tff(2666,plain,
% 0.95/1.19 (~r(s(z), z)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2665, 2633, 390, 363, 166, 1488, 129, 682])).
% 0.95/1.19 tff(2667,plain,
% 0.95/1.19 (b(s(z), z)),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[194, 2666])).
% 0.95/1.19 tff(2668,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2669,plain,
% 0.95/1.19 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2670,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1)))))),
% 0.95/1.19 inference(monotonicity,[status(thm)],[2669])).
% 0.95/1.19 tff(2671,plain,
% 0.95/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1))))),
% 0.95/1.19 inference(transitivity,[status(thm)],[2670, 2668])).
% 0.95/1.19 tff(2672,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 0.95/1.19 inference(quant_inst,[status(thm)],[])).
% 0.95/1.19 tff(2673,plain,
% 0.95/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1)))),
% 0.95/1.19 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 0.95/1.19 tff(2674,plain,
% 0.95/1.19 ((~b(s(z), s(elem!1))) | (~b(s(z), z))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2673, 224, 1488, 684, 407])).
% 0.95/1.19 tff(2675,plain,
% 0.95/1.19 (~b(s(z), s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[2674, 2667])).
% 0.95/1.19 tff(2676,plain,
% 0.95/1.19 (r(s(z), s(elem!1))),
% 0.95/1.19 inference(unit_resolution,[status(thm)],[670, 2675, 415])).
% 0.95/1.19 tff(2677,plain,
% 0.95/1.19 (((~![X0: $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(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2678,plain,
% 0.95/1.19 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.95/1.19 inference(rewrite,[status(thm)],[])).
% 0.95/1.19 tff(2679,plain,
% 0.95/1.19 (((~![X0: $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(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 0.95/1.20 inference(monotonicity,[status(thm)],[2678])).
% 0.95/1.20 tff(2680,plain,
% 0.95/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.95/1.20 inference(transitivity,[status(thm)],[2679, 2677])).
% 0.95/1.20 tff(2681,plain,
% 0.95/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 0.95/1.20 inference(quant_inst,[status(thm)],[])).
% 0.95/1.20 tff(2682,plain,
% 0.95/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 0.95/1.20 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 0.95/1.20 tff(2683,plain,
% 0.95/1.20 ($false),
% 0.95/1.20 inference(unit_resolution,[status(thm)],[2682, 112, 2633, 656, 2676])).
% 0.95/1.20 tff(2684,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.95/1.20 tff(2685,plain,
% 0.95/1.20 (~b(s(elem!1), elem!1)),
% 0.95/1.20 inference(unit_resolution,[status(thm)],[2684, 2631, 2629, 2623, 361, 363, 166, 129, 2627, 319])).
% 0.95/1.20 tff(2686,plain,
% 0.95/1.20 (r(s(elem!1), elem!1)),
% 0.95/1.20 inference(unit_resolution,[status(thm)],[939, 2685, 303])).
% 0.95/1.20 tff(2687,plain,
% 0.95/1.20 (((~![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(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 0.95/1.20 inference(rewrite,[status(thm)],[])).
% 0.95/1.20 tff(2688,plain,
% 0.95/1.20 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 0.95/1.20 inference(rewrite,[status(thm)],[])).
% 0.95/1.20 tff(2689,plain,
% 0.95/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 0.95/1.20 inference(monotonicity,[status(thm)],[2688])).
% 0.95/1.20 tff(2690,plain,
% 0.95/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 0.95/1.20 inference(transitivity,[status(thm)],[2689, 2687])).
% 0.95/1.20 tff(2691,plain,
% 0.95/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 0.95/1.20 inference(quant_inst,[status(thm)],[])).
% 0.95/1.20 tff(2692,plain,
% 0.95/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 0.95/1.20 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 0.95/1.20 tff(2693,plain,
% 0.95/1.20 ($false),
% 0.95/1.20 inference(unit_resolution,[status(thm)],[2692, 112, 408, 363, 467])).
% 1.03/1.20 tff(2694,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2695,plain,
% 1.03/1.20 (~r(s(elem!1), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2694, 408, 363])).
% 1.03/1.20 tff(2696,plain,
% 1.03/1.20 (b(s(elem!1), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[498, 2695])).
% 1.03/1.20 tff(2697,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2698,plain,
% 1.03/1.20 (((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2699,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2698])).
% 1.03/1.20 tff(2700,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2699, 2697])).
% 1.03/1.20 tff(2701,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2702,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 1.03/1.20 tff(2703,plain,
% 1.03/1.20 (~b(s(s(z)), s(elem!1))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2702, 224, 2696, 407, 1118])).
% 1.03/1.20 tff(2704,plain,
% 1.03/1.20 (((~![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(z)), 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(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2705,plain,
% 1.03/1.20 (((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2706,plain,
% 1.03/1.20 (((~![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(z)), elem!1)) | (~r(s(elem!1), 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), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2705])).
% 1.03/1.20 tff(2707,plain,
% 1.03/1.20 (((~![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(z)), elem!1)) | (~r(s(elem!1), 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), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2706, 2704])).
% 1.03/1.20 tff(2708,plain,
% 1.03/1.20 ((~![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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2709,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 1.03/1.20 tff(2710,plain,
% 1.03/1.20 (~r(s(s(z)), s(elem!1))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2709, 112, 408, 1047])).
% 1.03/1.20 tff(2711,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.03/1.20 tff(2712,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2532, 68, 2711, 2710, 2703])).
% 1.03/1.20 tff(2713,plain,((~r(s(elem!1), elem!1)) | (s(s(z)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2714,plain,
% 1.03/1.20 (~r(s(s(z)), elem!1)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2713, 2686, 2624, 2623, 2611, 363])).
% 1.03/1.20 tff(2715,plain,
% 1.03/1.20 (b(s(s(z)), elem!1)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1135, 2714, 2616])).
% 1.03/1.20 tff(2716,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2717,plain,
% 1.03/1.20 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2718,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2717])).
% 1.03/1.20 tff(2719,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2718, 2716])).
% 1.03/1.20 tff(2720,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2721,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.03/1.20 tff(2722,plain,
% 1.03/1.20 (~b(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2721, 224, 77, 2631, 2715, 2611])).
% 1.03/1.20 tff(2723,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.03/1.20 tff(2724,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.03/1.20 tff(2725,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[213, 68, 210, 2724, 2723])).
% 1.03/1.20 tff(2726,plain,(r(s(s(z)), s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2727,plain,
% 1.03/1.20 (r(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2726, 2722])).
% 1.03/1.20 tff(2728,plain,
% 1.03/1.20 (~b(s(s(z)), s(s(elem!1)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2606, 2714, 152, 3, 363, 177, 328, 2583])).
% 1.03/1.20 tff(2729,plain,
% 1.03/1.20 (r(s(s(z)), s(s(elem!1)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[265, 2728, 2579])).
% 1.03/1.20 tff(2730,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2731,plain,
% 1.03/1.20 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2732,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2731])).
% 1.03/1.20 tff(2733,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2732, 2730])).
% 1.03/1.20 tff(2734,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2735,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.03/1.20 tff(2736,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2735, 112, 2629, 2729, 2727])).
% 1.03/1.20 tff(2737,plain,((~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2738,plain,
% 1.03/1.20 (~r(elem!1, z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2737, 3, 152, 77, 73, 2578, 160, 149, 2576, 102, 2552])).
% 1.03/1.20 tff(2739,plain,
% 1.03/1.20 (b(elem!1, z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[403, 2738, 11])).
% 1.03/1.20 tff(2740,plain,
% 1.03/1.20 (~(s(s(s(z))) = elem!1)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2437, 2739, 12])).
% 1.03/1.20 tff(2741,plain,
% 1.03/1.20 (b(s(s(s(z))), elem!1)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[374, 2740, 2577])).
% 1.03/1.20 tff(2742,plain,
% 1.03/1.20 (b(s(s(elem!1)), elem!1)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[360, 2578, 353])).
% 1.03/1.20 tff(2743,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2744,plain,
% 1.03/1.20 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2745,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2744])).
% 1.03/1.20 tff(2746,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2745, 2743])).
% 1.03/1.20 tff(2747,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2748,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 1.03/1.20 tff(2749,plain,
% 1.03/1.20 (~b(s(s(elem!1)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2748, 224, 2742, 2552, 2741, 152])).
% 1.03/1.20 tff(2750,plain,
% 1.03/1.20 (r(s(s(elem!1)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[901, 2749])).
% 1.03/1.20 tff(2751,plain,
% 1.03/1.20 (~r(s(z), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[895, 2750, 102])).
% 1.03/1.20 tff(2752,plain,
% 1.03/1.20 (b(s(z), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[194, 2751])).
% 1.03/1.20 tff(2753,plain,
% 1.03/1.20 (~b(elem!1, s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1466, 224, 77, 2739, 2752])).
% 1.03/1.20 tff(2754,plain,
% 1.03/1.20 (r(elem!1, s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1277, 2753, 88])).
% 1.03/1.20 tff(2755,plain,
% 1.03/1.20 (~r(elem!1, s(s(elem!1)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1001, 2754, 2750])).
% 1.03/1.20 tff(2756,plain,
% 1.03/1.20 (b(elem!1, s(s(elem!1)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[558, 2755, 3])).
% 1.03/1.20 tff(2757,plain,
% 1.03/1.20 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2758,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2757])).
% 1.03/1.20 tff(2759,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2758, 1031])).
% 1.03/1.20 tff(2760,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2761,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.03/1.21 tff(2762,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2761, 224, 2756, 2742, 2741, 151])).
% 1.03/1.21 tff(2763,plain,((elem!1 = s(s(elem!1))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | b(s(s(s(z))), z) | b(z, s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2764,plain,
% 1.03/1.21 (elem!1 = s(s(elem!1))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2763, 102, 77, 83, 148, 12, 74, 4])).
% 1.03/1.21 tff(2765,plain,
% 1.03/1.21 (s(s(elem!1)) = elem!1),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2764, 76])).
% 1.03/1.21 tff(2766,plain,
% 1.03/1.21 (s(s(s(s(elem!1)))) = elem!1),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1306, 2764])).
% 1.03/1.21 tff(2767,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.03/1.21 tff(2768,plain,
% 1.03/1.21 (elem!1 = s(s(s(s(elem!1))))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2767])).
% 1.03/1.21 tff(2769,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 1.03/1.21 tff(2770,plain,
% 1.03/1.21 (s(s(z)) = elem!1),
% 1.03/1.21 inference(symmetry,[status(thm)],[2769])).
% 1.03/1.21 tff(2771,plain,
% 1.03/1.21 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2770, 2768])).
% 1.03/1.21 tff(2772,plain,
% 1.03/1.21 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2771])).
% 1.03/1.21 tff(2773,plain,
% 1.03/1.21 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2772])).
% 1.03/1.21 tff(2774,plain,
% 1.03/1.21 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2767, 1296])).
% 1.03/1.21 tff(2775,plain,
% 1.03/1.21 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2774])).
% 1.03/1.21 tff(2776,plain,
% 1.03/1.21 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2775])).
% 1.03/1.21 tff(2777,plain,
% 1.03/1.21 (s(elem!1) = s(z)),
% 1.03/1.21 inference(transitivity,[status(thm)],[164, 2776, 2773, 49])).
% 1.03/1.21 tff(2778,plain,
% 1.03/1.21 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = z)),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2767])).
% 1.03/1.21 tff(2779,plain,
% 1.03/1.21 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = z))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2778])).
% 1.03/1.21 tff(2780,plain,
% 1.03/1.21 (~(elem!1 = z)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1334, 2779])).
% 1.03/1.21 tff(2781,plain,
% 1.03/1.21 (~(s(elem!1) = s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[159, 2780])).
% 1.03/1.21 tff(2782,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2781, 2777])).
% 1.03/1.21 tff(2783,plain,((~(elem!1 = s(s(z)))) | (~(elem!1 = s(s(elem!1)))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2784,plain,
% 1.03/1.21 (~(elem!1 = s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2783, 2766, 2764])).
% 1.03/1.21 tff(2785,plain,
% 1.03/1.21 (elem!1 = s(s(z))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1169, 2587])).
% 1.03/1.21 tff(2786,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 1.03/1.21 tff(2787,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2786, 2785])).
% 1.03/1.21 tff(2788,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2789,plain,
% 1.03/1.21 (~(s(s(z)) = elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2788, 2784])).
% 1.03/1.21 tff(2790,plain,
% 1.03/1.21 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.21 tff(2791,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.03/1.21 inference(symmetry,[status(thm)],[2790])).
% 1.03/1.21 tff(2792,plain,
% 1.03/1.21 (b(s(s(s(z))), elem!1)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[136, 2791])).
% 1.03/1.21 tff(2793,plain,
% 1.03/1.21 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.21 tff(2794,plain,
% 1.03/1.21 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2793])).
% 1.03/1.21 tff(2795,plain,
% 1.03/1.21 (b(elem!1, s(s(s(z))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[148, 2794])).
% 1.03/1.21 tff(2796,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.03/1.21 tff(2797,plain,
% 1.03/1.21 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 1.03/1.21 inference(monotonicity,[status(thm)],[349])).
% 1.03/1.21 tff(2798,plain,
% 1.03/1.21 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2797])).
% 1.03/1.21 tff(2799,plain,
% 1.03/1.21 (r(s(s(z)), s(s(elem!1)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1047, 2798])).
% 1.03/1.21 tff(2800,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[260, 2799])).
% 1.03/1.21 tff(2801,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(elem!1))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2802,plain,
% 1.03/1.21 (~r(s(s(z)), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2801, 2584, 349])).
% 1.03/1.21 tff(2803,plain,
% 1.03/1.21 (b(s(s(z)), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1135, 2802, 2796])).
% 1.03/1.21 tff(2804,plain,
% 1.03/1.21 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2412, 2803, 685, 787])).
% 1.03/1.21 tff(2805,plain,
% 1.03/1.21 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[249, 2804])).
% 1.03/1.21 tff(2806,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2807,plain,
% 1.03/1.21 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2808,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2807])).
% 1.03/1.21 tff(2809,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.03/1.21 tff(2810,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2811,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.03/1.21 tff(2812,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2811, 112, 2805, 689, 268])).
% 1.03/1.21 tff(2813,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(s(z)) = elem!1) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2814,plain,
% 1.03/1.21 (~r(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2813, 2795, 101, 2792, 2789, 2765, 102])).
% 1.03/1.21 tff(2815,plain,
% 1.03/1.21 (b(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[281, 2814])).
% 1.03/1.21 tff(2816,plain,
% 1.03/1.21 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.21 tff(2817,plain,
% 1.03/1.21 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.03/1.21 inference(symmetry,[status(thm)],[2816])).
% 1.03/1.21 tff(2818,plain,
% 1.03/1.21 (r(elem!1, z)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[102, 2817])).
% 1.03/1.21 tff(2819,plain,
% 1.03/1.21 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.21 tff(2820,plain,
% 1.03/1.21 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.21 tff(2821,plain,
% 1.03/1.21 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2820])).
% 1.03/1.21 tff(2822,plain,
% 1.03/1.21 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.03/1.21 inference(transitivity,[status(thm)],[2821, 284])).
% 1.03/1.21 tff(2823,plain,
% 1.03/1.21 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2822])).
% 1.03/1.21 tff(2824,plain,
% 1.03/1.21 (~(s(s(s(z))) = elem!1)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2, 2823])).
% 1.03/1.21 tff(2825,plain,
% 1.03/1.21 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.21 tff(2826,plain,
% 1.03/1.21 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.21 tff(2827,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.03/1.21 inference(symmetry,[status(thm)],[2826])).
% 1.03/1.21 tff(2828,plain,
% 1.03/1.21 (b(s(s(s(z))), elem!1)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[295, 2827])).
% 1.03/1.21 tff(2829,plain,
% 1.03/1.21 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1300])).
% 1.03/1.21 tff(2830,plain,
% 1.03/1.21 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.03/1.21 inference(symmetry,[status(thm)],[2829])).
% 1.03/1.21 tff(2831,plain,
% 1.03/1.21 (s(s(s(s(elem!1)))) = elem!1),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1306, 1296])).
% 1.03/1.21 tff(2832,plain,
% 1.03/1.21 (~(elem!1 = s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2783, 2831, 1296])).
% 1.03/1.21 tff(2833,plain,
% 1.03/1.21 (~(s(s(z)) = elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2788, 2832])).
% 1.03/1.21 tff(2834,plain,
% 1.03/1.21 (s(s(elem!1)) = elem!1),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1296, 76])).
% 1.03/1.21 tff(2835,plain,
% 1.03/1.21 (~r(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2813, 685, 689, 787, 2833, 2834, 102])).
% 1.03/1.21 tff(2836,plain,
% 1.03/1.21 (b(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[281, 2835])).
% 1.03/1.21 tff(2837,plain,
% 1.03/1.21 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.21 tff(2838,plain,
% 1.03/1.21 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.03/1.21 inference(symmetry,[status(thm)],[2837])).
% 1.03/1.21 tff(2839,plain,
% 1.03/1.21 (r(elem!1, z)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[102, 2838])).
% 1.03/1.21 tff(2840,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2639, 112, 363, 179, 416])).
% 1.03/1.21 tff(2841,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2842,plain,
% 1.03/1.21 (~r(s(z), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2841, 416, 2839])).
% 1.03/1.21 tff(2843,plain,
% 1.03/1.21 (b(s(z), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[194, 2842])).
% 1.03/1.21 tff(2844,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.03/1.21 tff(2845,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[230, 224, 77, 1, 1118, 2844])).
% 1.03/1.21 tff(2846,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2847,plain,
% 1.03/1.21 (~b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2846, 2843, 77, 2836])).
% 1.03/1.21 tff(2848,plain,
% 1.03/1.21 (r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2726, 2847])).
% 1.03/1.21 tff(2849,plain,
% 1.03/1.21 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.21 tff(2850,plain,
% 1.03/1.21 (r(s(z), s(s(elem!1)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[416, 2849])).
% 1.03/1.21 tff(2851,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.03/1.21 tff(2852,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2735, 112, 656, 267, 2851])).
% 1.03/1.21 tff(2853,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2854,plain,
% 1.03/1.21 (~r(s(s(z)), s(s(elem!1)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2853, 2850, 2848])).
% 1.03/1.21 tff(2855,plain,
% 1.03/1.21 (~r(s(s(z)), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2801, 2854, 2834])).
% 1.03/1.21 tff(2856,plain,
% 1.03/1.21 (b(s(s(z)), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1135, 2855, 2833])).
% 1.03/1.21 tff(2857,plain,
% 1.03/1.21 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2412, 2856, 685, 787])).
% 1.03/1.21 tff(2858,plain,
% 1.03/1.21 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[249, 2857])).
% 1.03/1.21 tff(2859,plain,
% 1.03/1.21 (~r(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1104, 112, 2858, 689])).
% 1.03/1.21 tff(2860,plain,
% 1.03/1.21 (b(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1088, 2859])).
% 1.03/1.21 tff(2861,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.03/1.21 tff(2862,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2863,plain,
% 1.03/1.21 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2864,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2863])).
% 1.03/1.21 tff(2865,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2864, 2862])).
% 1.03/1.21 tff(2866,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2867,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 1.03/1.21 tff(2868,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2867, 224, 344, 2861, 1109, 2191])).
% 1.03/1.21 tff(2869,plain,((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2870,plain,
% 1.03/1.21 (~b(elem!1, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2869, 2860, 344, 2856])).
% 1.03/1.21 tff(2871,plain,
% 1.03/1.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2872,plain,
% 1.03/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2873,plain,
% 1.03/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.03/1.21 tff(2874,plain,
% 1.03/1.21 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2873, 68])).
% 1.03/1.21 tff(2875,plain,
% 1.03/1.21 (r(elem!1, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2874, 2870, 2832])).
% 1.03/1.21 tff(2876,plain,
% 1.03/1.21 (r(s(s(elem!1)), s(s(z)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2875, 2830])).
% 1.03/1.21 tff(2877,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2878,plain,
% 1.03/1.21 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2879,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2878])).
% 1.03/1.21 tff(2880,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2879, 2877])).
% 1.03/1.21 tff(2881,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2882,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2881, 2880])).
% 1.03/1.21 tff(2883,plain,
% 1.03/1.21 (~b(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2882, 224, 2843, 2860, 2836])).
% 1.03/1.21 tff(2884,plain,
% 1.03/1.21 (r(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1071, 2883])).
% 1.03/1.21 tff(2885,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2886,plain,
% 1.03/1.21 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2887,plain,
% 1.03/1.21 (((~![X0: $i, 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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2886])).
% 1.03/1.21 tff(2888,plain,
% 1.03/1.21 (((~![X0: $i, 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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2887, 2885])).
% 1.03/1.21 tff(2889,plain,
% 1.03/1.21 ((~![X0: $i, 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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2890,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 1.03/1.21 tff(2891,plain,
% 1.03/1.21 (~r(s(s(elem!1)), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2890, 112, 102, 2850, 2884])).
% 1.03/1.21 tff(2892,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2891, 2876])).
% 1.03/1.21 tff(2893,plain,((~r(s(z), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2894,plain,
% 1.03/1.21 (~r(s(z), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2893, 344, 102, 1296, 689, 685, 2828, 77])).
% 1.03/1.21 tff(2895,plain,
% 1.03/1.21 (b(s(z), elem!1)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[454, 2894, 149])).
% 1.03/1.21 tff(2896,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.03/1.21 tff(2897,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2898,plain,
% 1.03/1.21 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2899,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2898])).
% 1.03/1.21 tff(2900,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.03/1.22 tff(2901,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2902,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.03/1.22 tff(2903,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2902, 224, 77, 684, 2896, 344])).
% 1.03/1.22 tff(2904,plain,((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2905,plain,
% 1.03/1.22 (~b(elem!1, s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2904, 2895, 77, 344])).
% 1.03/1.22 tff(2906,plain,
% 1.03/1.22 (r(elem!1, s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1277, 2905, 88])).
% 1.03/1.22 tff(2907,plain,
% 1.03/1.22 (r(s(s(elem!1)), s(z))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2906, 2825])).
% 1.03/1.22 tff(2908,plain,
% 1.03/1.22 (~r(s(s(z)), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2813, 685, 689, 2828, 2833, 2834, 102])).
% 1.03/1.22 tff(2909,plain,
% 1.03/1.22 (b(s(s(z)), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[281, 2908])).
% 1.03/1.22 tff(2910,plain,
% 1.03/1.22 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.22 tff(2911,plain,
% 1.03/1.22 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.03/1.22 inference(symmetry,[status(thm)],[2910])).
% 1.03/1.22 tff(2912,plain,
% 1.03/1.22 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2911])).
% 1.03/1.22 tff(2913,plain,
% 1.03/1.22 (~r(elem!1, s(s(s(z))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[312, 2912])).
% 1.03/1.22 tff(2914,plain,
% 1.03/1.22 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.22 tff(2915,plain,
% 1.03/1.22 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 1.03/1.22 inference(symmetry,[status(thm)],[2914])).
% 1.03/1.22 tff(2916,plain,
% 1.03/1.22 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2915])).
% 1.03/1.22 tff(2917,plain,
% 1.03/1.22 (~r(s(s(s(z))), elem!1)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[294, 2916])).
% 1.03/1.22 tff(2918,plain,
% 1.03/1.22 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.22 tff(2919,plain,
% 1.03/1.22 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 1.03/1.22 inference(symmetry,[status(thm)],[2918])).
% 1.03/1.22 tff(2920,plain,
% 1.03/1.22 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2919])).
% 1.03/1.22 tff(2921,plain,
% 1.03/1.22 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.03/1.22 inference(bind,[status(th)],[])).
% 1.03/1.22 tff(2922,plain,
% 1.03/1.22 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.03/1.22 inference(quant_intro,[status(thm)],[2921])).
% 1.03/1.22 tff(2923,plain,
% 1.03/1.22 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2924,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.03/1.22 tff(2925,plain,
% 1.03/1.22 (![X: $i] : (~b(X, X))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 1.03/1.22 tff(2926,plain,(
% 1.03/1.22 ![X: $i] : (~b(X, X))),
% 1.03/1.22 inference(skolemize,[status(sab)],[2925])).
% 1.03/1.22 tff(2927,plain,
% 1.03/1.22 (![X: $i] : (~b(X, X))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2926, 2922])).
% 1.03/1.22 tff(2928,plain,
% 1.03/1.22 ((~![X: $i] : (~b(X, X))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2929,plain,
% 1.03/1.22 (~b(s(s(elem!1)), s(s(elem!1)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2928, 2927])).
% 1.03/1.22 tff(2930,plain,
% 1.03/1.22 (~b(s(s(elem!1)), elem!1)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2929, 2920])).
% 1.03/1.22 tff(2931,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.03/1.22 tff(2932,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.03/1.22 tff(2933,plain,
% 1.03/1.22 (b(s(s(s(z))), elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[374, 362, 2932])).
% 1.03/1.22 tff(2934,plain,
% 1.03/1.22 (b(elem!1, s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[388, 377, 2440])).
% 1.03/1.22 tff(2935,plain,
% 1.03/1.22 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2936,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2935])).
% 1.03/1.22 tff(2937,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2936, 709])).
% 1.03/1.22 tff(2938,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2939,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 1.03/1.22 tff(2940,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2939, 224, 684, 685, 1090, 787])).
% 1.03/1.22 tff(2941,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2942,plain,
% 1.03/1.22 (~b(s(z), elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2941, 2934, 1090, 2933])).
% 1.03/1.22 tff(2943,plain,
% 1.03/1.22 (s(z) = elem!1),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[454, 2942, 2931])).
% 1.03/1.22 tff(2944,plain,
% 1.03/1.22 (s(s(z)) = s(elem!1)),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2943])).
% 1.03/1.22 tff(2945,plain,
% 1.03/1.22 (s(s(s(z))) = s(s(elem!1))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2944])).
% 1.03/1.22 tff(2946,plain,
% 1.03/1.22 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2945])).
% 1.03/1.22 tff(2947,plain,
% 1.03/1.22 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.03/1.22 inference(symmetry,[status(thm)],[2946])).
% 1.03/1.22 tff(2948,plain,
% 1.03/1.22 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2947])).
% 1.03/1.22 tff(2949,plain,
% 1.03/1.22 (~b(s(s(s(z))), elem!1)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[354, 2948])).
% 1.03/1.22 tff(2950,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2933, 2949])).
% 1.03/1.22 tff(2951,plain,((s(s(s(z))) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2952,plain,
% 1.03/1.22 (~b(s(z), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2951, 2894, 2930, 362, 2917, 2913])).
% 1.03/1.22 tff(2953,plain,
% 1.03/1.22 (r(s(z), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[175, 2952])).
% 1.03/1.22 tff(2954,plain,
% 1.03/1.22 (~r(s(z), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[187, 2953, 177])).
% 1.03/1.22 tff(2955,plain,
% 1.03/1.22 (b(s(z), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[194, 2954])).
% 1.03/1.22 tff(2956,plain,
% 1.03/1.22 (~b(s(s(z)), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2846, 2955, 77, 2909])).
% 1.03/1.22 tff(2957,plain,
% 1.03/1.22 (r(s(s(z)), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2726, 2956])).
% 1.03/1.22 tff(2958,plain,
% 1.03/1.22 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2412, 1109, 787, 685])).
% 1.03/1.22 tff(2959,plain,
% 1.03/1.22 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[249, 2958])).
% 1.03/1.22 tff(2960,plain,
% 1.03/1.22 (~r(z, s(s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1104, 112, 2959, 689])).
% 1.03/1.22 tff(2961,plain,
% 1.03/1.22 (b(z, s(s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1088, 2960])).
% 1.03/1.22 tff(2962,plain,
% 1.03/1.22 (~r(s(s(z)), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2811, 112, 2959, 689])).
% 1.03/1.22 tff(2963,plain,
% 1.03/1.22 (b(s(s(z)), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[234, 68, 42, 2962])).
% 1.03/1.22 tff(2964,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2965,plain,
% 1.03/1.22 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2966,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2965])).
% 1.03/1.22 tff(2967,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2966, 2964])).
% 1.03/1.22 tff(2968,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2969,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 1.03/1.22 tff(2970,plain,
% 1.03/1.22 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2969, 224, 1, 344, 1109])).
% 1.03/1.22 tff(2971,plain,
% 1.03/1.22 (~b(s(s(z)), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2970, 2963])).
% 1.03/1.22 tff(2972,plain,
% 1.03/1.22 (r(s(s(z)), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[213, 68, 210, 2971])).
% 1.03/1.22 tff(2973,plain,
% 1.03/1.22 (((~![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(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2974,plain,
% 1.03/1.22 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2975,plain,
% 1.03/1.22 (((~![X0: $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(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2974])).
% 1.03/1.22 tff(2976,plain,
% 1.03/1.22 (((~![X0: $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(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2975, 2973])).
% 1.03/1.22 tff(2977,plain,
% 1.03/1.22 ((~![X0: $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(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2978,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 1.03/1.22 tff(2979,plain,
% 1.03/1.22 (~r(elem!1, s(s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2978, 112, 993, 2972])).
% 1.03/1.22 tff(2980,plain,
% 1.03/1.22 (b(elem!1, s(s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2874, 2979, 2786])).
% 1.03/1.22 tff(2981,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2867, 224, 344, 2980, 1109, 2961])).
% 1.03/1.22 tff(2982,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2983,plain,
% 1.03/1.22 (~b(s(s(z)), elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2982, 2955, 685, 344, 2828, 689, 2906, 2832])).
% 1.03/1.22 tff(2984,plain,
% 1.03/1.22 (r(s(s(z)), elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1135, 2983, 2833])).
% 1.03/1.22 tff(2985,plain,
% 1.03/1.22 (r(s(s(z)), s(s(elem!1)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2801, 2984, 2834])).
% 1.03/1.22 tff(2986,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2987,plain,
% 1.03/1.22 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2988,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2987])).
% 1.03/1.22 tff(2989,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2988, 2986])).
% 1.03/1.22 tff(2990,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2991,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 1.03/1.22 tff(2992,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2991, 112, 887, 267, 2851])).
% 1.03/1.22 tff(2993,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2994,plain,
% 1.03/1.22 (~r(s(s(elem!1)), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2993, 2985, 2957])).
% 1.03/1.22 tff(2995,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2994, 2907])).
% 1.03/1.22 tff(2996,plain,((~b(z, elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(z)) | (s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2997,plain,
% 1.03/1.22 (~b(z, elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2996, 2764, 2795, 101, 77, 73, 83, 2824, 102])).
% 1.03/1.22 tff(2998,plain,
% 1.03/1.22 (r(z, elem!1)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[289, 2997, 4])).
% 1.03/1.22 tff(2999,plain,
% 1.03/1.22 (r(z, s(s(elem!1)))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2998, 2819])).
% 1.03/1.22 tff(3000,plain,
% 1.03/1.22 (~r(s(s(s(z))), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[932, 112, 179, 177])).
% 1.03/1.22 tff(3001,plain,
% 1.03/1.22 (b(s(s(s(z))), s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[925, 3000])).
% 1.03/1.22 tff(3002,plain,
% 1.03/1.22 (b(elem!1, s(z))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1277, 2651, 88])).
% 1.03/1.22 tff(3003,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(3004,plain,
% 1.03/1.22 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(3005,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3004])).
% 1.03/1.22 tff(3006,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[3005, 3003])).
% 1.03/1.22 tff(3007,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(3008,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.03/1.22 tff(3009,plain,
% 1.03/1.22 (~b(elem!1, s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[3008, 224, 3002, 1090, 3001])).
% 1.03/1.22 tff(3010,plain,
% 1.03/1.22 (elem!1 = s(s(s(z)))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[388, 3009, 384])).
% 1.03/1.22 tff(3011,plain,
% 1.03/1.22 (s(elem!1) = s(s(s(s(z))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3010])).
% 1.03/1.22 tff(3012,plain,
% 1.03/1.22 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3011])).
% 1.03/1.22 tff(3013,plain,
% 1.03/1.22 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3012])).
% 1.03/1.22 tff(3014,plain,
% 1.03/1.22 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3013])).
% 1.03/1.22 tff(3015,plain,
% 1.03/1.22 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3014])).
% 1.03/1.22 tff(3016,plain,
% 1.03/1.22 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3010])).
% 1.03/1.22 tff(3017,plain,
% 1.03/1.22 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3010])).
% 1.03/1.22 tff(3018,plain,
% 1.03/1.22 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[3017, 304])).
% 1.03/1.22 tff(3019,plain,
% 1.03/1.22 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3018])).
% 1.03/1.22 tff(3020,plain,
% 1.03/1.22 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3019])).
% 1.03/1.22 tff(3021,plain,
% 1.03/1.22 (~(elem!1 = s(s(elem!1)))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[311, 3020])).
% 1.03/1.22 tff(3022,plain,
% 1.03/1.22 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3010, 3012])).
% 1.03/1.22 tff(3023,plain,
% 1.03/1.22 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3022])).
% 1.03/1.22 tff(3024,plain,
% 1.03/1.22 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3023])).
% 1.03/1.22 tff(3025,plain,
% 1.03/1.22 (s(elem!1) = s(s(s(s(z))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2471])).
% 1.03/1.22 tff(3026,plain,
% 1.03/1.22 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3025])).
% 1.03/1.22 tff(3027,plain,
% 1.03/1.22 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3026])).
% 1.03/1.22 tff(3028,plain,
% 1.03/1.22 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[3027])).
% 1.03/1.22 tff(3029,plain,
% 1.03/1.22 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.03/1.22 inference(symmetry,[status(thm)],[3028])).
% 1.03/1.22 tff(3030,plain,
% 1.03/1.22 (r(z, s(s(s(s(s(z))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[293, 3029])).
% 1.03/1.22 tff(3031,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.03/1.22 tff(3032,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[3031, 3030])).
% 1.03/1.22 tff(3033,plain,(r(z, s(s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(3034,plain,
% 1.03/1.22 (r(z, s(s(s(s(s(z))))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[3033, 3010, 293])).
% 1.03/1.22 tff(3035,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.03/1.22 tff(3036,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.03/1.22 tff(3037,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(3038,plain,
% 1.03/1.22 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(3039,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3038])).
% 1.03/1.23 tff(3040,plain,
% 1.03/1.23 (((~![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(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3039, 3037])).
% 1.03/1.23 tff(3041,plain,
% 1.03/1.23 ((~![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(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3042,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 1.03/1.23 tff(3043,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3042, 112, 689, 3036, 3035])).
% 1.03/1.23 tff(3044,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3045,plain,
% 1.03/1.23 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3044, 3034, 689])).
% 1.03/1.23 tff(3046,plain,
% 1.03/1.23 (~r(elem!1, s(s(elem!1)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3045, 3024])).
% 1.03/1.23 tff(3047,plain,
% 1.03/1.23 (b(elem!1, s(s(elem!1)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[558, 3046, 3021])).
% 1.03/1.23 tff(3048,plain,
% 1.03/1.23 (b(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3047, 3016])).
% 1.03/1.23 tff(3049,plain,
% 1.03/1.23 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3048, 3015])).
% 1.03/1.23 tff(3050,plain,
% 1.03/1.23 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3012])).
% 1.03/1.23 tff(3051,plain,
% 1.03/1.23 (b(s(z), elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[454, 2640, 149])).
% 1.03/1.23 tff(3052,plain,
% 1.03/1.23 (~b(z, elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2904, 3051, 77, 3002])).
% 1.03/1.23 tff(3053,plain,
% 1.03/1.23 (r(z, elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[289, 3052, 4])).
% 1.03/1.23 tff(3054,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3055,plain,
% 1.03/1.23 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3056,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3055])).
% 1.03/1.23 tff(3057,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3056, 3054])).
% 1.03/1.23 tff(3058,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3059,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 1.03/1.23 tff(3060,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3059, 112, 179, 656, 688, 293])).
% 1.03/1.23 tff(3061,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3062,plain,
% 1.03/1.23 (~r(s(z), s(s(elem!1)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3061, 3053, 179, 293])).
% 1.03/1.23 tff(3063,plain,
% 1.03/1.23 (b(s(z), s(s(elem!1)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[653, 3062])).
% 1.03/1.23 tff(3064,plain,
% 1.03/1.23 (b(s(z), s(s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3063, 3050])).
% 1.03/1.23 tff(3065,plain,
% 1.03/1.23 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3013])).
% 1.03/1.23 tff(3066,plain,
% 1.03/1.23 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3065])).
% 1.03/1.23 tff(3067,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3068,plain,
% 1.03/1.23 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3069,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3068])).
% 1.03/1.23 tff(3070,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3069, 3067])).
% 1.03/1.23 tff(3071,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3072,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 1.03/1.23 tff(3073,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3072, 112, 827, 689, 293])).
% 1.03/1.23 tff(3074,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3075,plain,
% 1.03/1.23 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3074, 293, 689])).
% 1.03/1.23 tff(3076,plain,
% 1.03/1.23 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[147, 3075, 311])).
% 1.03/1.23 tff(3077,plain,
% 1.03/1.23 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3076, 3066])).
% 1.03/1.23 tff(3078,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(z))))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3079,plain,
% 1.03/1.23 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(s(s(s(z))))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3080,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(s(z)))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3079])).
% 1.03/1.23 tff(3081,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(s(z))))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3080, 3078])).
% 1.03/1.23 tff(3082,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3083,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 1.03/1.23 tff(3084,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3083, 224, 1090, 3077, 3064, 3049])).
% 1.03/1.23 tff(3085,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (z = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3086,plain,
% 1.03/1.23 (~b(s(z), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3085, 179, 689, 293, 363, 4, 77, 177, 88])).
% 1.03/1.23 tff(3087,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[175, 3086, 2082])).
% 1.03/1.23 tff(3088,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (z = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3089,plain,
% 1.03/1.23 (~r(s(z), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3088, 2999, 77, 2818, 4, 101, 73, 83])).
% 1.03/1.23 tff(3090,plain,
% 1.03/1.23 (b(s(z), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[194, 3089])).
% 1.03/1.23 tff(3091,plain,
% 1.03/1.23 (~b(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2846, 3090, 77, 2815])).
% 1.03/1.23 tff(3092,plain,
% 1.03/1.23 (r(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2726, 3091])).
% 1.03/1.23 tff(3093,plain,
% 1.03/1.23 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.23 tff(3094,plain,
% 1.03/1.23 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3093])).
% 1.03/1.23 tff(3095,plain,
% 1.03/1.23 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3094])).
% 1.03/1.23 tff(3096,plain,
% 1.03/1.23 (~r(elem!1, s(s(s(z))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[143, 3095])).
% 1.03/1.23 tff(3097,plain,
% 1.03/1.23 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2764])).
% 1.03/1.23 tff(3098,plain,
% 1.03/1.23 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 1.03/1.23 inference(symmetry,[status(thm)],[3097])).
% 1.03/1.23 tff(3099,plain,
% 1.03/1.23 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3098])).
% 1.03/1.23 tff(3100,plain,
% 1.03/1.23 (~r(s(s(s(z))), elem!1)),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[119, 3099])).
% 1.03/1.23 tff(3101,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1300])).
% 1.03/1.23 tff(3102,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3101])).
% 1.03/1.23 tff(3103,plain,
% 1.03/1.23 (elem!1 = s(s(elem!1))),
% 1.03/1.23 inference(symmetry,[status(thm)],[349])).
% 1.03/1.23 tff(3104,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.03/1.23 tff(3105,plain,
% 1.03/1.23 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3104, 3103])).
% 1.03/1.23 tff(3106,plain,
% 1.03/1.23 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3105])).
% 1.03/1.23 tff(3107,plain,
% 1.03/1.23 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3106])).
% 1.03/1.23 tff(3108,plain,
% 1.03/1.23 (s(elem!1) = s(s(s(z)))),
% 1.03/1.23 inference(transitivity,[status(thm)],[164, 3107, 1223])).
% 1.03/1.23 tff(3109,plain,
% 1.03/1.23 (elem!1 = s(s(elem!1))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[352, 349])).
% 1.03/1.23 tff(3110,plain,
% 1.03/1.23 (s(s(s(s(elem!1)))) = elem!1),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1306, 3109])).
% 1.03/1.23 tff(3111,plain,
% 1.03/1.23 (~(elem!1 = s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2783, 3110, 3109])).
% 1.03/1.23 tff(3112,plain,
% 1.03/1.23 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.03/1.23 inference(transitivity,[status(thm)],[778, 1297])).
% 1.03/1.23 tff(3113,plain,
% 1.03/1.23 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3112])).
% 1.03/1.23 tff(3114,plain,
% 1.03/1.23 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3113])).
% 1.03/1.23 tff(3115,plain,
% 1.03/1.23 (elem!1 = s(s(z))),
% 1.03/1.23 inference(transitivity,[status(thm)],[1296, 1376, 3114, 31])).
% 1.03/1.23 tff(3116,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2786, 3115])).
% 1.03/1.23 tff(3117,plain,((~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(z))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3118,plain,
% 1.03/1.23 (~(s(elem!1) = s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3117, 3111, 3109])).
% 1.03/1.23 tff(3119,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3118, 3108])).
% 1.03/1.23 tff(3120,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(3121,plain,
% 1.03/1.23 (~(s(s(s(s(z)))) = elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3120, 2834])).
% 1.03/1.23 tff(3122,plain,
% 1.03/1.23 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1300])).
% 1.03/1.23 tff(3123,plain,
% 1.03/1.23 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3122])).
% 1.03/1.23 tff(3124,plain,
% 1.03/1.23 (b(s(s(s(z))), elem!1)),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[968, 2827])).
% 1.03/1.23 tff(3125,plain,
% 1.03/1.23 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.23 tff(3126,plain,
% 1.03/1.23 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.03/1.23 inference(symmetry,[status(thm)],[3125])).
% 1.03/1.23 tff(3127,plain,
% 1.03/1.23 (b(elem!1, s(s(s(z))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[152, 3126])).
% 1.03/1.23 tff(3128,plain,
% 1.03/1.23 (~r(s(s(z)), elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2801, 260, 2834])).
% 1.03/1.23 tff(3129,plain,
% 1.03/1.23 (b(s(s(z)), elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1135, 3128, 2833])).
% 1.03/1.23 tff(3130,plain,
% 1.03/1.23 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2412, 3129, 3127, 3124])).
% 1.03/1.23 tff(3131,plain,
% 1.03/1.23 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[249, 3130])).
% 1.03/1.23 tff(3132,plain,
% 1.03/1.23 (~r(s(z), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[243, 3131, 77, 1, 177])).
% 1.03/1.23 tff(3133,plain,
% 1.03/1.23 (b(s(z), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[175, 3132])).
% 1.03/1.23 tff(3134,plain,
% 1.03/1.23 (r(s(z), elem!1)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2951, 3133, 2930, 362, 2932, 2440])).
% 1.03/1.23 tff(3135,plain,
% 1.03/1.23 (r(s(z), s(s(elem!1)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3134, 2849])).
% 1.03/1.23 tff(3136,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.03/1.23 tff(3137,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3138,plain,
% 1.03/1.23 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3139,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[3138])).
% 1.03/1.23 tff(3140,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[3139, 3137])).
% 1.03/1.23 tff(3141,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3142,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[3141, 3140])).
% 1.03/1.23 tff(3143,plain,
% 1.03/1.23 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3142, 112, 689, 293])).
% 1.03/1.23 tff(3144,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[3143, 3136])).
% 1.03/1.23 tff(3145,plain,
% 1.03/1.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(3146,plain,
% 1.03/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(3147,plain,
% 1.03/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.03/1.24 tff(3148,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 3144])).
% 1.03/1.24 tff(3149,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3150,plain,
% 1.03/1.24 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3151,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3150])).
% 1.03/1.24 tff(3152,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.03/1.24 tff(3153,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3154,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.03/1.24 tff(3155,plain,
% 1.03/1.24 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3154, 112, 656])).
% 1.03/1.24 tff(3156,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3155, 3136])).
% 1.03/1.24 tff(3157,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.03/1.24 tff(3158,plain,
% 1.03/1.24 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3157])).
% 1.03/1.24 tff(3159,plain,
% 1.03/1.24 (s(s(s(z))) = z),
% 1.03/1.24 inference(transitivity,[status(thm)],[1679, 3158, 27])).
% 1.03/1.24 tff(3160,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[58, 3159])).
% 1.03/1.24 tff(3161,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(3162,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.03/1.24 tff(3163,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.03/1.24 tff(3164,plain,
% 1.03/1.24 (((~![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)))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3165,plain,
% 1.03/1.24 ((~![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)))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3166,plain,
% 1.03/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.03/1.24 tff(3167,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3166, 68, 3163, 3162, 3161])).
% 1.03/1.24 tff(3168,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(3169,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3168, 3156])).
% 1.03/1.24 tff(3170,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3171,plain,
% 1.03/1.24 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3172,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3171])).
% 1.03/1.24 tff(3173,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3172, 3170])).
% 1.03/1.24 tff(3174,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3175,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3174, 3173])).
% 1.03/1.24 tff(3176,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3175, 224, 77, 1, 3169, 3148])).
% 1.03/1.24 tff(3177,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(3178,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3177, 3135, 1, 689, 293, 77])).
% 1.03/1.24 tff(3179,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), elem!1)),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3178, 3123])).
% 1.03/1.24 tff(3180,plain,
% 1.03/1.24 (((~![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))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3181,plain,
% 1.03/1.24 ((~![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))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3182,plain,
% 1.03/1.24 ((~![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)),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 1.03/1.24 tff(3183,plain,
% 1.03/1.24 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3182, 68])).
% 1.03/1.24 tff(3184,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), elem!1)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3183, 3179, 3121])).
% 1.03/1.24 tff(3185,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3184, 3102])).
% 1.03/1.24 tff(3186,plain,
% 1.03/1.24 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.24 tff(3187,plain,
% 1.03/1.24 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2829])).
% 1.03/1.24 tff(3188,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.03/1.24 tff(3189,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3190,plain,
% 1.03/1.24 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3191,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3190])).
% 1.03/1.24 tff(3192,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3191, 3189])).
% 1.03/1.24 tff(3193,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3194,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3193, 3192])).
% 1.03/1.24 tff(3195,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3194, 112, 196, 3188, 2851])).
% 1.03/1.24 tff(3196,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(3197,plain,
% 1.03/1.24 (~r(s(s(s(z))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3196, 3131, 2851])).
% 1.03/1.24 tff(3198,plain,
% 1.03/1.24 (b(s(s(s(z))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[925, 3197])).
% 1.03/1.24 tff(3199,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3200,plain,
% 1.03/1.24 (((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3201,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3200])).
% 1.03/1.24 tff(3202,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3201, 3199])).
% 1.03/1.24 tff(3203,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3204,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3203, 3202])).
% 1.03/1.24 tff(3205,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3204, 224, 1241, 1090, 152, 560])).
% 1.03/1.24 tff(3206,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(3207,plain,
% 1.03/1.24 (~b(s(s(elem!1)), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3206, 3198, 3133, 152])).
% 1.03/1.24 tff(3208,plain,
% 1.03/1.24 (r(s(s(elem!1)), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[901, 3207])).
% 1.03/1.24 tff(3209,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3210,plain,
% 1.03/1.24 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3211,plain,
% 1.03/1.24 (((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3210])).
% 1.03/1.24 tff(3212,plain,
% 1.03/1.24 (((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3211, 3209])).
% 1.03/1.24 tff(3213,plain,
% 1.03/1.24 ((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3214,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 1.03/1.24 tff(3215,plain,
% 1.03/1.24 (~r(s(s(elem!1)), s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3214, 112, 3208, 3131, 2851])).
% 1.03/1.24 tff(3216,plain,
% 1.03/1.24 (~r(elem!1, s(s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3215, 3187])).
% 1.03/1.24 tff(3217,plain,
% 1.03/1.24 (b(elem!1, s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2874, 3216, 2832])).
% 1.03/1.24 tff(3218,plain,
% 1.03/1.24 (b(s(s(elem!1)), s(s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3217, 3186])).
% 1.03/1.24 tff(3219,plain,
% 1.03/1.24 (b(s(s(z)), s(s(elem!1)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[265, 260, 259])).
% 1.03/1.24 tff(3220,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3221,plain,
% 1.03/1.24 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(3222,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[3221])).
% 1.03/1.24 tff(3223,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[3222, 3220])).
% 1.03/1.24 tff(3224,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(3225,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 1.03/1.24 tff(3226,plain,
% 1.03/1.24 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3225, 224, 3219, 3218])).
% 1.03/1.24 tff(3227,plain,
% 1.03/1.24 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[3226, 3185])).
% 1.03/1.24 tff(3228,plain,
% 1.03/1.24 (((~![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))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3229,plain,
% 1.03/1.25 ((~![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))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3230,plain,
% 1.03/1.25 ((~![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)))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 1.03/1.25 tff(3231,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 3227])).
% 1.03/1.25 tff(3232,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3233,plain,
% 1.03/1.25 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3234,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3233])).
% 1.03/1.25 tff(3235,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3234, 3232])).
% 1.03/1.25 tff(3236,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3237,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 1.03/1.25 tff(3238,plain,
% 1.03/1.25 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3237, 224, 152, 968])).
% 1.03/1.25 tff(3239,plain,
% 1.03/1.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3238, 3185])).
% 1.03/1.25 tff(3240,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.03/1.25 tff(3241,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.03/1.25 tff(3242,plain,
% 1.03/1.25 (s(s(s(z))) = s(s(s(s(z))))),
% 1.03/1.25 inference(symmetry,[status(thm)],[3241])).
% 1.03/1.25 tff(3243,plain,
% 1.03/1.25 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3242])).
% 1.03/1.25 tff(3244,plain,
% 1.03/1.25 (s(s(z)) = s(s(s(z)))),
% 1.03/1.25 inference(transitivity,[status(thm)],[32, 3243, 1223])).
% 1.03/1.25 tff(3245,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[55, 3244])).
% 1.03/1.25 tff(3246,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(3247,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.03/1.25 tff(3248,plain,
% 1.03/1.25 (((~![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)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3249,plain,
% 1.03/1.25 ((~![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)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3250,plain,
% 1.03/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.03/1.25 tff(3251,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3250, 68, 3247, 3246, 3240])).
% 1.03/1.25 tff(3252,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(3253,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3252, 3239])).
% 1.03/1.25 tff(3254,plain,
% 1.03/1.25 (((~![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(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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3255,plain,
% 1.03/1.25 (((~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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3256,plain,
% 1.03/1.25 (((~![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(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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3255])).
% 1.03/1.25 tff(3257,plain,
% 1.03/1.25 (((~![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(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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3256, 3254])).
% 1.03/1.25 tff(3258,plain,
% 1.03/1.25 ((~![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(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3259,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 1.03/1.25 tff(3260,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3259, 112, 3131, 3253, 3231])).
% 1.03/1.25 tff(3261,plain,(r(s(s(z)), s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z)))) | (~r(s(s(s(z))), z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(3262,plain,
% 1.03/1.25 (r(s(s(z)), s(s(elem!1)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3261, 148, 136, 2764, 3090, 101, 2999, 77, 3092, 2824, 3100, 3096, 73, 169])).
% 1.03/1.25 tff(3263,plain,
% 1.03/1.25 (~r(s(s(elem!1)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2993, 3262, 3092])).
% 1.03/1.25 tff(3264,plain,
% 1.03/1.25 (b(s(s(elem!1)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[901, 3263])).
% 1.03/1.25 tff(3265,plain,
% 1.03/1.25 (~r(s(z), s(s(elem!1)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2853, 3262, 3092])).
% 1.03/1.25 tff(3266,plain,
% 1.03/1.25 (b(s(z), s(s(elem!1)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[653, 3265])).
% 1.03/1.25 tff(3267,plain,
% 1.03/1.25 (~b(s(s(s(z))), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2158, 224, 3266, 3264, 136])).
% 1.03/1.25 tff(3268,plain,
% 1.03/1.25 (r(s(s(s(z))), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[925, 3267])).
% 1.03/1.25 tff(3269,plain,
% 1.03/1.25 (s(s(elem!1)) = elem!1),
% 1.03/1.25 inference(symmetry,[status(thm)],[2764])).
% 1.03/1.25 tff(3270,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3269])).
% 1.03/1.25 tff(3271,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.25 inference(symmetry,[status(thm)],[3270])).
% 1.03/1.25 tff(3272,plain,
% 1.03/1.25 (~(s(s(s(s(z)))) = elem!1)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3120, 2765])).
% 1.03/1.25 tff(3273,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3269])).
% 1.03/1.25 tff(3274,plain,
% 1.03/1.25 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3273])).
% 1.03/1.25 tff(3275,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3142, 112, 689, 293, 3136])).
% 1.03/1.25 tff(3276,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 3275])).
% 1.03/1.25 tff(3277,plain,
% 1.03/1.25 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3278,plain,
% 1.03/1.25 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3279,plain,
% 1.03/1.25 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(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(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3278])).
% 1.03/1.25 tff(3280,plain,
% 1.03/1.25 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(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(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3279, 3277])).
% 1.03/1.25 tff(3281,plain,
% 1.03/1.25 ((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3282,plain,
% 1.03/1.25 ((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 1.03/1.25 tff(3283,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3282, 112, 267, 3136])).
% 1.03/1.25 tff(3284,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 3283])).
% 1.03/1.25 tff(3285,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3286,plain,
% 1.03/1.25 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3287,plain,
% 1.03/1.25 (((~![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(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3286])).
% 1.03/1.25 tff(3288,plain,
% 1.03/1.25 (((~![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(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3287, 3285])).
% 1.03/1.25 tff(3289,plain,
% 1.03/1.25 ((~![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(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3290,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3289, 3288])).
% 1.03/1.25 tff(3291,plain,
% 1.03/1.25 (~r(z, s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3290, 112, 293, 267])).
% 1.03/1.25 tff(3292,plain,
% 1.03/1.25 (b(z, s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1088, 3291])).
% 1.03/1.25 tff(3293,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3294,plain,
% 1.03/1.25 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3295,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3294])).
% 1.03/1.25 tff(3296,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3295, 3293])).
% 1.03/1.25 tff(3297,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(3298,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3297, 3296])).
% 1.03/1.25 tff(3299,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3298, 224, 3292, 1118, 3284, 3276])).
% 1.03/1.25 tff(3300,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(3301,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3300, 2815, 3262, 101, 2999])).
% 1.03/1.25 tff(3302,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), elem!1)),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3301, 3274])).
% 1.03/1.25 tff(3303,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), elem!1)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[3183, 3302, 3272])).
% 1.03/1.25 tff(3304,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[3303, 3271])).
% 1.03/1.25 tff(3305,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3306,plain,
% 1.03/1.25 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(3307,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[3306])).
% 1.03/1.25 tff(3308,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[3307, 3305])).
% 1.03/1.26 tff(3309,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3310,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3309, 3308])).
% 1.03/1.26 tff(3311,plain,
% 1.03/1.26 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3310, 224, 3266, 3264])).
% 1.03/1.26 tff(3312,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3311, 3304])).
% 1.03/1.26 tff(3313,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3168, 3312])).
% 1.03/1.26 tff(3314,plain,
% 1.03/1.26 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3237, 224, 148, 136])).
% 1.03/1.26 tff(3315,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3314, 3304])).
% 1.03/1.26 tff(3316,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3252, 3315])).
% 1.03/1.26 tff(3317,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.03/1.26 tff(3318,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.03/1.26 tff(3319,plain,
% 1.03/1.26 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3320,plain,
% 1.03/1.26 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3321,plain,
% 1.03/1.26 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3320])).
% 1.03/1.26 tff(3322,plain,
% 1.03/1.26 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3321, 3319])).
% 1.03/1.26 tff(3323,plain,
% 1.03/1.26 ((~![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(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))))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3324,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 1.03/1.26 tff(3325,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3324, 112, 3188, 3318, 3317])).
% 1.03/1.26 tff(3326,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3327,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3326, 3316, 3313, 3268])).
% 1.03/1.26 tff(3328,plain,((~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3329,plain,
% 1.03/1.26 (~r(s(s(elem!1)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3328, 77, 4, 2, 12, 74])).
% 1.03/1.26 tff(3330,plain,
% 1.03/1.26 (b(s(s(elem!1)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[593, 3329])).
% 1.03/1.26 tff(3331,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2464, 112, 179, 416, 688])).
% 1.03/1.26 tff(3332,plain,((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3333,plain,
% 1.03/1.26 (~r(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3332, 688, 179])).
% 1.03/1.26 tff(3334,plain,
% 1.03/1.26 (~r(s(s(s(z))), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2431, 688, 177])).
% 1.03/1.26 tff(3335,plain,
% 1.03/1.26 (~r(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2420, 688, 689])).
% 1.03/1.26 tff(3336,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2951, 3335, 3334, 2083, 362, 354, 3333])).
% 1.03/1.26 tff(3337,plain,((~r(z, elem!1)) | (s(s(s(z))) = elem!1) | b(s(s(elem!1)), elem!1) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3338,plain,
% 1.03/1.26 (~r(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3337, 354, 362, 179, 689, 177])).
% 1.03/1.26 tff(3339,plain,
% 1.03/1.26 (b(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[289, 3338, 4])).
% 1.03/1.26 tff(3340,plain,
% 1.03/1.26 (r(s(s(elem!1)), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[360, 354, 353])).
% 1.03/1.26 tff(3341,plain,
% 1.03/1.26 (~b(z, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1205, 416, 77, 1181])).
% 1.03/1.26 tff(3342,plain,
% 1.03/1.26 (r(z, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[752, 3341])).
% 1.03/1.26 tff(3343,plain,
% 1.03/1.26 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3074, 3342, 689])).
% 1.03/1.26 tff(3344,plain,
% 1.03/1.26 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[147, 3343, 2])).
% 1.03/1.26 tff(3345,plain,
% 1.03/1.26 (~b(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3206, 3344, 1090, 560])).
% 1.03/1.26 tff(3346,plain,
% 1.03/1.26 (r(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[901, 3345])).
% 1.03/1.26 tff(3347,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1187, 112, 1181, 416, 3346])).
% 1.03/1.26 tff(3348,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3349,plain,
% 1.03/1.26 (~r(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3348, 3340, 2083, 3001, 2, 689, 77])).
% 1.03/1.26 tff(3350,plain,
% 1.03/1.26 (b(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[454, 3349, 91])).
% 1.03/1.26 tff(3351,plain,
% 1.03/1.26 (~b(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2904, 3350, 77, 3339])).
% 1.03/1.26 tff(3352,plain,
% 1.03/1.26 (r(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1277, 3351, 83])).
% 1.03/1.26 tff(3353,plain,
% 1.03/1.26 (b(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[454, 2931, 91])).
% 1.03/1.26 tff(3354,plain,
% 1.03/1.26 (~b(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2904, 3353, 77, 344])).
% 1.03/1.26 tff(3355,plain,
% 1.03/1.26 (r(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1277, 3354, 83])).
% 1.03/1.26 tff(3356,plain,
% 1.03/1.26 (r(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2951, 2931, 1090, 362, 354, 2932])).
% 1.03/1.26 tff(3357,plain,
% 1.03/1.26 (~r(z, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3074, 827, 689])).
% 1.03/1.26 tff(3358,plain,
% 1.03/1.26 (b(z, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[752, 3357])).
% 1.03/1.26 tff(3359,plain,
% 1.03/1.26 (~b(elem!1, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[613, 3358, 1240, 405])).
% 1.03/1.26 tff(3360,plain,
% 1.03/1.26 (r(elem!1, s(s(elem!1)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[558, 3359, 3])).
% 1.03/1.26 tff(3361,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3362,plain,
% 1.03/1.26 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3363,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3362])).
% 1.03/1.26 tff(3364,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3363, 3361])).
% 1.03/1.26 tff(3365,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3366,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3365, 3364])).
% 1.03/1.26 tff(3367,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3366, 112, 3360, 1020, 827])).
% 1.03/1.26 tff(3368,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3369,plain,
% 1.03/1.26 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3368, 3356, 3, 1240, 405, 689])).
% 1.03/1.26 tff(3370,plain,
% 1.03/1.26 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[147, 3369, 2])).
% 1.03/1.26 tff(3371,plain,
% 1.03/1.26 (~b(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3206, 3370, 1090, 560])).
% 1.03/1.26 tff(3372,plain,
% 1.03/1.26 (r(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[901, 3371])).
% 1.03/1.26 tff(3373,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3374,plain,
% 1.03/1.26 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3375,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3374])).
% 1.03/1.26 tff(3376,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3375, 3373])).
% 1.03/1.26 tff(3377,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3378,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3377, 3376])).
% 1.03/1.26 tff(3379,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3378, 112, 3340, 3372, 3356, 3355])).
% 1.03/1.26 tff(3380,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, 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,[]))).
% 1.03/1.26 tff(3381,plain,
% 1.03/1.26 (r(s(s(s(z))), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3380, 3349, 3001, 2, 3, 1240, 405, 689, 77, 3339, 362, 354, 2083])).
% 1.03/1.26 tff(3382,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3383,plain,
% 1.03/1.26 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3384,plain,
% 1.03/1.26 (((~![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))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3383])).
% 1.03/1.26 tff(3385,plain,
% 1.03/1.26 (((~![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))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3384, 3382])).
% 1.03/1.26 tff(3386,plain,
% 1.03/1.26 ((~![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))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3387,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3386, 3385])).
% 1.03/1.26 tff(3388,plain,
% 1.03/1.26 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3387, 112, 3340, 3381])).
% 1.03/1.26 tff(3389,plain,
% 1.03/1.26 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[147, 3388, 2])).
% 1.03/1.26 tff(3390,plain,
% 1.03/1.26 (~b(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3206, 3389, 2083, 3001])).
% 1.03/1.26 tff(3391,plain,
% 1.03/1.26 (r(s(s(elem!1)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[901, 3390])).
% 1.03/1.26 tff(3392,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3393,plain,
% 1.03/1.26 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3394,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3393])).
% 1.03/1.26 tff(3395,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3394, 3392])).
% 1.03/1.26 tff(3396,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3397,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 1.03/1.26 tff(3398,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3397, 112, 3340, 3391, 3352])).
% 1.03/1.26 tff(3399,plain,(b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (z = elem!1) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3400,plain,
% 1.03/1.26 (b(s(s(elem!1)), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3399, 405, 77, 3, 1240, 2, 689, 2438, 4, 179, 73])).
% 1.03/1.26 tff(3401,plain,
% 1.03/1.26 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(3402,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[3401])).
% 1.03/1.26 tff(3403,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.03/1.26 inference(transitivity,[status(thm)],[3402, 879])).
% 1.03/1.26 tff(3404,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(3405,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.03/1.26 tff(3406,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3405, 224, 405, 1240, 344, 390])).
% 1.03/1.26 tff(3407,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3408,plain,
% 1.03/1.26 (~b(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3407, 405, 1240, 3400])).
% 1.03/1.26 tff(3409,plain,
% 1.03/1.26 (r(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[289, 3408, 4])).
% 1.03/1.26 tff(3410,plain,
% 1.03/1.26 (~r(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3332, 3409, 179])).
% 1.03/1.26 tff(3411,plain,
% 1.03/1.26 (b(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[454, 3410, 91])).
% 1.03/1.26 tff(3412,plain,
% 1.03/1.26 (~r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[187, 179, 73])).
% 1.03/1.26 tff(3413,plain,
% 1.03/1.26 (b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[175, 3412])).
% 1.03/1.26 tff(3414,plain,
% 1.03/1.26 (~r(s(s(s(z))), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2431, 3409, 73])).
% 1.03/1.26 tff(3415,plain,
% 1.03/1.26 (b(s(s(s(z))), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[374, 3414, 2438])).
% 1.03/1.26 tff(3416,plain,
% 1.03/1.26 (s(s(s(z))) = elem!1),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2471, 284])).
% 1.03/1.26 tff(3417,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[362, 3416])).
% 1.03/1.26 tff(3418,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3419,plain,
% 1.03/1.26 (~(elem!1 = s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3418, 2438])).
% 1.03/1.26 tff(3420,plain,
% 1.03/1.26 (~r(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2420, 3409, 689])).
% 1.03/1.26 tff(3421,plain,
% 1.03/1.26 (b(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[388, 3420, 3419])).
% 1.03/1.26 tff(3422,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2941, 3421, 3415, 3413, 3411])).
% 1.03/1.26 tff(3423,plain,((~b(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (z = elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(3424,plain,
% 1.03/1.26 (~b(elem!1, z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3423, 179, 689, 4, 1240, 77, 3, 2, 12])).
% 1.03/1.26 tff(3425,plain,
% 1.03/1.26 (r(elem!1, z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[403, 3424, 11])).
% 1.03/1.26 tff(3426,plain,
% 1.03/1.26 (~r(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2841, 3425, 179])).
% 1.03/1.26 tff(3427,plain,
% 1.03/1.26 (b(s(z), elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[454, 3426, 91])).
% 1.03/1.26 tff(3428,plain,
% 1.03/1.26 (~r(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1259, 3425, 179])).
% 1.03/1.26 tff(3429,plain,
% 1.03/1.26 (b(elem!1, s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1277, 3428, 83])).
% 1.03/1.26 tff(3430,plain,
% 1.03/1.26 (~b(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2904, 3429, 77, 3427])).
% 1.03/1.26 tff(3431,plain,
% 1.03/1.26 (r(z, elem!1)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[289, 3430, 4])).
% 1.03/1.26 tff(3432,plain,
% 1.03/1.26 (~r(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2420, 3431, 689])).
% 1.03/1.26 tff(3433,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[932, 112, 179, 73])).
% 1.03/1.26 tff(3434,plain,
% 1.03/1.26 (b(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[925, 3433])).
% 1.03/1.26 tff(3435,plain,
% 1.03/1.26 (~b(elem!1, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[3008, 224, 3429, 3413, 3434])).
% 1.03/1.27 tff(3436,plain,
% 1.03/1.27 (elem!1 = s(s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[388, 3435, 3432])).
% 1.03/1.27 tff(3437,plain,
% 1.03/1.27 (s(elem!1) = s(s(s(s(z))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3436])).
% 1.03/1.27 tff(3438,plain,
% 1.03/1.27 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3437])).
% 1.03/1.27 tff(3439,plain,
% 1.03/1.27 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.03/1.27 inference(symmetry,[status(thm)],[3438])).
% 1.03/1.27 tff(3440,plain,
% 1.03/1.27 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3439])).
% 1.03/1.27 tff(3441,plain,
% 1.03/1.27 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.03/1.27 inference(symmetry,[status(thm)],[3440])).
% 1.03/1.27 tff(3442,plain,
% 1.03/1.27 (~r(z, s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3088, 3425, 77, 179, 4, 689, 73, 83])).
% 1.03/1.27 tff(3443,plain,
% 1.03/1.27 (b(z, s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[752, 3442])).
% 1.03/1.27 tff(3444,plain,
% 1.03/1.27 (b(z, s(s(s(s(s(z))))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3443, 3441])).
% 1.03/1.27 tff(3445,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3027])).
% 1.03/1.27 tff(3446,plain,
% 1.03/1.27 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.03/1.27 inference(symmetry,[status(thm)],[3445])).
% 1.03/1.27 tff(3447,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[2596, 3446])).
% 1.03/1.27 tff(3448,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.03/1.27 tff(3449,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3448, 3447])).
% 1.03/1.27 tff(3450,plain,(b(s(s(z)), s(s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3451,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3450, 3436, 2596])).
% 1.03/1.27 tff(3452,plain,
% 1.03/1.27 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3438])).
% 1.03/1.27 tff(3453,plain,
% 1.03/1.27 (b(s(s(s(s(s(z))))), z)),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[1240, 3452])).
% 1.03/1.27 tff(3454,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2811, 112, 196, 689, 268])).
% 1.03/1.27 tff(3455,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3456,plain,
% 1.03/1.27 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3455, 268, 689])).
% 1.03/1.27 tff(3457,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[249, 3456])).
% 1.03/1.27 tff(3458,plain,
% 1.03/1.27 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(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(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3459,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3458])).
% 1.03/1.27 tff(3460,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3459, 1091])).
% 1.03/1.27 tff(3461,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3462,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.03/1.27 tff(3463,plain,
% 1.03/1.27 (~b(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3462, 224, 3457, 1090, 560])).
% 1.03/1.27 tff(3464,plain,
% 1.03/1.27 (r(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2726, 3463])).
% 1.03/1.27 tff(3465,plain,
% 1.03/1.27 (((~![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(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3466,plain,
% 1.03/1.27 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3467,plain,
% 1.03/1.27 (((~![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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3466])).
% 1.03/1.27 tff(3468,plain,
% 1.03/1.27 (((~![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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3467, 3465])).
% 1.03/1.27 tff(3469,plain,
% 1.03/1.27 ((~![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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3470,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 1.03/1.27 tff(3471,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3470, 112, 179, 268, 3464])).
% 1.03/1.27 tff(3472,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3473,plain,
% 1.03/1.27 (~r(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3472, 179, 3413, 3434, 689])).
% 1.03/1.27 tff(3474,plain,
% 1.03/1.27 (b(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[281, 3473])).
% 1.03/1.27 tff(3475,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3476,plain,
% 1.03/1.27 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3477,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3476])).
% 1.03/1.27 tff(3478,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3477, 3475])).
% 1.03/1.27 tff(3479,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3480,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 1.03/1.27 tff(3481,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3480, 224, 3474, 3453, 3451, 3444])).
% 1.03/1.27 tff(3482,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (z = elem!1) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3483,plain,
% 1.03/1.27 (~r(s(z), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3482, 2596, 3330, 101, 4, 77, 3, 2, 12])).
% 1.03/1.27 tff(3484,plain,
% 1.03/1.27 (b(s(z), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[194, 3483])).
% 1.03/1.27 tff(3485,plain,
% 1.03/1.27 (~b(s(s(elem!1)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1249, 1, 77, 1240])).
% 1.03/1.27 tff(3486,plain,
% 1.03/1.27 (r(s(s(elem!1)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[901, 3485])).
% 1.03/1.27 tff(3487,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.03/1.27 tff(3488,plain,
% 1.03/1.27 (s(s(z)) = s(s(elem!1))),
% 1.03/1.27 inference(symmetry,[status(thm)],[3487])).
% 1.03/1.27 tff(3489,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[259, 3488])).
% 1.03/1.27 tff(3490,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3491,plain,
% 1.03/1.27 (~(s(s(elem!1)) = s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3490, 169])).
% 1.03/1.27 tff(3492,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.03/1.27 tff(3493,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3494,plain,
% 1.03/1.27 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3495,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3494])).
% 1.03/1.27 tff(3496,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3495, 3493])).
% 1.03/1.27 tff(3497,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3498,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 1.03/1.27 tff(3499,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3498, 112, 1181, 688, 293])).
% 1.03/1.27 tff(3500,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3501,plain,
% 1.03/1.27 (~r(z, s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3500, 688, 1181])).
% 1.03/1.27 tff(3502,plain,
% 1.03/1.27 (b(z, s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[752, 3501])).
% 1.03/1.27 tff(3503,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3504,plain,
% 1.03/1.27 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3505,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3504])).
% 1.03/1.27 tff(3506,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3505, 3503])).
% 1.03/1.27 tff(3507,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3508,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 1.03/1.27 tff(3509,plain,
% 1.03/1.27 (~b(s(z), s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3508, 224, 1240, 1, 3502])).
% 1.03/1.27 tff(3510,plain,
% 1.03/1.27 (r(s(z), s(s(elem!1)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[653, 3509])).
% 1.03/1.27 tff(3511,plain,
% 1.03/1.27 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[835, 3510, 176])).
% 1.03/1.27 tff(3512,plain,
% 1.03/1.27 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[147, 3511, 2])).
% 1.03/1.27 tff(3513,plain,
% 1.03/1.27 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[243, 176, 77, 1, 177])).
% 1.03/1.27 tff(3514,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[249, 3513])).
% 1.03/1.27 tff(3515,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3516,plain,
% 1.03/1.27 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3517,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3516])).
% 1.03/1.27 tff(3518,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3517, 3515])).
% 1.03/1.27 tff(3519,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3520,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 1.03/1.27 tff(3521,plain,
% 1.03/1.27 (~b(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3520, 224, 3514, 3502, 3512, 2596])).
% 1.03/1.27 tff(3522,plain,
% 1.03/1.27 (r(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[281, 3521])).
% 1.03/1.27 tff(3523,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.03/1.27 tff(3524,plain,
% 1.03/1.27 (((~![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(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3525,plain,
% 1.03/1.27 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3526,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), 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))), z)) | (~r(s(s(z)), z))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3525])).
% 1.03/1.28 tff(3527,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), 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))), z)) | (~r(s(s(z)), z)))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3526, 3524])).
% 1.03/1.28 tff(3528,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3529,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3528, 3527])).
% 1.03/1.28 tff(3530,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3529, 112, 177, 268, 3523])).
% 1.03/1.28 tff(3531,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3532,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3531, 3522, 177])).
% 1.03/1.28 tff(3533,plain,
% 1.03/1.28 (((~![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))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3534,plain,
% 1.03/1.28 ((~![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))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3535,plain,
% 1.03/1.28 ((~![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)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.03/1.28 tff(3536,plain,
% 1.03/1.28 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3535, 68, 3532])).
% 1.03/1.28 tff(3537,plain,
% 1.03/1.28 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3536, 56])).
% 1.03/1.28 tff(3538,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3539,plain,
% 1.03/1.28 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3540,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3539])).
% 1.03/1.28 tff(3541,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3540, 3538])).
% 1.03/1.28 tff(3542,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3543,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 1.03/1.28 tff(3544,plain,
% 1.03/1.28 (~b(s(s(elem!1)), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3543, 224, 3514, 3512, 3537])).
% 1.03/1.28 tff(3545,plain,
% 1.03/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3546,plain,
% 1.03/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3547,plain,
% 1.03/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.03/1.28 tff(3548,plain,
% 1.03/1.28 (r(s(s(elem!1)), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3547, 68, 3544, 3492])).
% 1.03/1.28 tff(3549,plain,
% 1.03/1.28 (~r(s(z), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1205, 3502, 77, 1181])).
% 1.03/1.28 tff(3550,plain,
% 1.03/1.28 (b(s(z), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[454, 3549, 91])).
% 1.03/1.28 tff(3551,plain,
% 1.03/1.28 (~(elem!1 = s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2477, 3550, 170])).
% 1.03/1.28 tff(3552,plain,
% 1.03/1.28 (~(s(s(s(z))) = elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2487, 3551])).
% 1.03/1.28 tff(3553,plain,
% 1.03/1.28 (b(s(s(s(z))), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[374, 3552, 3334])).
% 1.03/1.28 tff(3554,plain,
% 1.03/1.28 (b(elem!1, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[388, 3551, 3335])).
% 1.03/1.28 tff(3555,plain,
% 1.03/1.28 (~b(s(s(z)), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2412, 3554, 3514, 3553])).
% 1.03/1.28 tff(3556,plain,
% 1.03/1.28 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[1170])).
% 1.03/1.28 tff(3557,plain,
% 1.03/1.28 (r(s(z), s(elem!1))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[178, 3556])).
% 1.03/1.28 tff(3558,plain,
% 1.03/1.28 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[1170])).
% 1.03/1.28 tff(3559,plain,
% 1.03/1.28 (b(s(s(elem!1)), s(elem!1))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[152, 3558])).
% 1.03/1.28 tff(3560,plain,
% 1.03/1.28 (b(s(s(z)), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[1169])).
% 1.03/1.28 tff(3561,plain,
% 1.03/1.28 (b(elem!1, s(s(elem!1)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[2596, 3560])).
% 1.03/1.28 tff(3562,plain,
% 1.03/1.28 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[1170])).
% 1.03/1.28 tff(3563,plain,
% 1.03/1.28 (b(elem!1, s(elem!1))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[685, 3562])).
% 1.03/1.28 tff(3564,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3565,plain,
% 1.03/1.28 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3566,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3565])).
% 1.03/1.28 tff(3567,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.03/1.28 tff(3568,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3569,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.03/1.28 tff(3570,plain,
% 1.03/1.28 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3569, 224])).
% 1.03/1.28 tff(3571,plain,
% 1.03/1.28 (~b(s(elem!1), s(s(elem!1)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3570, 3563, 3561, 3559])).
% 1.03/1.28 tff(3572,plain,
% 1.03/1.28 (r(s(elem!1), s(s(elem!1)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1521, 3571, 523])).
% 1.03/1.28 tff(3573,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2682, 112, 3572, 656, 3557])).
% 1.03/1.28 tff(3574,plain,((~(s(s(z)) = elem!1)) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3575,plain,
% 1.03/1.28 (~(s(s(z)) = elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3574, 3510, 523, 3512, 176, 3554, 2596])).
% 1.03/1.28 tff(3576,plain,
% 1.03/1.28 (r(s(s(z)), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1135, 3575, 3555])).
% 1.03/1.28 tff(3577,plain,
% 1.03/1.28 (((~![X0: $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(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(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3578,plain,
% 1.03/1.28 (((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3579,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3578])).
% 1.03/1.28 tff(3580,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3579, 3577])).
% 1.03/1.28 tff(3581,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3582,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3581, 3580])).
% 1.03/1.28 tff(3583,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3582, 112, 1181, 3576, 3548])).
% 1.03/1.28 tff(3584,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | b(s(z), s(s(s(z)))) | (~b(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3585,plain,
% 1.03/1.28 (~r(z, elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3584, 1181, 523, 2596, 3491, 177, 2, 1240, 1, 170, 77, 689])).
% 1.03/1.28 tff(3586,plain,
% 1.03/1.28 (b(z, elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[289, 3585, 4])).
% 1.03/1.28 tff(3587,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3397, 112, 1181, 887, 993])).
% 1.03/1.28 tff(3588,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3589,plain,
% 1.03/1.28 (~r(elem!1, s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3588, 1181, 3486])).
% 1.03/1.28 tff(3590,plain,
% 1.03/1.28 (b(elem!1, s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1277, 3589, 83])).
% 1.03/1.28 tff(3591,plain,
% 1.03/1.28 (~b(s(z), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2904, 3590, 77, 3586])).
% 1.03/1.28 tff(3592,plain,
% 1.03/1.28 (r(s(z), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[454, 3591, 91])).
% 1.03/1.28 tff(3593,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1187, 112, 1181, 3592, 3486])).
% 1.03/1.28 tff(3594,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (z = elem!1) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | b(s(z), s(s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3595,plain,
% 1.03/1.28 (~r(s(s(elem!1)), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3594, 170, 4, 319, 2596, 73, 2, 3330, 3484, 77, 101])).
% 1.03/1.28 tff(3596,plain,
% 1.03/1.28 (r(z, s(s(elem!1)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[752, 750])).
% 1.03/1.28 tff(3597,plain,
% 1.03/1.28 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3074, 3596, 101])).
% 1.03/1.28 tff(3598,plain,
% 1.03/1.28 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[147, 3597, 311])).
% 1.03/1.28 tff(3599,plain,
% 1.03/1.28 (~(s(s(s(z))) = elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[347, 344, 74])).
% 1.03/1.28 tff(3600,plain,
% 1.03/1.28 (~b(s(s(elem!1)), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3405, 224, 405, 1240, 344])).
% 1.03/1.28 tff(3601,plain,
% 1.03/1.28 (s(s(elem!1)) = elem!1),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[360, 3600, 328])).
% 1.03/1.28 tff(3602,plain,
% 1.03/1.28 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3601])).
% 1.03/1.28 tff(3603,plain,
% 1.03/1.28 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.03/1.28 inference(symmetry,[status(thm)],[3602])).
% 1.03/1.28 tff(3604,plain,
% 1.03/1.28 (b(z, s(s(elem!1)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[344, 3603])).
% 1.03/1.28 tff(3605,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[750, 3604])).
% 1.03/1.28 tff(3606,plain,((~b(z, elem!1)) | b(z, s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3607,plain,
% 1.03/1.28 (~b(elem!1, z)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3606, 344, 328, 750, 1240])).
% 1.03/1.28 tff(3608,plain,
% 1.03/1.28 (r(elem!1, z)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[403, 3607, 157])).
% 1.03/1.28 tff(3609,plain,
% 1.03/1.28 (~b(s(s(elem!1)), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[398, 3608, 152, 3599, 177])).
% 1.03/1.28 tff(3610,plain,
% 1.03/1.28 (s(s(elem!1)) = elem!1),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[360, 3609, 328])).
% 1.03/1.28 tff(3611,plain,
% 1.03/1.28 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3610])).
% 1.03/1.28 tff(3612,plain,
% 1.03/1.28 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.03/1.28 inference(symmetry,[status(thm)],[3611])).
% 1.03/1.28 tff(3613,plain,
% 1.03/1.28 ((~b(elem!1, z)) <=> (~b(s(s(elem!1)), z))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3612])).
% 1.03/1.28 tff(3614,plain,
% 1.03/1.28 (~b(s(s(elem!1)), z)),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3607, 3613])).
% 1.03/1.28 tff(3615,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1240, 3614])).
% 1.03/1.28 tff(3616,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | r(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (elem!1 = z) | b(z, s(s(elem!1))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3617,plain,
% 1.03/1.28 (~b(z, elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3616, 11, 328, 3598, 73, 1240, 750, 74])).
% 1.03/1.28 tff(3618,plain,
% 1.03/1.28 (r(z, elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[289, 3617, 4])).
% 1.03/1.28 tff(3619,plain,
% 1.03/1.28 (~r(s(s(s(z))), elem!1)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2431, 3618, 73])).
% 1.03/1.28 tff(3620,plain,
% 1.03/1.28 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.03/1.28 inference(commutativity,[status(thm)],[])).
% 1.03/1.28 tff(3621,plain,
% 1.03/1.28 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.03/1.28 inference(symmetry,[status(thm)],[3620])).
% 1.03/1.28 tff(3622,plain,
% 1.03/1.28 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3621])).
% 1.03/1.28 tff(3623,plain,
% 1.03/1.28 (~(s(s(elem!1)) = s(s(z)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[169, 3622])).
% 1.03/1.28 tff(3624,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(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(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3625,plain,
% 1.03/1.28 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3626,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3625])).
% 1.03/1.28 tff(3627,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3626, 3624])).
% 1.03/1.28 tff(3628,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3629,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3628, 3627])).
% 1.03/1.29 tff(3630,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3629, 112, 545, 688, 293])).
% 1.03/1.29 tff(3631,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3632,plain,
% 1.03/1.29 (~r(elem!1, s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3631, 688, 3596])).
% 1.03/1.29 tff(3633,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.03/1.29 tff(3634,plain,
% 1.03/1.29 (r(elem!1, z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[403, 3633, 11])).
% 1.03/1.29 tff(3635,plain,
% 1.03/1.29 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3074, 3596, 689])).
% 1.03/1.29 tff(3636,plain,
% 1.03/1.29 (b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[147, 3635, 311])).
% 1.03/1.29 tff(3637,plain,
% 1.03/1.29 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.03/1.29 inference(monotonicity,[status(thm)],[1296])).
% 1.03/1.29 tff(3638,plain,
% 1.03/1.29 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.03/1.29 inference(symmetry,[status(thm)],[3637])).
% 1.03/1.29 tff(3639,plain,
% 1.03/1.29 (b(elem!1, z)),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[1240, 3638])).
% 1.03/1.29 tff(3640,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3633, 3639])).
% 1.03/1.29 tff(3641,plain,((~(elem!1 = s(s(elem!1)))) | b(elem!1, z) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3642,plain,
% 1.03/1.29 (~(elem!1 = s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3641, 3633, 1240])).
% 1.03/1.29 tff(3643,plain,
% 1.03/1.29 (~r(elem!1, s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3631, 688, 293])).
% 1.03/1.29 tff(3644,plain,
% 1.03/1.29 (~r(s(s(z)), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2468, 416, 77, 688])).
% 1.03/1.29 tff(3645,plain,
% 1.03/1.29 (~b(s(s(z)), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2606, 3644, 3, 152, 363, 177, 328, 3643])).
% 1.03/1.29 tff(3646,plain,
% 1.03/1.29 (r(s(s(z)), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[263, 68, 259, 3645])).
% 1.03/1.29 tff(3647,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3648,plain,
% 1.03/1.29 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3649,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3648])).
% 1.03/1.29 tff(3650,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.03/1.29 tff(3651,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3652,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.03/1.29 tff(3653,plain,
% 1.03/1.29 (~r(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3652, 112, 688, 293, 3646])).
% 1.03/1.29 tff(3654,plain,
% 1.03/1.29 (b(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[281, 3653])).
% 1.03/1.29 tff(3655,plain,
% 1.03/1.29 (~r(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3332, 416, 688])).
% 1.03/1.29 tff(3656,plain,
% 1.03/1.29 (b(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[194, 3655])).
% 1.03/1.29 tff(3657,plain,
% 1.03/1.29 (~b(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1593, 224, 77, 3656, 3654])).
% 1.03/1.29 tff(3658,plain,
% 1.03/1.29 (r(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[213, 68, 210, 3657])).
% 1.03/1.29 tff(3659,plain,
% 1.03/1.29 (~(s(s(elem!1)) = s(s(z)))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[259, 3622])).
% 1.03/1.29 tff(3660,plain,
% 1.03/1.29 (~r(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3290, 112, 293, 3646])).
% 1.03/1.29 tff(3661,plain,
% 1.03/1.29 (b(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1088, 3660])).
% 1.03/1.29 tff(3662,plain,
% 1.03/1.29 (b(s(s(z)), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1135, 3644, 2595])).
% 1.03/1.29 tff(3663,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3664,plain,
% 1.03/1.29 (((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3665,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3664])).
% 1.03/1.29 tff(3666,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3665, 3663])).
% 1.03/1.29 tff(3667,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3668,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 1.03/1.29 tff(3669,plain,
% 1.03/1.29 (~b(s(s(elem!1)), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3668, 224, 1240, 2589, 3662, 3661])).
% 1.03/1.29 tff(3670,plain,
% 1.03/1.29 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3547, 68, 3669])).
% 1.03/1.29 tff(3671,plain,
% 1.03/1.29 (r(s(s(elem!1)), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3670, 3659])).
% 1.03/1.29 tff(3672,plain,
% 1.03/1.29 (~b(s(s(elem!1)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1249, 3656, 77, 1240])).
% 1.03/1.29 tff(3673,plain,
% 1.03/1.29 (r(s(s(elem!1)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[901, 3672])).
% 1.03/1.29 tff(3674,plain,
% 1.03/1.29 (((~![X0: $i, 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(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3675,plain,
% 1.03/1.29 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3676,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3675])).
% 1.03/1.29 tff(3677,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3676, 3674])).
% 1.03/1.29 tff(3678,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3679,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 1.03/1.29 tff(3680,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3679, 112, 3673, 3671, 3658])).
% 1.03/1.29 tff(3681,plain,((~r(s(z), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3682,plain,
% 1.03/1.29 (~r(s(z), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3681, 3642, 77, 1240, 688, 3596, 169, 3636, 3634, 177, 328])).
% 1.03/1.29 tff(3683,plain,
% 1.03/1.29 (b(s(z), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[454, 3682, 149])).
% 1.03/1.29 tff(3684,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[634, 224, 682, 2252, 684, 390])).
% 1.03/1.29 tff(3685,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3686,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3685, 2589, 2598, 684, 2252])).
% 1.03/1.29 tff(3687,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3688,plain,
% 1.03/1.29 (~b(s(z), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3687, 3683, 3642, 328, 3632])).
% 1.03/1.29 tff(3689,plain,
% 1.03/1.29 (r(s(z), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[653, 3688])).
% 1.03/1.29 tff(3690,plain,
% 1.03/1.29 (~r(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2735, 112, 656, 267])).
% 1.03/1.29 tff(3691,plain,
% 1.03/1.29 (b(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[213, 68, 210, 3690])).
% 1.03/1.29 tff(3692,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(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(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3693,plain,
% 1.03/1.29 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3694,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(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), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3693])).
% 1.03/1.29 tff(3695,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(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), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3694, 3692])).
% 1.03/1.29 tff(3696,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3697,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3696, 3695])).
% 1.03/1.29 tff(3698,plain,
% 1.03/1.29 (~r(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3697, 112, 656, 267])).
% 1.03/1.29 tff(3699,plain,
% 1.03/1.29 (b(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1071, 3698])).
% 1.03/1.29 tff(3700,plain,
% 1.03/1.29 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3701,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3700])).
% 1.03/1.29 tff(3702,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3701, 1073])).
% 1.03/1.29 tff(3703,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3704,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.03/1.29 tff(3705,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3704, 224, 77, 3292, 3699, 3691])).
% 1.03/1.29 tff(3706,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3707,plain,
% 1.03/1.29 (~r(s(s(z)), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3706, 3689, 77, 3596])).
% 1.03/1.29 tff(3708,plain,
% 1.03/1.29 (b(s(s(z)), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[265, 3707, 169])).
% 1.03/1.29 tff(3709,plain,
% 1.03/1.29 (r(s(s(z)), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2606, 3708, 3642, 3636, 3634, 177, 328, 3632])).
% 1.03/1.29 tff(3710,plain,
% 1.03/1.29 (~r(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2456, 112, 688, 3709])).
% 1.03/1.29 tff(3711,plain,
% 1.03/1.29 (b(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[281, 3710])).
% 1.03/1.29 tff(3712,plain,
% 1.03/1.29 (~(s(s(elem!1)) = elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[352, 3642])).
% 1.03/1.29 tff(3713,plain,
% 1.03/1.29 (b(s(s(elem!1)), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[360, 3712, 328])).
% 1.03/1.29 tff(3714,plain,
% 1.03/1.29 (s(s(s(z))) = elem!1),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[398, 3713, 3636, 3634, 177])).
% 1.03/1.29 tff(3715,plain,
% 1.03/1.29 (elem!1 = s(s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2487, 3714])).
% 1.03/1.29 tff(3716,plain,
% 1.03/1.29 (b(s(z), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2477, 3683, 3715])).
% 1.03/1.29 tff(3717,plain,
% 1.03/1.29 (~r(elem!1, z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3085, 179, 689, 3596, 1090, 4, 77, 177, 88])).
% 1.03/1.29 tff(3718,plain,
% 1.03/1.29 (b(elem!1, z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[403, 3717, 11])).
% 1.03/1.29 tff(3719,plain,
% 1.03/1.29 (~b(z, elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3606, 3718, 328, 750, 1240])).
% 1.03/1.29 tff(3720,plain,
% 1.03/1.29 (r(z, elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[289, 3719, 4])).
% 1.03/1.29 tff(3721,plain,
% 1.03/1.29 (~r(s(z), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3332, 179, 3720])).
% 1.03/1.29 tff(3722,plain,
% 1.03/1.29 (b(s(z), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[454, 3721, 149])).
% 1.03/1.29 tff(3723,plain,
% 1.03/1.29 (~r(elem!1, s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3631, 3720, 3596])).
% 1.03/1.29 tff(3724,plain,
% 1.03/1.29 (~r(s(z), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3061, 3720, 179, 3596])).
% 1.03/1.29 tff(3725,plain,
% 1.03/1.29 (b(s(z), s(s(elem!1)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[653, 3724])).
% 1.03/1.29 tff(3726,plain,
% 1.03/1.29 (elem!1 = s(s(elem!1))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3687, 3722, 3725, 328, 3723])).
% 1.03/1.29 tff(3727,plain,
% 1.03/1.29 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3726])).
% 1.03/1.29 tff(3728,plain,
% 1.03/1.29 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.03/1.29 inference(symmetry,[status(thm)],[3727])).
% 1.03/1.29 tff(3729,plain,
% 1.03/1.29 (b(elem!1, s(s(s(z))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3636, 3728])).
% 1.03/1.29 tff(3730,plain,
% 1.03/1.29 (~r(s(s(s(z))), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2431, 3720, 177])).
% 1.03/1.29 tff(3731,plain,
% 1.03/1.29 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3726])).
% 1.03/1.29 tff(3732,plain,
% 1.03/1.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.03/1.29 inference(symmetry,[status(thm)],[3731])).
% 1.03/1.29 tff(3733,plain,
% 1.03/1.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.03/1.29 inference(transitivity,[status(thm)],[3732, 284])).
% 1.03/1.29 tff(3734,plain,
% 1.03/1.29 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3733])).
% 1.03/1.29 tff(3735,plain,
% 1.03/1.29 (~(s(s(s(z))) = elem!1)),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[311, 3734])).
% 1.03/1.29 tff(3736,plain,
% 1.03/1.29 (b(s(s(s(z))), elem!1)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[374, 3735, 3730])).
% 1.03/1.29 tff(3737,plain,
% 1.03/1.29 (~b(s(s(s(z))), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[706, 224, 77, 684, 787, 560])).
% 1.03/1.29 tff(3738,plain,
% 1.03/1.29 (r(s(s(s(z))), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[72, 3737])).
% 1.03/1.29 tff(3739,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[185, 112, 179, 796, 3738])).
% 1.03/1.29 tff(3740,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3741,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3740, 3736, 3729, 3001, 3722, 77, 179])).
% 1.03/1.29 tff(3742,plain,((~r(s(z), z)) | (~b(z, s(z))) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), z)) | (z = elem!1) | b(z, s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3743,plain,
% 1.03/1.29 (~r(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3742, 3716, 328, 177, 4, 750, 1240, 689, 77, 88])).
% 1.03/1.29 tff(3744,plain,
% 1.03/1.29 (b(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[194, 3743])).
% 1.03/1.29 tff(3745,plain,
% 1.03/1.29 (~b(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1593, 224, 77, 3744, 3711])).
% 1.03/1.29 tff(3746,plain,
% 1.03/1.29 (r(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[213, 68, 210, 3745])).
% 1.03/1.29 tff(3747,plain,
% 1.03/1.29 (~b(s(s(elem!1)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1249, 3744, 77, 1240])).
% 1.03/1.29 tff(3748,plain,
% 1.03/1.29 (r(s(s(elem!1)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[901, 3747])).
% 1.03/1.29 tff(3749,plain,
% 1.03/1.29 (~r(s(s(elem!1)), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3679, 112, 3748, 3746])).
% 1.03/1.29 tff(3750,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.03/1.29 tff(3751,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3752,plain,
% 1.03/1.29 (((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3753,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3752])).
% 1.03/1.29 tff(3754,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3753, 3751])).
% 1.03/1.29 tff(3755,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3756,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3755, 3754])).
% 1.03/1.29 tff(3757,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3756, 112, 688, 1047, 3750])).
% 1.03/1.29 tff(3758,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3759,plain,
% 1.03/1.29 (~r(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3758, 3709, 688])).
% 1.03/1.29 tff(3760,plain,
% 1.03/1.29 (b(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1088, 3759])).
% 1.03/1.29 tff(3761,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3762,plain,
% 1.13/1.30 (((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3763,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3762])).
% 1.13/1.30 tff(3764,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3763, 3761])).
% 1.13/1.30 tff(3765,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3766,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 1.13/1.30 tff(3767,plain,
% 1.13/1.30 (~b(s(s(elem!1)), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3766, 224, 1240, 3760, 3711])).
% 1.13/1.30 tff(3768,plain,
% 1.13/1.30 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3547, 68, 3767])).
% 1.13/1.30 tff(3769,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3768, 3749, 3623])).
% 1.13/1.30 tff(3770,plain,(b(elem!1, z) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1) | (z = elem!1) | b(z, s(s(elem!1))) | (~r(z, s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3771,plain,
% 1.13/1.30 (b(elem!1, z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3770, 3618, 77, 1240, 73, 328, 4, 750, 101, 88])).
% 1.13/1.30 tff(3772,plain,
% 1.13/1.30 (~(s(s(s(z))) = elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2437, 3771, 12])).
% 1.13/1.30 tff(3773,plain,
% 1.13/1.30 (b(s(s(s(z))), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[374, 3772, 3619])).
% 1.13/1.30 tff(3774,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3775,plain,
% 1.13/1.30 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3776,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3775])).
% 1.13/1.30 tff(3777,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3776, 3774])).
% 1.13/1.30 tff(3778,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3779,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 1.13/1.30 tff(3780,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3779, 224, 405, 1240, 390, 787, 152])).
% 1.13/1.30 tff(3781,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3782,plain,
% 1.13/1.30 (~b(s(s(elem!1)), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3781, 3773, 1240, 3771, 3598])).
% 1.13/1.30 tff(3783,plain,
% 1.13/1.30 (s(s(elem!1)) = elem!1),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[360, 3782, 328])).
% 1.13/1.30 tff(3784,plain,
% 1.13/1.30 (elem!1 = s(s(elem!1))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[352, 3783])).
% 1.13/1.30 tff(3785,plain,
% 1.13/1.30 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3783])).
% 1.13/1.30 tff(3786,plain,
% 1.13/1.30 (b(elem!1, s(s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3598, 3785])).
% 1.13/1.30 tff(3787,plain,
% 1.13/1.30 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.13/1.30 inference(monotonicity,[status(thm)],[1300])).
% 1.13/1.30 tff(3788,plain,
% 1.13/1.30 (b(elem!1, z)),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[1240, 3787])).
% 1.13/1.30 tff(3789,plain,
% 1.13/1.30 (~(s(s(z)) = elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2788, 2786])).
% 1.13/1.30 tff(3790,plain,
% 1.13/1.30 (b(s(s(z)), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1135, 3644, 3789])).
% 1.13/1.30 tff(3791,plain,
% 1.13/1.30 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2412, 3790, 685, 787])).
% 1.13/1.30 tff(3792,plain,
% 1.13/1.30 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[249, 3791])).
% 1.13/1.30 tff(3793,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3794,plain,
% 1.13/1.30 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3795,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3794])).
% 1.13/1.30 tff(3796,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3795, 3793])).
% 1.13/1.30 tff(3797,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3798,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3797, 3796])).
% 1.13/1.30 tff(3799,plain,
% 1.13/1.30 (~r(s(s(z)), z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3798, 112, 3792, 688, 689])).
% 1.13/1.30 tff(3800,plain,
% 1.13/1.30 (b(s(s(z)), z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[281, 3799])).
% 1.13/1.30 tff(3801,plain,
% 1.13/1.30 (~r(z, s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1104, 112, 3792, 689])).
% 1.13/1.30 tff(3802,plain,
% 1.13/1.30 (b(z, s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1088, 3801])).
% 1.13/1.30 tff(3803,plain,
% 1.13/1.30 (~b(s(z), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2882, 224, 1, 3802, 3800])).
% 1.13/1.30 tff(3804,plain,
% 1.13/1.30 (r(s(z), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1071, 3803])).
% 1.13/1.30 tff(3805,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3806,plain,
% 1.13/1.30 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3807,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3806])).
% 1.13/1.30 tff(3808,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3807, 3805])).
% 1.13/1.30 tff(3809,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3810,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3809, 3808])).
% 1.13/1.30 tff(3811,plain,
% 1.13/1.30 (~b(elem!1, s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3810, 224, 405, 3802, 3800])).
% 1.13/1.30 tff(3812,plain,
% 1.13/1.30 (r(elem!1, s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2874, 3811, 2786])).
% 1.13/1.30 tff(3813,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, 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), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3814,plain,
% 1.13/1.30 (((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3815,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, 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(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3814])).
% 1.13/1.30 tff(3816,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, 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(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3815, 3813])).
% 1.13/1.30 tff(3817,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3818,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 1.13/1.30 tff(3819,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3818, 112, 416, 3812, 3804])).
% 1.13/1.30 tff(3820,plain,((~r(s(z), elem!1)) | (elem!1 = s(s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3821,plain,
% 1.13/1.30 (~r(s(z), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3820, 1, 2832, 3788, 688, 689, 685, 787, 77])).
% 1.13/1.30 tff(3822,plain,
% 1.13/1.30 (b(s(z), elem!1)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[454, 3821, 129])).
% 1.13/1.30 tff(3823,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3824,plain,
% 1.13/1.30 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3825,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3824])).
% 1.13/1.31 tff(3826,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3825, 3823])).
% 1.13/1.31 tff(3827,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3828,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 1.13/1.31 tff(3829,plain,
% 1.13/1.31 ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3828, 224, 3788, 1, 787])).
% 1.13/1.31 tff(3830,plain,
% 1.13/1.31 (~b(s(z), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3829, 3822])).
% 1.13/1.31 tff(3831,plain,
% 1.13/1.31 (r(s(z), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[175, 3830])).
% 1.13/1.31 tff(3832,plain,
% 1.13/1.31 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[243, 3831, 77, 1, 177])).
% 1.13/1.31 tff(3833,plain,
% 1.13/1.31 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[249, 3832])).
% 1.13/1.31 tff(3834,plain,
% 1.13/1.31 (~b(s(s(z)), elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2412, 3833, 685, 787])).
% 1.13/1.31 tff(3835,plain,
% 1.13/1.31 (r(s(s(z)), elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1135, 3834, 2833])).
% 1.13/1.31 tff(3836,plain,
% 1.13/1.31 (~r(s(s(z)), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2456, 112, 688, 3835])).
% 1.13/1.31 tff(3837,plain,
% 1.13/1.31 (b(s(s(z)), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[281, 3836])).
% 1.13/1.31 tff(3838,plain,
% 1.13/1.31 (~r(z, s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3758, 3835, 688])).
% 1.13/1.31 tff(3839,plain,
% 1.13/1.31 (b(z, s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1088, 3838])).
% 1.13/1.31 tff(3840,plain,
% 1.13/1.31 (~b(s(z), s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2882, 224, 1, 3839, 3837])).
% 1.13/1.31 tff(3841,plain,
% 1.13/1.31 (r(s(z), s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1071, 3840])).
% 1.13/1.31 tff(3842,plain,
% 1.13/1.31 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[1300])).
% 1.13/1.31 tff(3843,plain,
% 1.13/1.31 (r(elem!1, s(z))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3486, 3842])).
% 1.13/1.31 tff(3844,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3845,plain,
% 1.13/1.31 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3846,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3845])).
% 1.13/1.31 tff(3847,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3846, 3844])).
% 1.13/1.31 tff(3848,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3849,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3848, 3847])).
% 1.13/1.31 tff(3850,plain,
% 1.13/1.31 (~b(elem!1, s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3849, 224, 3788, 3833, 685, 3839])).
% 1.13/1.31 tff(3851,plain,
% 1.13/1.31 (r(elem!1, s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2874, 3850, 2832])).
% 1.13/1.31 tff(3852,plain,
% 1.13/1.31 (((~![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(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3853,plain,
% 1.13/1.31 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3854,plain,
% 1.13/1.31 (((~![X0: $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(elem!1, s(s(z)))) | (~r(s(z), 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(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3853])).
% 1.13/1.31 tff(3855,plain,
% 1.13/1.31 (((~![X0: $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(elem!1, s(s(z)))) | (~r(s(z), 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(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3854, 3852])).
% 1.13/1.31 tff(3856,plain,
% 1.13/1.31 ((~![X0: $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(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3857,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 1.13/1.31 tff(3858,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3857, 112, 3851, 3843, 3841])).
% 1.13/1.31 tff(3859,plain,((~b(s(z), z)) | (~b(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (s(z) = elem!1) | (~r(z, s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3860,plain,
% 1.13/1.31 (~b(s(z), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3859, 3786, 3618, 3784, 77, 73, 149, 101, 3773, 1240])).
% 1.13/1.31 tff(3861,plain,
% 1.13/1.31 (r(s(z), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[194, 3860])).
% 1.13/1.31 tff(3862,plain,
% 1.13/1.31 (~r(s(z), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[187, 3861, 73])).
% 1.13/1.31 tff(3863,plain,
% 1.13/1.31 (~b(s(z), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3742, 3861, 328, 73, 4, 750, 1240, 101, 77, 88])).
% 1.13/1.31 tff(3864,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[175, 3863, 3862])).
% 1.13/1.31 tff(3865,plain,((z = elem!1) | r(s(s(elem!1)), elem!1) | b(z, s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3866,plain,
% 1.13/1.31 (z = elem!1),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3865, 1240, 750, 328, 77, 88, 12, 74])).
% 1.13/1.31 tff(3867,plain,
% 1.13/1.31 (s(z) = s(elem!1)),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3866])).
% 1.13/1.31 tff(3868,plain,
% 1.13/1.31 (s(s(z)) = s(s(elem!1))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3867])).
% 1.13/1.31 tff(3869,plain,
% 1.13/1.31 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3868])).
% 1.13/1.31 tff(3870,plain,
% 1.13/1.31 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.13/1.31 inference(symmetry,[status(thm)],[3869])).
% 1.13/1.31 tff(3871,plain,
% 1.13/1.31 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3870])).
% 1.13/1.31 tff(3872,plain,
% 1.13/1.31 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.31 inference(symmetry,[status(thm)],[3871])).
% 1.13/1.31 tff(3873,plain,
% 1.13/1.31 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3867])).
% 1.13/1.31 tff(3874,plain,
% 1.13/1.31 (s(s(elem!1)) = s(s(z))),
% 1.13/1.31 inference(symmetry,[status(thm)],[1619])).
% 1.13/1.31 tff(3875,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.31 tff(3876,plain,
% 1.13/1.31 (s(s(s(elem!1))) = s(s(z))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3875, 3874])).
% 1.13/1.31 tff(3877,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1162, 3876])).
% 1.13/1.31 tff(3878,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3879,plain,
% 1.13/1.31 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3878, 3866])).
% 1.13/1.31 tff(3880,plain,
% 1.13/1.31 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3866])).
% 1.13/1.31 tff(3881,plain,
% 1.13/1.31 (r(elem!1, s(s(elem!1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3596, 3880])).
% 1.13/1.31 tff(3882,plain,
% 1.13/1.31 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3870])).
% 1.13/1.31 tff(3883,plain,
% 1.13/1.31 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.13/1.31 inference(symmetry,[status(thm)],[3882])).
% 1.13/1.31 tff(3884,plain,
% 1.13/1.31 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3866])).
% 1.13/1.31 tff(3885,plain,
% 1.13/1.31 (r(elem!1, s(s(s(z))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[101, 3884])).
% 1.13/1.31 tff(3886,plain,
% 1.13/1.31 (r(elem!1, s(s(s(elem!1))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3885, 3883])).
% 1.13/1.31 tff(3887,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.31 tff(3888,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.31 tff(3889,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3890,plain,
% 1.13/1.31 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3891,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3890])).
% 1.13/1.31 tff(3892,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3891, 3889])).
% 1.13/1.31 tff(3893,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3894,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 1.13/1.31 tff(3895,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3894, 112, 545, 3888, 3887])).
% 1.13/1.31 tff(3896,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3897,plain,
% 1.13/1.31 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3896, 3886, 3881])).
% 1.13/1.31 tff(3898,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.31 tff(3899,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.31 tff(3900,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.31 tff(3901,plain,
% 1.13/1.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3902,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3903,plain,
% 1.13/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 1.13/1.31 tff(3904,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3903, 68, 3900, 3899, 3898])).
% 1.13/1.31 tff(3905,plain,(b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3906,plain,
% 1.13/1.31 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3905, 3897, 3879])).
% 1.13/1.31 tff(3907,plain,
% 1.13/1.31 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3866])).
% 1.13/1.31 tff(3908,plain,
% 1.13/1.31 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3907])).
% 1.13/1.31 tff(3909,plain,
% 1.13/1.31 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[1334, 3908])).
% 1.13/1.31 tff(3910,plain,
% 1.13/1.31 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3870])).
% 1.13/1.31 tff(3911,plain,
% 1.13/1.31 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.31 inference(symmetry,[status(thm)],[3910])).
% 1.13/1.31 tff(3912,plain,
% 1.13/1.31 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3598, 3911])).
% 1.13/1.31 tff(3913,plain,
% 1.13/1.31 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1401, 68, 2027, 1694])).
% 1.13/1.31 tff(3914,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1916, 112, 545, 1798, 3913])).
% 1.13/1.31 tff(3915,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3916,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3915, 3906, 3881, 3912, 3866, 3885])).
% 1.13/1.31 tff(3917,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1294, 3916, 3909])).
% 1.13/1.31 tff(3918,plain,
% 1.13/1.31 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1380, 1733])).
% 1.13/1.31 tff(3919,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.13/1.31 tff(3920,plain,
% 1.13/1.31 (b(s(elem!1), elem!1)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[1, 1928])).
% 1.13/1.31 tff(3921,plain,
% 1.13/1.31 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2054, 224, 1636, 3920, 3919])).
% 1.13/1.31 tff(3922,plain,
% 1.13/1.31 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1345, 3921, 1832])).
% 1.13/1.31 tff(3923,plain,
% 1.13/1.31 (r(s(s(elem!1)), s(elem!1))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3486, 1929])).
% 1.13/1.31 tff(3924,plain,
% 1.13/1.31 (((~![X0: $i, 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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3925,plain,
% 1.13/1.31 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3926,plain,
% 1.13/1.31 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3925])).
% 1.13/1.31 tff(3927,plain,
% 1.13/1.31 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3926, 3924])).
% 1.13/1.31 tff(3928,plain,
% 1.13/1.31 ((~![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(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3929,plain,
% 1.13/1.31 ((~![X0: $i, 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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 1.13/1.31 tff(3930,plain,
% 1.13/1.31 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3929, 112, 3923, 3922])).
% 1.13/1.31 tff(3931,plain,
% 1.13/1.31 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1422, 68, 3930, 3918])).
% 1.13/1.31 tff(3932,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.31 inference(symmetry,[status(thm)],[1699])).
% 1.13/1.31 tff(3933,plain,
% 1.13/1.31 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3932])).
% 1.13/1.31 tff(3934,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3935,plain,
% 1.13/1.31 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3936,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3935])).
% 1.13/1.31 tff(3937,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3936, 3934])).
% 1.13/1.31 tff(3938,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3939,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3938, 3937])).
% 1.13/1.31 tff(3940,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3939, 112, 3923, 3922])).
% 1.13/1.31 tff(3941,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1401, 68, 1694, 3940])).
% 1.13/1.31 tff(3942,plain,
% 1.13/1.31 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.13/1.31 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.31 tff(3943,plain,
% 1.13/1.31 (b(s(s(elem!1)), elem!1)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[1240, 3942])).
% 1.13/1.31 tff(3944,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3945,plain,
% 1.13/1.32 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3946,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3945])).
% 1.13/1.32 tff(3947,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3946, 3944])).
% 1.13/1.32 tff(3948,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3949,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 1.13/1.32 tff(3950,plain,
% 1.13/1.32 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3949, 224, 3919, 3943, 1698])).
% 1.13/1.32 tff(3951,plain,
% 1.13/1.32 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3950, 3941])).
% 1.13/1.32 tff(3952,plain,
% 1.13/1.32 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3951, 3933])).
% 1.13/1.32 tff(3953,plain,
% 1.13/1.32 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1884, 3952])).
% 1.13/1.32 tff(3954,plain,
% 1.13/1.32 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3953, 1786])).
% 1.13/1.32 tff(3955,plain,
% 1.13/1.32 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1794, 112, 3954, 3887])).
% 1.13/1.32 tff(3956,plain,
% 1.13/1.32 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1439, 3955, 1782])).
% 1.13/1.32 tff(3957,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3958,plain,
% 1.13/1.32 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3959,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3958])).
% 1.13/1.32 tff(3960,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3959, 3957])).
% 1.13/1.32 tff(3961,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3962,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 1.13/1.32 tff(3963,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3962, 224, 3919, 3943, 3956, 3931])).
% 1.13/1.32 tff(3964,plain,((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3965,plain,
% 1.13/1.32 (~b(s(z), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3964, 3917, 3886, 3866, 3906, 77, 1240])).
% 1.13/1.32 tff(3966,plain,
% 1.13/1.32 (r(s(z), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[194, 3965])).
% 1.13/1.32 tff(3967,plain,
% 1.13/1.32 (~r(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[187, 3966, 73])).
% 1.13/1.32 tff(3968,plain,
% 1.13/1.32 (b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[175, 3967])).
% 1.13/1.32 tff(3969,plain,
% 1.13/1.32 (b(s(elem!1), s(s(s(z))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3968, 3873])).
% 1.13/1.32 tff(3970,plain,
% 1.13/1.32 (b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3969, 3872])).
% 1.13/1.32 tff(3971,plain,
% 1.13/1.32 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3867])).
% 1.13/1.32 tff(3972,plain,
% 1.13/1.32 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3971, 519])).
% 1.13/1.32 tff(3973,plain,
% 1.13/1.32 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3972, 520])).
% 1.13/1.32 tff(3974,plain,
% 1.13/1.32 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3973])).
% 1.13/1.32 tff(3975,plain,
% 1.13/1.32 (~(s(elem!1) = s(s(elem!1)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[648, 3974])).
% 1.13/1.32 tff(3976,plain,
% 1.13/1.32 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3866])).
% 1.13/1.32 tff(3977,plain,
% 1.13/1.32 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3976, 320])).
% 1.13/1.32 tff(3978,plain,
% 1.13/1.32 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.13/1.32 inference(transitivity,[status(thm)],[3977, 321])).
% 1.13/1.32 tff(3979,plain,
% 1.13/1.32 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3978])).
% 1.13/1.32 tff(3980,plain,
% 1.13/1.32 (~(s(elem!1) = elem!1)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[494, 3979])).
% 1.13/1.32 tff(3981,plain,
% 1.13/1.32 (elem!1 = z),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[338, 3866])).
% 1.13/1.32 tff(3982,plain,
% 1.13/1.32 (s(elem!1) = s(z)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[7])).
% 1.13/1.32 tff(3983,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[166, 3982])).
% 1.13/1.32 tff(3984,plain,((~(elem!1 = z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3985,plain,
% 1.13/1.32 (s(elem!1) = s(z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3984, 3981])).
% 1.13/1.32 tff(3986,plain,
% 1.13/1.32 (s(z) = s(elem!1)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[153, 464])).
% 1.13/1.32 tff(3987,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[666, 3986])).
% 1.13/1.32 tff(3988,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3989,plain,
% 1.13/1.32 (s(z) = s(elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3988, 3985])).
% 1.13/1.32 tff(3990,plain,
% 1.13/1.32 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[411])).
% 1.13/1.32 tff(3991,plain,
% 1.13/1.32 (z = inj_0(s(z))),
% 1.13/1.32 inference(symmetry,[status(thm)],[27])).
% 1.13/1.32 tff(3992,plain,
% 1.13/1.32 (z = elem!1),
% 1.13/1.32 inference(transitivity,[status(thm)],[3991, 3990, 121])).
% 1.13/1.32 tff(3993,plain,
% 1.13/1.32 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3992])).
% 1.13/1.32 tff(3994,plain,
% 1.13/1.32 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.13/1.32 inference(symmetry,[status(thm)],[3993])).
% 1.13/1.32 tff(3995,plain,
% 1.13/1.32 (b(s(elem!1), z)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[1488, 3994])).
% 1.13/1.32 tff(3996,plain,
% 1.13/1.32 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[411])).
% 1.13/1.32 tff(3997,plain,
% 1.13/1.32 ((~b(s(z), z)) <=> (~b(s(elem!1), z))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3996])).
% 1.13/1.32 tff(3998,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.13/1.32 tff(3999,plain,
% 1.13/1.32 (~b(s(elem!1), z)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.13/1.32 tff(4000,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3999, 3995])).
% 1.13/1.32 tff(4001,plain,((~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4002,plain,
% 1.13/1.32 (~b(s(elem!1), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4001, 3965, 3989])).
% 1.13/1.32 tff(4003,plain,
% 1.13/1.32 (r(s(elem!1), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[939, 4002, 3980])).
% 1.13/1.32 tff(4004,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4005,plain,
% 1.13/1.32 (((~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), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4006,plain,
% 1.13/1.32 (((~![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(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), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[4005])).
% 1.13/1.32 tff(4007,plain,
% 1.13/1.32 (((~![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(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), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[4006, 4004])).
% 1.13/1.32 tff(4008,plain,
% 1.13/1.32 ((~![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(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(4009,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[4008, 4007])).
% 1.13/1.32 tff(4010,plain,
% 1.13/1.32 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4009, 112])).
% 1.13/1.32 tff(4011,plain,
% 1.13/1.32 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4010, 4003, 3881])).
% 1.13/1.32 tff(4012,plain,
% 1.13/1.32 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1521, 4011, 3975])).
% 1.13/1.32 tff(4013,plain,
% 1.13/1.32 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4014,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[4013])).
% 1.13/1.32 tff(4015,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[4014, 1956])).
% 1.13/1.32 tff(4016,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(4017,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[4016, 4015])).
% 1.13/1.32 tff(4018,plain,
% 1.13/1.32 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4017, 224, 4012, 3906, 3912])).
% 1.13/1.32 tff(4019,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4018, 3970])).
% 1.13/1.32 tff(4020,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | b(z, s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4021,plain,
% 1.13/1.32 (b(z, s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4020, 3595, 77, 3330, 83, 12, 74])).
% 1.13/1.32 tff(4022,plain,
% 1.13/1.32 (b(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[360, 3595, 353])).
% 1.13/1.32 tff(4023,plain,
% 1.13/1.32 (~b(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1214, 344, 390, 77, 1180])).
% 1.13/1.32 tff(4024,plain,
% 1.13/1.32 (~r(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1269, 344, 77, 157, 1240, 3, 1180, 390])).
% 1.13/1.32 tff(4025,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1277, 4024, 4023, 88])).
% 1.13/1.32 tff(4026,plain,((~b(z, elem!1)) | (elem!1 = s(z)) | (~b(z, s(z))) | (elem!1 = z) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4027,plain,
% 1.13/1.32 (~b(z, elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4026, 4022, 77, 11, 3330, 3, 4021, 83])).
% 1.13/1.32 tff(4028,plain,
% 1.13/1.32 (r(z, elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[289, 4027, 4])).
% 1.13/1.32 tff(4029,plain,
% 1.13/1.32 (~r(s(s(s(z))), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2431, 4028, 73])).
% 1.13/1.32 tff(4030,plain,
% 1.13/1.32 (~b(s(s(elem!1)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1249, 3484, 77, 3330])).
% 1.13/1.32 tff(4031,plain,
% 1.13/1.32 (r(s(s(elem!1)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[901, 4030])).
% 1.13/1.32 tff(4032,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4033,plain,
% 1.13/1.32 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4034,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[4033])).
% 1.13/1.32 tff(4035,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[4034, 4032])).
% 1.13/1.32 tff(4036,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(4037,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 1.13/1.32 tff(4038,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4037, 112, 887, 178, 827])).
% 1.13/1.32 tff(4039,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4040,plain,
% 1.13/1.32 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4039, 176, 4031])).
% 1.13/1.32 tff(4041,plain,
% 1.13/1.32 (b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[147, 4040, 2])).
% 1.13/1.32 tff(4042,plain,
% 1.13/1.32 (~r(elem!1, z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[398, 362, 390, 152, 177])).
% 1.13/1.32 tff(4043,plain,
% 1.13/1.32 (~b(elem!1, z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3781, 2933, 1240, 390, 152])).
% 1.13/1.32 tff(4044,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[403, 4043, 4042, 157])).
% 1.13/1.32 tff(4045,plain,((s(s(s(z))) = elem!1) | (elem!1 = z) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4046,plain,
% 1.13/1.32 (s(s(s(z))) = elem!1),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4045, 4022, 3330, 11, 4041, 73, 4029])).
% 1.13/1.32 tff(4047,plain,
% 1.13/1.32 (elem!1 = s(s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2487, 4046])).
% 1.13/1.32 tff(4048,plain,
% 1.13/1.32 (~b(s(z), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2477, 4047, 170])).
% 1.13/1.32 tff(4049,plain,
% 1.13/1.32 (r(s(z), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[454, 4048, 91])).
% 1.13/1.32 tff(4050,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3508, 224, 1240, 1, 2252, 1180])).
% 1.13/1.32 tff(4051,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4052,plain,
% 1.13/1.32 (~b(s(z), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4051, 4021, 3484, 3330])).
% 1.13/1.32 tff(4053,plain,
% 1.13/1.32 (r(s(z), s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[653, 4052])).
% 1.13/1.32 tff(4054,plain,
% 1.13/1.32 (~b(elem!1, z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2437, 4046, 12])).
% 1.13/1.32 tff(4055,plain,
% 1.13/1.32 (r(elem!1, z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[403, 4054, 11])).
% 1.13/1.32 tff(4056,plain,
% 1.13/1.32 (~r(s(s(z)), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2468, 4049, 77, 4028])).
% 1.13/1.32 tff(4057,plain,
% 1.13/1.32 (r(elem!1, s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2606, 4056, 3, 2596, 3595, 73, 4041, 4055])).
% 1.13/1.32 tff(4058,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2573, 112, 4057, 4053, 4049])).
% 1.13/1.32 tff(4059,plain,(b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4060,plain,
% 1.13/1.32 (b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4059, 2596, 3, 77, 12, 2, 4, 74])).
% 1.13/1.32 tff(4061,plain,
% 1.13/1.32 (r(s(s(elem!1)), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[360, 354, 355])).
% 1.13/1.32 tff(4062,plain,
% 1.13/1.32 (~r(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3588, 4061, 887])).
% 1.13/1.32 tff(4063,plain,
% 1.13/1.32 (b(elem!1, s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1277, 4062, 88])).
% 1.13/1.32 tff(4064,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1187, 112, 1181, 416, 887])).
% 1.13/1.32 tff(4065,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(4066,plain,
% 1.13/1.32 (~r(s(z), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[4065, 4061, 887])).
% 1.13/1.32 tff(4067,plain,
% 1.13/1.32 (b(s(z), elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[454, 4066, 149])).
% 1.13/1.32 tff(4068,plain,
% 1.13/1.32 (~b(z, elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2904, 4067, 77, 4063])).
% 1.13/1.32 tff(4069,plain,
% 1.13/1.32 (r(z, elem!1)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[289, 4068, 4])).
% 1.13/1.32 tff(4070,plain,
% 1.13/1.32 (~r(z, s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3500, 4069, 4061])).
% 1.13/1.32 tff(4071,plain,
% 1.13/1.32 (b(z, s(s(elem!1)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[752, 4070])).
% 1.13/1.32 tff(4072,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(4073,plain,
% 1.13/1.32 (((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4074,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4073])).
% 1.13/1.33 tff(4075,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4074, 4072])).
% 1.13/1.33 tff(4076,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4077,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4076, 4075])).
% 1.13/1.33 tff(4078,plain,
% 1.13/1.33 (~b(s(s(z)), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4077, 224, 1240, 4071, 2596])).
% 1.13/1.33 tff(4079,plain,
% 1.13/1.33 (r(s(s(z)), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[281, 4078])).
% 1.13/1.33 tff(4080,plain,
% 1.13/1.33 (b(s(z), elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[454, 2931, 129])).
% 1.13/1.33 tff(4081,plain,
% 1.13/1.33 (~b(z, elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2904, 4080, 77, 2896])).
% 1.13/1.33 tff(4082,plain,
% 1.13/1.33 (r(z, elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[289, 4081, 4])).
% 1.13/1.33 tff(4083,plain,
% 1.13/1.33 (~r(s(s(s(z))), elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2431, 4082, 177])).
% 1.13/1.33 tff(4084,plain,
% 1.13/1.33 (~r(elem!1, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2420, 4082, 689])).
% 1.13/1.33 tff(4085,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2951, 4084, 4083, 1090, 354, 362, 2931])).
% 1.13/1.33 tff(4086,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | b(s(s(elem!1)), elem!1) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (z = elem!1) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(4087,plain,
% 1.13/1.33 (s(s(s(z))) = elem!1),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4086, 4066, 354, 1090, 689, 177, 4, 77, 4063, 149])).
% 1.13/1.33 tff(4088,plain,
% 1.13/1.33 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4087])).
% 1.13/1.33 tff(4089,plain,
% 1.13/1.33 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.13/1.33 inference(symmetry,[status(thm)],[4088])).
% 1.13/1.33 tff(4090,plain,
% 1.13/1.33 (b(s(s(s(z))), s(z))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4063, 4089])).
% 1.13/1.33 tff(4091,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4087])).
% 1.13/1.33 tff(4092,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.33 inference(symmetry,[status(thm)],[4091])).
% 1.13/1.33 tff(4093,plain,
% 1.13/1.33 (s(s(s(s(z)))) = s(elem!1)),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4087])).
% 1.13/1.33 tff(4094,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4093])).
% 1.13/1.33 tff(4095,plain,
% 1.13/1.33 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.13/1.33 inference(symmetry,[status(thm)],[4094])).
% 1.13/1.33 tff(4096,plain,
% 1.13/1.33 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4095, 4092])).
% 1.13/1.33 tff(4097,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4098,plain,
% 1.13/1.33 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4099,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4098])).
% 1.13/1.33 tff(4100,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4099, 4097])).
% 1.13/1.33 tff(4101,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4102,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 1.13/1.33 tff(4103,plain,
% 1.13/1.33 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4102, 112, 408, 1181])).
% 1.13/1.33 tff(4104,plain,
% 1.13/1.33 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1521, 4103, 523])).
% 1.13/1.33 tff(4105,plain,
% 1.13/1.33 (~r(z, s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3500, 1181, 688])).
% 1.13/1.33 tff(4106,plain,
% 1.13/1.33 (b(z, s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[752, 4105])).
% 1.13/1.33 tff(4107,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4108,plain,
% 1.13/1.33 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4109,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4108])).
% 1.13/1.33 tff(4110,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4109, 4107])).
% 1.13/1.33 tff(4111,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4112,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 1.13/1.33 tff(4113,plain,
% 1.13/1.33 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4112, 112, 408, 1181])).
% 1.13/1.33 tff(4114,plain,
% 1.13/1.33 (b(s(s(elem!1)), s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[530, 4113, 1923])).
% 1.13/1.33 tff(4115,plain,
% 1.13/1.33 (~r(z, s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2497, 112, 408, 688])).
% 1.13/1.33 tff(4116,plain,
% 1.13/1.33 (b(z, s(elem!1))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[625, 4115])).
% 1.13/1.33 tff(4117,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4118,plain,
% 1.13/1.33 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4119,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4118])).
% 1.13/1.33 tff(4120,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4119, 4117])).
% 1.13/1.33 tff(4121,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4122,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4121, 4120])).
% 1.13/1.33 tff(4123,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4122, 224, 1391, 1390, 1180, 407])).
% 1.13/1.33 tff(4124,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(4125,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4124, 4116, 4114, 4106, 4104])).
% 1.13/1.33 tff(4126,plain,((~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(4127,plain,
% 1.13/1.33 (~r(s(elem!1), elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4126, 4069, 4061, 523])).
% 1.13/1.33 tff(4128,plain,
% 1.13/1.33 (b(s(elem!1), elem!1)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[939, 4127, 324])).
% 1.13/1.33 tff(4129,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4128, 4096])).
% 1.13/1.33 tff(4130,plain,
% 1.13/1.33 (~b(s(s(s(s(z)))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1579, 4129, 1090, 4090])).
% 1.13/1.33 tff(4131,plain,
% 1.13/1.33 (s(s(s(s(z)))) = s(elem!1)),
% 1.13/1.33 inference(monotonicity,[status(thm)],[341])).
% 1.13/1.33 tff(4132,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4131])).
% 1.13/1.33 tff(4133,plain,
% 1.13/1.33 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.13/1.33 inference(symmetry,[status(thm)],[4132])).
% 1.13/1.33 tff(4134,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[1347, 4133])).
% 1.13/1.33 tff(4135,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3163, 4134])).
% 1.13/1.33 tff(4136,plain,((~b(s(elem!1), s(z))) | b(s(s(s(s(z)))), s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(4137,plain,
% 1.13/1.33 (~b(s(elem!1), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4136, 4130, 4087])).
% 1.13/1.33 tff(4138,plain,
% 1.13/1.33 (r(s(elem!1), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1476, 4137, 160])).
% 1.13/1.33 tff(4139,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), 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(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4140,plain,
% 1.13/1.33 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4141,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(elem!1), s(z)))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4140])).
% 1.13/1.33 tff(4142,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4141, 4139])).
% 1.13/1.33 tff(4143,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4144,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 1.13/1.33 tff(4145,plain,
% 1.13/1.33 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4144, 112, 4061, 887, 4138])).
% 1.13/1.33 tff(4146,plain,
% 1.13/1.33 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1521, 4145, 523])).
% 1.13/1.33 tff(4147,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4148,plain,
% 1.13/1.33 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4149,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[4148])).
% 1.13/1.33 tff(4150,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[4149, 4147])).
% 1.13/1.33 tff(4151,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(4152,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 1.13/1.33 tff(4153,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4152, 224, 1390, 1240, 500, 1180])).
% 1.13/1.33 tff(4154,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(4155,plain,
% 1.13/1.33 (~b(s(elem!1), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[4154, 4146, 1240, 4071])).
% 1.13/1.33 tff(4156,plain,
% 1.13/1.33 (r(s(elem!1), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[498, 4155])).
% 1.13/1.33 tff(4157,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4158,plain,
% 1.13/1.33 (((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(4159,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4158])).
% 1.13/1.34 tff(4160,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[4159, 4157])).
% 1.13/1.34 tff(4161,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(4162,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.13/1.34 tff(4163,plain,
% 1.13/1.34 (~r(s(s(z)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4162, 112, 4156, 4079])).
% 1.13/1.34 tff(4164,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4087])).
% 1.13/1.34 tff(4165,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3455, 4079, 689])).
% 1.13/1.34 tff(4166,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[249, 4165])).
% 1.13/1.34 tff(4167,plain,
% 1.13/1.34 (b(s(s(z)), elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4166, 4164])).
% 1.13/1.34 tff(4168,plain,
% 1.13/1.34 (((~![X0: $i, 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(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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4169,plain,
% 1.13/1.34 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4170,plain,
% 1.13/1.34 (((~![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(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4169])).
% 1.13/1.34 tff(4171,plain,
% 1.13/1.34 (((~![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(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[4170, 4168])).
% 1.13/1.34 tff(4172,plain,
% 1.13/1.34 ((~![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(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(4173,plain,
% 1.13/1.34 ((~![X0: $i, 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(z))) | (~r(s(elem!1), s(z)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4172, 4171])).
% 1.13/1.34 tff(4174,plain,
% 1.13/1.34 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4173, 112, 887, 4138])).
% 1.13/1.34 tff(4175,plain,
% 1.13/1.34 (b(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[530, 4174, 1923])).
% 1.13/1.34 tff(4176,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4177,plain,
% 1.13/1.34 (((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4178,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4177])).
% 1.13/1.34 tff(4179,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[4178, 4176])).
% 1.13/1.34 tff(4180,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(4181,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4180, 4179])).
% 1.13/1.34 tff(4182,plain,
% 1.13/1.34 (~b(s(s(z)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4181, 224, 4128, 4175, 4167, 2596])).
% 1.13/1.34 tff(4183,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2532, 68, 2529, 4182, 4163])).
% 1.13/1.34 tff(4184,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = elem!1) | (z = elem!1) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(z)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4185,plain,
% 1.13/1.34 (b(s(s(elem!1)), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4184, 2596, 3330, 101, 319, 4031, 4060, 303, 4, 77, 73, 83, 353])).
% 1.13/1.34 tff(4186,plain,
% 1.13/1.34 (b(s(s(elem!1)), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4184, 2596, 1240, 101, 319, 3486, 1090, 303, 4, 77, 73, 88, 353])).
% 1.13/1.34 tff(4187,plain,
% 1.13/1.34 (~b(z, s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4026, 344, 77, 11, 1240, 3, 390, 88])).
% 1.13/1.34 tff(4188,plain,
% 1.13/1.34 (r(s(s(elem!1)), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3865, 4187, 4, 77, 1240, 88, 12, 74])).
% 1.13/1.34 tff(4189,plain,
% 1.13/1.34 (~b(elem!1, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2904, 344, 77, 684])).
% 1.13/1.34 tff(4190,plain,
% 1.13/1.34 (r(elem!1, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1277, 4189, 88])).
% 1.13/1.34 tff(4191,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3588, 4190, 4188, 887])).
% 1.13/1.34 tff(4192,plain,((~b(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (z = elem!1) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | b(s(s(s(z))), z) | b(z, s(s(s(z)))) | (~b(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4193,plain,
% 1.13/1.34 (~b(z, elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4192, 684, 88, 4, 77, 1240, 12, 74, 3486, 3, 4186])).
% 1.13/1.34 tff(4194,plain,
% 1.13/1.34 (r(z, elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[289, 4193, 4])).
% 1.13/1.34 tff(4195,plain,
% 1.13/1.34 (~r(s(s(s(z))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2431, 4194, 73])).
% 1.13/1.34 tff(4196,plain,
% 1.13/1.34 (~r(elem!1, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2420, 4194, 101])).
% 1.13/1.34 tff(4197,plain,
% 1.13/1.34 (~(elem!1 = s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3418, 362])).
% 1.13/1.34 tff(4198,plain,
% 1.13/1.34 (b(elem!1, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[388, 4197, 2440])).
% 1.13/1.34 tff(4199,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2941, 4198, 2933, 1090, 684])).
% 1.13/1.34 tff(4200,plain,((s(s(s(z))) = elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4201,plain,
% 1.13/1.34 (s(s(s(z))) = elem!1),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4200, 684, 1090, 4196, 4195])).
% 1.13/1.34 tff(4202,plain,
% 1.13/1.34 (~b(elem!1, z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2437, 4201, 12])).
% 1.13/1.34 tff(4203,plain,
% 1.13/1.34 (r(elem!1, z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[403, 4202, 11])).
% 1.13/1.34 tff(4204,plain,
% 1.13/1.34 (~(s(z) = s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[414, 160])).
% 1.13/1.34 tff(4205,plain,
% 1.13/1.34 (b(s(elem!1), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[939, 2617, 303])).
% 1.13/1.34 tff(4206,plain,
% 1.13/1.34 (b(elem!1, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[515, 2507, 327])).
% 1.13/1.34 tff(4207,plain,
% 1.13/1.34 (~b(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1496, 4206, 390, 4205])).
% 1.13/1.34 tff(4208,plain,
% 1.13/1.34 (~(s(z) = s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4001, 3998, 1488])).
% 1.13/1.34 tff(4209,plain,
% 1.13/1.34 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[410])).
% 1.13/1.34 tff(4210,plain,
% 1.13/1.34 (~(s(elem!1) = s(z))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4208, 4209])).
% 1.13/1.34 tff(4211,plain,
% 1.13/1.34 (~(elem!1 = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3984, 4210])).
% 1.13/1.34 tff(4212,plain,
% 1.13/1.34 (~r(elem!1, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[615, 4211, 3, 568, 544])).
% 1.13/1.34 tff(4213,plain,
% 1.13/1.34 (b(elem!1, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[515, 4212, 327])).
% 1.13/1.34 tff(4214,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4215,plain,
% 1.13/1.34 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4216,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4215])).
% 1.13/1.34 tff(4217,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[4216, 4214])).
% 1.13/1.34 tff(4218,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(4219,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4218, 4217])).
% 1.13/1.34 tff(4220,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4219, 224, 501, 1488, 684, 683])).
% 1.13/1.34 tff(4221,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4222,plain,
% 1.13/1.34 (~b(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4221, 4213, 684, 1488])).
% 1.13/1.34 tff(4223,plain,
% 1.13/1.34 (r(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[194, 3998])).
% 1.13/1.34 tff(4224,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4225,plain,
% 1.13/1.34 (((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4226,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4225])).
% 1.13/1.34 tff(4227,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[4226, 4224])).
% 1.13/1.34 tff(4228,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(4229,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 1.13/1.34 tff(4230,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4229, 112, 179, 568, 655])).
% 1.13/1.34 tff(4231,plain,((~r(s(z), s(elem!1))) | (~r(s(z), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4232,plain,
% 1.13/1.34 (~r(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4231, 4223, 568])).
% 1.13/1.34 tff(4233,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[426, 68, 4232, 4222, 4208])).
% 1.13/1.34 tff(4234,plain,(b(s(z), z) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4235,plain,
% 1.13/1.34 (b(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4234, 1488, 684, 3, 568, 544])).
% 1.13/1.34 tff(4236,plain,
% 1.13/1.34 (~b(s(z), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3508, 224, 594, 4235, 582])).
% 1.13/1.34 tff(4237,plain,
% 1.13/1.34 (r(s(z), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[653, 4236])).
% 1.13/1.34 tff(4238,plain,
% 1.13/1.34 (~r(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[664, 4237, 544])).
% 1.13/1.34 tff(4239,plain,
% 1.13/1.34 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[426, 68, 4238])).
% 1.13/1.34 tff(4240,plain,
% 1.13/1.34 (b(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4239, 415])).
% 1.13/1.34 tff(4241,plain,
% 1.13/1.34 (~(elem!1 = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3984, 166])).
% 1.13/1.34 tff(4242,plain,
% 1.13/1.34 (~r(elem!1, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[615, 4241, 3, 568, 544])).
% 1.13/1.34 tff(4243,plain,
% 1.13/1.34 (b(elem!1, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[515, 4242, 327])).
% 1.13/1.34 tff(4244,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4221, 4243, 4240, 684, 1488])).
% 1.13/1.34 tff(4245,plain,((s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4246,plain,
% 1.13/1.34 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4245, 4205, 3, 166, 684, 568])).
% 1.13/1.34 tff(4247,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[530, 4246, 4207, 526])).
% 1.13/1.34 tff(4248,plain,((~r(z, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4249,plain,
% 1.13/1.34 (~r(z, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4248, 684, 160, 3, 4186, 4194, 4203])).
% 1.13/1.34 tff(4250,plain,
% 1.13/1.34 (b(z, s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[625, 4249])).
% 1.13/1.34 tff(4251,plain,
% 1.13/1.34 (b(z, s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4020, 328, 77, 1240, 88, 12, 74])).
% 1.13/1.34 tff(4252,plain,
% 1.13/1.34 (~b(s(z), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4051, 4251, 1, 1240])).
% 1.13/1.34 tff(4253,plain,
% 1.13/1.34 (r(s(z), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[653, 4252])).
% 1.13/1.34 tff(4254,plain,
% 1.13/1.34 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[341])).
% 1.13/1.34 tff(4255,plain,
% 1.13/1.34 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[4254])).
% 1.13/1.34 tff(4256,plain,
% 1.13/1.34 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[341])).
% 1.13/1.34 tff(4257,plain,
% 1.13/1.34 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[4256])).
% 1.13/1.34 tff(4258,plain,
% 1.13/1.34 (b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[390, 4257])).
% 1.13/1.34 tff(4259,plain,
% 1.13/1.34 (r(s(s(z)), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2606, 2597, 3, 2596, 328, 177, 4258, 363])).
% 1.13/1.34 tff(4260,plain,
% 1.13/1.34 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[4259, 4255])).
% 1.13/1.34 tff(4261,plain,
% 1.13/1.34 (b(elem!1, s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[558, 2597, 3])).
% 1.13/1.34 tff(4262,plain,
% 1.13/1.34 (~r(s(elem!1), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2713, 407, 2711, 1118, 1047, 363])).
% 1.13/1.34 tff(4263,plain,
% 1.13/1.34 (b(s(elem!1), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[939, 4262, 324])).
% 1.13/1.34 tff(4264,plain,
% 1.13/1.34 (~b(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2673, 224, 4263, 1, 684, 407])).
% 1.13/1.34 tff(4265,plain,
% 1.13/1.34 (r(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[670, 4264, 666])).
% 1.13/1.34 tff(4266,plain,
% 1.13/1.34 (~b(s(elem!1), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2541, 224, 4263, 682, 390])).
% 1.13/1.34 tff(4267,plain,
% 1.13/1.34 (r(s(elem!1), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1521, 4266, 523])).
% 1.13/1.34 tff(4268,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2682, 112, 4267, 656, 4265])).
% 1.13/1.34 tff(4269,plain,((~b(z, s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = elem!1) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4270,plain,
% 1.13/1.34 (~b(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4269, 4261, 666, 319, 1, 390, 684, 407, 303, 2711, 656, 4259, 363])).
% 1.13/1.34 tff(4271,plain,
% 1.13/1.34 (r(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[281, 4270])).
% 1.13/1.34 tff(4272,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3455, 4271, 689])).
% 1.13/1.34 tff(4273,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4272, 4260])).
% 1.13/1.34 tff(4274,plain,(r(elem!1, s(s(elem!1))) | (~(s(s(s(z))) = elem!1)) | (~r(z, s(s(s(z))))) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4275,plain,
% 1.13/1.34 (r(elem!1, s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4274, 4253, 101, 666, 1, 390, 684, 407, 2529, 341, 363, 3, 2596, 328, 73])).
% 1.13/1.34 tff(4276,plain,
% 1.13/1.34 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4010, 408, 545])).
% 1.13/1.34 tff(4277,plain,
% 1.13/1.34 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1521, 4276, 523])).
% 1.13/1.34 tff(4278,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4154, 4277, 2696, 1240, 1180])).
% 1.13/1.34 tff(4279,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(4280,plain,
% 1.13/1.34 (~r(s(elem!1), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[4279, 4251, 1240, 319, 4275, 363])).
% 1.13/1.34 tff(4281,plain,
% 1.13/1.34 (b(s(elem!1), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[939, 4280, 303])).
% 1.13/1.34 tff(4282,plain,
% 1.13/1.34 (~b(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2673, 224, 4281, 1, 684, 407])).
% 1.13/1.34 tff(4283,plain,
% 1.13/1.34 (r(s(z), s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[670, 4282, 666])).
% 1.13/1.34 tff(4284,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4285,plain,
% 1.13/1.34 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(4286,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[4285])).
% 1.13/1.34 tff(4287,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4286, 4284])).
% 1.13/1.35 tff(4288,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4289,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4288, 4287])).
% 1.13/1.35 tff(4290,plain,
% 1.13/1.35 (~b(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4289, 224, 4281, 1240, 390, 407])).
% 1.13/1.35 tff(4291,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[530, 4290, 526])).
% 1.13/1.35 tff(4292,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[664, 4291, 4283, 4253])).
% 1.13/1.35 tff(4293,plain,(r(s(s(elem!1)), elem!1) | (s(z) = s(elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (elem!1 = s(z)) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4294,plain,
% 1.13/1.35 (r(s(s(elem!1)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4293, 4250, 1240, 4186, 4204, 1, 684, 4203, 4201, 3, 2596, 77, 88, 12, 74])).
% 1.13/1.35 tff(4295,plain,
% 1.13/1.35 (~r(z, s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3500, 4294, 4194])).
% 1.13/1.35 tff(4296,plain,
% 1.13/1.35 (b(z, s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[752, 4295])).
% 1.13/1.35 tff(4297,plain,
% 1.13/1.35 (~b(s(z), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4051, 4296, 1, 1240])).
% 1.13/1.35 tff(4298,plain,
% 1.13/1.35 (r(s(z), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[653, 4297])).
% 1.13/1.35 tff(4299,plain,
% 1.13/1.35 (~r(s(elem!1), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4126, 4294, 4194, 319])).
% 1.13/1.35 tff(4300,plain,
% 1.13/1.35 (b(s(elem!1), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[939, 4299, 303])).
% 1.13/1.35 tff(4301,plain,
% 1.13/1.35 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[539, 543, 1181])).
% 1.13/1.35 tff(4302,plain,
% 1.13/1.35 (b(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[530, 4301, 2505])).
% 1.13/1.35 tff(4303,plain,
% 1.13/1.35 (((~![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(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4304,plain,
% 1.13/1.35 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4305,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4304])).
% 1.13/1.35 tff(4306,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4305, 4303])).
% 1.13/1.35 tff(4307,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4308,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 1.13/1.35 tff(4309,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4308, 112, 543, 363, 467])).
% 1.13/1.35 tff(4310,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4311,plain,
% 1.13/1.35 (~r(s(elem!1), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4310, 543, 363])).
% 1.13/1.35 tff(4312,plain,
% 1.13/1.35 (b(s(elem!1), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[498, 4311])).
% 1.13/1.35 tff(4313,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4314,plain,
% 1.13/1.35 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4315,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4314])).
% 1.13/1.35 tff(4316,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4315, 4313])).
% 1.13/1.35 tff(4317,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4318,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 1.13/1.35 tff(4319,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4318, 224, 1391, 1240, 500, 407])).
% 1.13/1.35 tff(4320,plain,((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4321,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4320, 4312, 4302, 1240, 407])).
% 1.13/1.35 tff(4322,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4323,plain,
% 1.13/1.35 (~r(elem!1, s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4322, 4294, 1240, 526, 4203, 4250])).
% 1.13/1.35 tff(4324,plain,
% 1.13/1.35 (b(elem!1, s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[515, 4323, 327])).
% 1.13/1.35 tff(4325,plain,
% 1.13/1.35 (~b(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1496, 4324, 4186, 4300])).
% 1.13/1.35 tff(4326,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[530, 4325, 526])).
% 1.13/1.35 tff(4327,plain,
% 1.13/1.35 (~b(s(z), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4221, 4324, 684, 4300])).
% 1.13/1.35 tff(4328,plain,
% 1.13/1.35 (r(s(z), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[670, 4327, 4204])).
% 1.13/1.35 tff(4329,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[664, 4328, 4326, 4298])).
% 1.13/1.35 tff(4330,plain,((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (elem!1 = s(z)) | b(s(s(s(z))), z) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4331,plain,
% 1.13/1.35 (~b(s(z), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4330, 3484, 3330, 3, 2596, 77, 83, 12, 74, 4060, 4])).
% 1.13/1.35 tff(4332,plain,
% 1.13/1.35 (r(s(z), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[454, 4331, 91])).
% 1.13/1.35 tff(4333,plain,
% 1.13/1.35 (~r(s(s(elem!1)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4065, 4332, 4031])).
% 1.13/1.35 tff(4334,plain,
% 1.13/1.35 (b(z, s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4020, 4333, 77, 3330, 83, 12, 74])).
% 1.13/1.35 tff(4335,plain,
% 1.13/1.35 (~b(z, elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4026, 4334, 77, 11, 3330, 3, 4185, 83])).
% 1.13/1.35 tff(4336,plain,
% 1.13/1.35 (r(z, elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[289, 4335, 4])).
% 1.13/1.35 tff(4337,plain,
% 1.13/1.35 (~r(s(s(z)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2468, 4336, 77, 4332])).
% 1.13/1.35 tff(4338,plain,
% 1.13/1.35 (~r(s(elem!1), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2502, 4336, 160, 4332, 77])).
% 1.13/1.35 tff(4339,plain,
% 1.13/1.35 (b(s(elem!1), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[939, 4338, 303])).
% 1.13/1.35 tff(4340,plain,
% 1.13/1.35 (~b(s(z), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4051, 4334, 3484, 3330])).
% 1.13/1.35 tff(4341,plain,
% 1.13/1.35 (r(s(z), s(s(elem!1)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[653, 4340])).
% 1.13/1.35 tff(4342,plain,
% 1.13/1.35 (b(s(s(s(z))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[374, 362, 3334])).
% 1.13/1.35 tff(4343,plain,
% 1.13/1.35 (b(elem!1, s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[388, 4197, 3335])).
% 1.13/1.35 tff(4344,plain,
% 1.13/1.35 (~b(s(s(z)), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4077, 224, 1240, 1180, 2596])).
% 1.13/1.35 tff(4345,plain,
% 1.13/1.35 (r(s(s(z)), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[281, 4344])).
% 1.13/1.35 tff(4346,plain,
% 1.13/1.35 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3455, 4345, 689])).
% 1.13/1.35 tff(4347,plain,
% 1.13/1.35 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[249, 4346])).
% 1.13/1.35 tff(4348,plain,
% 1.13/1.35 (~b(s(s(z)), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2412, 4347, 4343, 4342])).
% 1.13/1.35 tff(4349,plain,
% 1.13/1.35 (s(s(z)) = elem!1),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1135, 4348, 2586])).
% 1.13/1.35 tff(4350,plain,
% 1.13/1.35 (s(s(s(z))) = s(elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4349])).
% 1.13/1.35 tff(4351,plain,
% 1.13/1.35 (s(elem!1) = s(s(s(z)))),
% 1.13/1.35 inference(symmetry,[status(thm)],[4350])).
% 1.13/1.35 tff(4352,plain,
% 1.13/1.35 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4351])).
% 1.13/1.35 tff(4353,plain,
% 1.13/1.35 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.13/1.35 inference(symmetry,[status(thm)],[4352])).
% 1.13/1.35 tff(4354,plain,
% 1.13/1.35 (b(elem!1, s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4343, 4353])).
% 1.13/1.35 tff(4355,plain,
% 1.13/1.35 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4356,plain,
% 1.13/1.35 (b(s(z), s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[1090, 4355])).
% 1.13/1.35 tff(4357,plain,
% 1.13/1.35 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4358,plain,
% 1.13/1.35 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4359,plain,
% 1.13/1.35 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4358])).
% 1.13/1.35 tff(4360,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.13/1.35 inference(symmetry,[status(thm)],[4359])).
% 1.13/1.35 tff(4361,plain,
% 1.13/1.35 (r(s(s(s(s(z)))), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[887, 4360])).
% 1.13/1.35 tff(4362,plain,
% 1.13/1.35 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4358, 4350])).
% 1.13/1.35 tff(4363,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[4362])).
% 1.13/1.35 tff(4364,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4365,plain,
% 1.13/1.35 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4045, 362, 1240, 157, 390, 177, 3334])).
% 1.13/1.35 tff(4366,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[147, 4365, 2])).
% 1.13/1.35 tff(4367,plain,
% 1.13/1.35 (r(s(s(elem!1)), s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4366, 4364])).
% 1.13/1.35 tff(4368,plain,
% 1.13/1.35 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4367, 4363])).
% 1.13/1.35 tff(4369,plain,
% 1.13/1.35 (~r(s(s(s(z))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3326, 4368, 4361])).
% 1.13/1.35 tff(4370,plain,
% 1.13/1.35 (b(s(s(s(z))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[925, 4369])).
% 1.13/1.35 tff(4371,plain,
% 1.13/1.35 (b(s(elem!1), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4370, 4357])).
% 1.13/1.35 tff(4372,plain,
% 1.13/1.35 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4373,plain,
% 1.13/1.35 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4372, 1143])).
% 1.13/1.35 tff(4374,plain,
% 1.13/1.35 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4373])).
% 1.13/1.35 tff(4375,plain,
% 1.13/1.35 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[1165, 4374])).
% 1.13/1.35 tff(4376,plain,
% 1.13/1.35 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4350])).
% 1.13/1.35 tff(4377,plain,
% 1.13/1.35 (r(z, s(elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[689, 4376])).
% 1.13/1.35 tff(4378,plain,
% 1.13/1.35 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4379,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4378])).
% 1.13/1.35 tff(4380,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4379, 2049])).
% 1.13/1.35 tff(4381,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4382,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4381, 4380])).
% 1.13/1.35 tff(4383,plain,
% 1.13/1.35 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4382, 224, 501, 1488, 1409])).
% 1.13/1.35 tff(4384,plain,
% 1.13/1.35 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1294, 4383, 1288])).
% 1.13/1.35 tff(4385,plain,
% 1.13/1.35 (((~![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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4386,plain,
% 1.13/1.35 (((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4387,plain,
% 1.13/1.35 (((~![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(elem!1)))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4386])).
% 1.13/1.35 tff(4388,plain,
% 1.13/1.35 (((~![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(elem!1)))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4387, 4385])).
% 1.13/1.35 tff(4389,plain,
% 1.13/1.35 ((~![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(elem!1)))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4390,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4389, 4388])).
% 1.13/1.35 tff(4391,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4390, 112, 4384, 656, 416, 1411])).
% 1.13/1.35 tff(4392,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(4393,plain,
% 1.13/1.35 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4392, 1288, 416, 656, 1347, 683, 501, 1488])).
% 1.13/1.35 tff(4394,plain,
% 1.13/1.35 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1345, 4393, 1286])).
% 1.13/1.35 tff(4395,plain,
% 1.13/1.35 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3929, 112, 544, 4394])).
% 1.13/1.35 tff(4396,plain,
% 1.13/1.35 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1422, 68, 4395, 1381])).
% 1.13/1.35 tff(4397,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4398,plain,
% 1.13/1.35 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4399,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4398])).
% 1.13/1.35 tff(4400,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[4399, 4397])).
% 1.13/1.35 tff(4401,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4402,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 1.13/1.35 tff(4403,plain,
% 1.13/1.35 (~r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4402, 112, 568, 4394])).
% 1.13/1.35 tff(4404,plain,
% 1.13/1.35 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(4405,plain,
% 1.13/1.35 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[4404])).
% 1.13/1.35 tff(4406,plain,
% 1.13/1.35 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[4405])).
% 1.13/1.35 tff(4407,plain,
% 1.13/1.35 (~(z = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[1334, 4406])).
% 1.13/1.35 tff(4408,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(4409,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(4410,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[4409, 4408])).
% 1.13/1.35 tff(4411,plain,
% 1.13/1.35 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4410, 68])).
% 1.13/1.35 tff(4412,plain,
% 1.13/1.35 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4411, 4407])).
% 1.13/1.35 tff(4413,plain,
% 1.13/1.35 (b(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[4412, 4403])).
% 1.13/1.36 tff(4414,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4415,plain,
% 1.13/1.36 (((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4416,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4415])).
% 1.13/1.36 tff(4417,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4416, 4414])).
% 1.13/1.36 tff(4418,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(4419,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 1.13/1.36 tff(4420,plain,
% 1.13/1.36 (~r(s(s(s(s(elem!1)))), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4419, 112, 688, 568, 4394])).
% 1.13/1.36 tff(4421,plain,
% 1.13/1.36 (b(s(s(s(s(elem!1)))), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1338, 4420])).
% 1.13/1.36 tff(4422,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4423,plain,
% 1.13/1.36 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4424,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4423])).
% 1.13/1.36 tff(4425,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4424, 4422])).
% 1.13/1.36 tff(4426,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(4427,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 1.13/1.36 tff(4428,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4427, 224, 1240, 4421, 4413, 4396])).
% 1.13/1.36 tff(4429,plain,((s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4430,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4429, 4377, 688, 1240, 4367, 4375, 416, 656, 4371, 4356, 4354, 1488])).
% 1.13/1.36 tff(4431,plain,
% 1.13/1.36 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4430])).
% 1.13/1.36 tff(4432,plain,
% 1.13/1.36 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4349, 4431])).
% 1.13/1.36 tff(4433,plain,
% 1.13/1.36 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4432])).
% 1.13/1.36 tff(4434,plain,
% 1.13/1.36 (s(z) = s(s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[50, 4433, 989])).
% 1.13/1.36 tff(4435,plain,
% 1.13/1.36 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4434])).
% 1.13/1.36 tff(4436,plain,
% 1.13/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4435])).
% 1.13/1.36 tff(4437,plain,
% 1.13/1.36 (s(s(elem!1)) = z),
% 1.13/1.36 inference(transitivity,[status(thm)],[1376, 4436, 27])).
% 1.13/1.36 tff(4438,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[566, 4437])).
% 1.13/1.36 tff(4439,plain,((s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | r(s(s(z)), elem!1) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4440,plain,
% 1.13/1.36 (s(s(s(z))) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4439, 4336, 3330, 4332, 4341, 4339, 4031, 101, 4060, 4337, 4334, 2596, 2, 11, 4185, 73])).
% 1.13/1.36 tff(4441,plain,
% 1.13/1.36 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4440])).
% 1.13/1.36 tff(4442,plain,
% 1.13/1.36 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4441])).
% 1.13/1.36 tff(4443,plain,
% 1.13/1.36 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4442])).
% 1.13/1.36 tff(4444,plain,
% 1.13/1.36 (~b(s(z), s(s(s(z))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4331, 4443])).
% 1.13/1.36 tff(4445,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4060, 4444])).
% 1.13/1.36 tff(4446,plain,((~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(z))) | (z = elem!1) | (elem!1 = s(s(elem!1))) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4447,plain,
% 1.13/1.36 (~b(s(s(z)), s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4446, 3, 77, 4, 2, 12, 74])).
% 1.13/1.36 tff(4448,plain,
% 1.13/1.36 (r(s(s(z)), s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[265, 4447, 169])).
% 1.13/1.36 tff(4449,plain,
% 1.13/1.36 (~r(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3588, 993, 1181])).
% 1.13/1.36 tff(4450,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[901, 4449])).
% 1.13/1.36 tff(4451,plain,
% 1.13/1.36 (~b(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1249, 4450, 77, 1240])).
% 1.13/1.36 tff(4452,plain,
% 1.13/1.36 (r(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[194, 4451])).
% 1.13/1.36 tff(4453,plain,
% 1.13/1.36 (~b(elem!1, z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3423, 4452, 689, 4, 1240, 77, 3, 2, 12])).
% 1.13/1.36 tff(4454,plain,
% 1.13/1.36 (~r(elem!1, z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1259, 4452, 993])).
% 1.13/1.36 tff(4455,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[403, 4454, 4453, 11])).
% 1.13/1.36 tff(4456,plain,((~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (z = elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4457,plain,
% 1.13/1.36 (~r(elem!1, s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4456, 3340, 4, 1240, 77, 3, 2, 12, 689])).
% 1.13/1.36 tff(4458,plain,
% 1.13/1.36 (b(elem!1, s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1277, 4457, 83])).
% 1.13/1.36 tff(4459,plain,
% 1.13/1.36 (~r(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4065, 416, 1181])).
% 1.13/1.36 tff(4460,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[901, 4459])).
% 1.13/1.36 tff(4461,plain,
% 1.13/1.36 (~b(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1249, 4460, 77, 1240])).
% 1.13/1.36 tff(4462,plain,
% 1.13/1.36 (r(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[194, 4461])).
% 1.13/1.36 tff(4463,plain,
% 1.13/1.36 (~b(elem!1, z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3423, 4462, 689, 4, 1240, 77, 3, 2, 12])).
% 1.13/1.36 tff(4464,plain,
% 1.13/1.36 (~r(elem!1, z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[2841, 4462, 416])).
% 1.13/1.36 tff(4465,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[403, 4464, 4463, 11])).
% 1.13/1.36 tff(4466,plain,((~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (z = elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4467,plain,
% 1.13/1.36 (~r(s(z), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4466, 3340, 4, 1240, 77, 3, 2, 12, 689])).
% 1.13/1.36 tff(4468,plain,
% 1.13/1.36 (b(s(z), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[454, 4467, 91])).
% 1.13/1.36 tff(4469,plain,
% 1.13/1.36 (~b(z, elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[2904, 4458, 77, 4468])).
% 1.13/1.36 tff(4470,plain,
% 1.13/1.36 (r(z, elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[289, 4469, 4])).
% 1.13/1.36 tff(4471,plain,
% 1.13/1.36 (~r(s(elem!1), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4126, 4470, 3340, 319])).
% 1.13/1.36 tff(4472,plain,
% 1.13/1.36 (b(s(elem!1), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[939, 4471, 303])).
% 1.13/1.36 tff(4473,plain,
% 1.13/1.36 (~b(s(elem!1), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[2662, 224, 4472, 4468, 4458])).
% 1.13/1.36 tff(4474,plain,
% 1.13/1.36 (r(s(elem!1), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1476, 4473, 160])).
% 1.13/1.36 tff(4475,plain,
% 1.13/1.36 (~r(z, s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3500, 4470, 3340])).
% 1.13/1.36 tff(4476,plain,
% 1.13/1.36 (b(z, s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[752, 4475])).
% 1.13/1.36 tff(4477,plain,
% 1.13/1.36 (~b(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1249, 1241, 77, 1240])).
% 1.13/1.36 tff(4478,plain,
% 1.13/1.36 (r(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[194, 4477])).
% 1.13/1.36 tff(4479,plain,
% 1.13/1.36 (s(s(s(z))) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3337, 4478, 354, 688, 689, 177])).
% 1.13/1.36 tff(4480,plain,
% 1.13/1.36 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4479])).
% 1.13/1.36 tff(4481,plain,
% 1.13/1.36 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4480, 2587])).
% 1.13/1.36 tff(4482,plain,
% 1.13/1.36 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.13/1.36 inference(transitivity,[status(thm)],[4481, 2588])).
% 1.13/1.36 tff(4483,plain,
% 1.13/1.36 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4482])).
% 1.13/1.36 tff(4484,plain,
% 1.13/1.36 (~(s(s(z)) = elem!1)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[55, 4483])).
% 1.13/1.36 tff(4485,plain,
% 1.13/1.36 (s(s(s(s(z)))) = s(elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4479])).
% 1.13/1.36 tff(4486,plain,
% 1.13/1.36 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4485])).
% 1.13/1.36 tff(4487,plain,
% 1.13/1.36 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4486])).
% 1.13/1.36 tff(4488,plain,
% 1.13/1.36 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4487])).
% 1.13/1.36 tff(4489,plain,
% 1.13/1.36 (b(s(s(s(s(s(z))))), s(z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[1241, 4488])).
% 1.13/1.36 tff(4490,plain,
% 1.13/1.36 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4486])).
% 1.13/1.36 tff(4491,plain,
% 1.13/1.36 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4490])).
% 1.13/1.36 tff(4492,plain,
% 1.13/1.36 (b(z, s(s(s(s(s(z))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[1180, 4491])).
% 1.13/1.36 tff(4493,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.36 tff(4494,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.36 tff(4495,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.13/1.36 tff(4496,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4497,plain,
% 1.13/1.36 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4498,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4497])).
% 1.13/1.36 tff(4499,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4498, 4496])).
% 1.13/1.36 tff(4500,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(4501,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 1.13/1.36 tff(4502,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4501, 224, 77, 4495, 4494, 4493])).
% 1.13/1.36 tff(4503,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4504,plain,
% 1.13/1.36 (~b(s(z), s(s(s(s(s(z))))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4503, 4492, 4489, 77])).
% 1.13/1.36 tff(4505,plain,
% 1.13/1.36 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4131])).
% 1.13/1.36 tff(4506,plain,
% 1.13/1.36 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4505])).
% 1.13/1.36 tff(4507,plain,
% 1.13/1.36 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4506])).
% 1.13/1.36 tff(4508,plain,
% 1.13/1.36 (b(s(z), s(s(s(s(s(z))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[2252, 4507])).
% 1.13/1.36 tff(4509,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.36 tff(4510,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4509, 4508])).
% 1.13/1.36 tff(4511,plain,((~b(s(z), s(s(elem!1)))) | b(s(z), s(s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4512,plain,
% 1.13/1.36 (~b(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4511, 4504, 4479])).
% 1.13/1.36 tff(4513,plain,
% 1.13/1.36 (r(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[653, 4512])).
% 1.13/1.36 tff(4514,plain,
% 1.13/1.36 (~r(s(s(z)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[2853, 4513, 267])).
% 1.13/1.36 tff(4515,plain,
% 1.13/1.36 (b(s(s(z)), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[2726, 4514])).
% 1.13/1.36 tff(4516,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4517,plain,
% 1.13/1.36 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4518,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4517])).
% 1.13/1.36 tff(4519,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4518, 4516])).
% 1.13/1.36 tff(4520,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(4521,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4520, 4519])).
% 1.13/1.36 tff(4522,plain,
% 1.13/1.36 (~b(s(s(z)), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4521, 224, 684, 2896, 4515])).
% 1.13/1.36 tff(4523,plain,
% 1.13/1.36 (r(s(s(z)), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[1135, 4522, 4484])).
% 1.13/1.36 tff(4524,plain,
% 1.13/1.36 (~r(s(z), s(s(z)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3697, 112, 4513, 267])).
% 1.13/1.37 tff(4525,plain,
% 1.13/1.37 (b(s(z), s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1071, 4524])).
% 1.13/1.37 tff(4526,plain,
% 1.13/1.37 (~b(z, s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1078, 224, 77, 4525, 4515])).
% 1.13/1.37 tff(4527,plain,
% 1.13/1.37 (r(z, s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1088, 4526])).
% 1.13/1.37 tff(4528,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3758, 4527, 4523, 688])).
% 1.13/1.37 tff(4529,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4530,plain,
% 1.13/1.37 (~b(s(s(elem!1)), s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4529, 4470, 77, 4468, 4458, 267, 4476, 354, 689, 73, 1240])).
% 1.13/1.37 tff(4531,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[901, 4530])).
% 1.13/1.37 tff(4532,plain,
% 1.13/1.37 (~r(s(elem!1), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4144, 112, 3340, 4531, 4474])).
% 1.13/1.37 tff(4533,plain,
% 1.13/1.37 (b(s(elem!1), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1521, 4532, 319])).
% 1.13/1.37 tff(4534,plain,
% 1.13/1.37 (~r(s(s(elem!1)), s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4173, 112, 4531, 4474])).
% 1.13/1.37 tff(4535,plain,
% 1.13/1.37 (b(s(s(elem!1)), s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[530, 4534, 526])).
% 1.13/1.37 tff(4536,plain,
% 1.13/1.37 (~b(z, s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4122, 224, 1391, 1390, 1180])).
% 1.13/1.37 tff(4537,plain,
% 1.13/1.37 (r(z, s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[625, 4536])).
% 1.13/1.37 tff(4538,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.13/1.37 tff(4539,plain,
% 1.13/1.37 ((s(elem!1) = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1618])).
% 1.13/1.37 tff(4540,plain,
% 1.13/1.37 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4539])).
% 1.13/1.37 tff(4541,plain,
% 1.13/1.37 ((~(s(z) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4540])).
% 1.13/1.37 tff(4542,plain,
% 1.13/1.37 (~(s(elem!1) = s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[45, 4541])).
% 1.13/1.37 tff(4543,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1621])).
% 1.13/1.37 tff(4544,plain,
% 1.13/1.37 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.37 inference(symmetry,[status(thm)],[4543])).
% 1.13/1.37 tff(4545,plain,
% 1.13/1.37 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.37 tff(4546,plain,
% 1.13/1.37 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4545, 283])).
% 1.13/1.37 tff(4547,plain,
% 1.13/1.37 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.37 inference(transitivity,[status(thm)],[4546, 284])).
% 1.13/1.37 tff(4548,plain,
% 1.13/1.37 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4547])).
% 1.13/1.37 tff(4549,plain,
% 1.13/1.37 (~(s(s(s(z))) = elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[58, 4548])).
% 1.13/1.37 tff(4550,plain,
% 1.13/1.37 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[3874])).
% 1.13/1.37 tff(4551,plain,
% 1.13/1.37 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4550])).
% 1.13/1.37 tff(4552,plain,
% 1.13/1.37 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4551])).
% 1.13/1.37 tff(4553,plain,
% 1.13/1.37 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1162, 4552])).
% 1.13/1.37 tff(4554,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1621, 1618])).
% 1.13/1.37 tff(4555,plain,
% 1.13/1.37 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4554])).
% 1.13/1.37 tff(4556,plain,
% 1.13/1.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1621])).
% 1.13/1.37 tff(4557,plain,
% 1.13/1.37 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4556])).
% 1.13/1.37 tff(4558,plain,
% 1.13/1.37 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1621])).
% 1.13/1.37 tff(4559,plain,
% 1.13/1.37 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4558])).
% 1.13/1.37 tff(4560,plain,
% 1.13/1.37 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4546])).
% 1.13/1.37 tff(4561,plain,
% 1.13/1.37 (~(elem!1 = s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[58, 4560])).
% 1.13/1.37 tff(4562,plain,
% 1.13/1.37 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.37 tff(4563,plain,
% 1.13/1.37 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4562])).
% 1.13/1.37 tff(4564,plain,
% 1.13/1.37 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1617])).
% 1.13/1.37 tff(4565,plain,
% 1.13/1.37 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4564])).
% 1.13/1.37 tff(4566,plain,
% 1.13/1.37 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4565, 4563])).
% 1.13/1.37 tff(4567,plain,
% 1.13/1.37 (r(z, s(z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[543, 4566])).
% 1.13/1.37 tff(4568,plain,
% 1.13/1.37 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1401, 68, 1694, 2023])).
% 1.13/1.37 tff(4569,assumption,(r(z, s(z))), introduced(assumption)).
% 1.13/1.37 tff(4570,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.37 tff(4571,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(symmetry,[status(thm)],[4570])).
% 1.13/1.37 tff(4572,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1687])).
% 1.13/1.37 tff(4573,plain,
% 1.13/1.37 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.13/1.37 inference(symmetry,[status(thm)],[4572])).
% 1.13/1.37 tff(4574,plain,
% 1.13/1.37 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(transitivity,[status(thm)],[4573, 4571])).
% 1.13/1.37 tff(4575,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), z)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1798, 4574])).
% 1.13/1.37 tff(4576,plain,
% 1.13/1.37 (s(z) = s(elem!1)),
% 1.13/1.37 inference(symmetry,[status(thm)],[3982])).
% 1.13/1.37 tff(4577,plain,
% 1.13/1.37 (s(s(elem!1)) = s(s(z))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[3982])).
% 1.13/1.37 tff(4578,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4577])).
% 1.13/1.37 tff(4579,plain,
% 1.13/1.37 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4578])).
% 1.13/1.37 tff(4580,plain,
% 1.13/1.37 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4579])).
% 1.13/1.37 tff(4581,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4580, 4576])).
% 1.13/1.37 tff(4582,plain,
% 1.13/1.37 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4581])).
% 1.13/1.37 tff(4583,plain,
% 1.13/1.37 (r(s(s(s(s(z)))), s(z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[1289, 4582])).
% 1.13/1.37 tff(4584,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4585,plain,
% 1.13/1.37 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4586,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4585])).
% 1.13/1.37 tff(4587,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4586, 4584])).
% 1.13/1.37 tff(4588,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4589,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 1.13/1.37 tff(4590,plain,
% 1.13/1.37 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4589, 112, 4569, 2276])).
% 1.13/1.37 tff(4591,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4590, 4583])).
% 1.13/1.37 tff(4592,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(elem!1 = z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4593,plain,
% 1.13/1.37 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4592, 4575, 4569, 1668])).
% 1.13/1.37 tff(4594,plain,
% 1.13/1.37 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1345, 4593, 1832])).
% 1.13/1.37 tff(4595,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 1390, 4594, 4568])).
% 1.13/1.37 tff(4596,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4597,plain,
% 1.13/1.37 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4596, 4567, 1390, 1391, 1181, 335])).
% 1.13/1.37 tff(4598,plain,
% 1.13/1.37 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1294, 4597, 1733])).
% 1.13/1.37 tff(4599,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4600,plain,
% 1.13/1.37 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.37 tff(4601,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4602,plain,
% 1.13/1.37 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4603,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4602])).
% 1.13/1.37 tff(4604,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4603, 4601])).
% 1.13/1.37 tff(4605,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4606,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 1.13/1.37 tff(4607,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4606, 112, 4569, 177, 3188])).
% 1.13/1.37 tff(4608,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4609,plain,
% 1.13/1.37 (~r(s(s(s(z))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4608, 3188, 4569])).
% 1.13/1.37 tff(4610,plain,
% 1.13/1.37 (b(s(s(s(z))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[72, 4609])).
% 1.13/1.37 tff(4611,plain,
% 1.13/1.37 (b(s(s(s(z))), elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4610, 4600])).
% 1.13/1.37 tff(4612,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4611, 4544])).
% 1.13/1.37 tff(4613,plain,
% 1.13/1.37 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.37 tff(4614,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4615,plain,
% 1.13/1.37 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4616,plain,
% 1.13/1.37 (((~![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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4615])).
% 1.13/1.37 tff(4617,plain,
% 1.13/1.37 (((~![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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4616, 4614])).
% 1.13/1.37 tff(4618,plain,
% 1.13/1.37 ((~![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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4619,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 1.13/1.37 tff(4620,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4619, 112, 4569, 689, 3188])).
% 1.13/1.37 tff(4621,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4622,plain,
% 1.13/1.37 (~r(z, s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4621, 3188, 4569])).
% 1.13/1.37 tff(4623,plain,
% 1.13/1.37 (b(z, s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[100, 4622])).
% 1.13/1.37 tff(4624,plain,
% 1.13/1.37 (b(elem!1, s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4623, 4613])).
% 1.13/1.37 tff(4625,plain,
% 1.13/1.37 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4624, 4559])).
% 1.13/1.37 tff(4626,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4627,plain,
% 1.13/1.37 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4628,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4627])).
% 1.13/1.37 tff(4629,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4628, 4626])).
% 1.13/1.37 tff(4630,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4631,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4630, 4629])).
% 1.13/1.37 tff(4632,plain,
% 1.13/1.37 ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4631, 224, 3919, 4599])).
% 1.13/1.37 tff(4633,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4632, 4625, 4612])).
% 1.13/1.37 tff(4634,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4635,plain,
% 1.13/1.37 (~r(s(s(s(z))), s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4634, 4599, 4598, 335, 4567])).
% 1.13/1.37 tff(4636,plain,
% 1.13/1.37 (b(s(s(s(z))), s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[925, 4635])).
% 1.13/1.37 tff(4637,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4636, 4555])).
% 1.13/1.37 tff(4638,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1621])).
% 1.13/1.37 tff(4639,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4638])).
% 1.13/1.37 tff(4640,plain,
% 1.13/1.37 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1619])).
% 1.13/1.37 tff(4641,plain,
% 1.13/1.37 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4640])).
% 1.13/1.37 tff(4642,plain,
% 1.13/1.37 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[55, 4641])).
% 1.13/1.37 tff(4643,plain,
% 1.13/1.37 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1695])).
% 1.13/1.37 tff(4644,plain,
% 1.13/1.37 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[1952])).
% 1.13/1.37 tff(4645,plain,
% 1.13/1.37 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[1617])).
% 1.13/1.37 tff(4646,plain,
% 1.13/1.37 (r(elem!1, s(z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[543, 4565])).
% 1.13/1.37 tff(4647,plain,
% 1.13/1.37 (~r(s(z), s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1028, 1020, 4646])).
% 1.13/1.37 tff(4648,plain,
% 1.13/1.37 (b(s(z), s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[175, 4647])).
% 1.13/1.37 tff(4649,plain,
% 1.13/1.37 (b(s(elem!1), s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4648, 4645])).
% 1.13/1.37 tff(4650,plain,
% 1.13/1.37 (b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4649, 4644])).
% 1.13/1.37 tff(4651,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.37 tff(4652,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4653,plain,
% 1.13/1.37 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4654,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4653])).
% 1.13/1.37 tff(4655,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4654, 4652])).
% 1.13/1.37 tff(4656,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4657,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 1.13/1.37 tff(4658,plain,
% 1.13/1.37 ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4657, 224, 1391, 4651])).
% 1.13/1.37 tff(4659,plain,
% 1.13/1.37 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4658, 4650])).
% 1.13/1.37 tff(4660,plain,
% 1.13/1.37 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4659, 4643])).
% 1.13/1.37 tff(4661,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[147, 4660, 4642])).
% 1.13/1.38 tff(4662,plain,
% 1.13/1.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4661, 4639])).
% 1.13/1.38 tff(4663,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4664,plain,
% 1.13/1.38 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4665,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4664])).
% 1.13/1.38 tff(4666,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4665, 4663])).
% 1.13/1.38 tff(4667,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4668,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4667, 4666])).
% 1.13/1.38 tff(4669,plain,
% 1.13/1.38 ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4668, 112, 543, 1181])).
% 1.13/1.38 tff(4670,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4669, 1785, 4662])).
% 1.13/1.38 tff(4671,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4672,plain,
% 1.13/1.38 (~r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4671, 4637, 1181, 335, 1391, 543])).
% 1.13/1.38 tff(4673,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[388, 4672, 4561])).
% 1.13/1.38 tff(4674,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4673, 4559])).
% 1.13/1.38 tff(4675,plain,
% 1.13/1.38 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4676,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4675])).
% 1.13/1.38 tff(4677,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4676, 1976])).
% 1.13/1.38 tff(4678,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4679,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 1.13/1.38 tff(4680,plain,
% 1.13/1.38 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4679, 224, 1391, 1390])).
% 1.13/1.38 tff(4681,plain,
% 1.13/1.38 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4680, 4637])).
% 1.13/1.38 tff(4682,plain,
% 1.13/1.38 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3903, 68, 4681])).
% 1.13/1.38 tff(4683,plain,
% 1.13/1.38 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4682, 4553])).
% 1.13/1.38 tff(4684,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4685,plain,
% 1.13/1.38 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4686,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4685])).
% 1.13/1.38 tff(4687,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4686, 4684])).
% 1.13/1.38 tff(4688,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4689,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4688, 4687])).
% 1.13/1.38 tff(4690,plain,
% 1.13/1.38 (~r(s(s(s(elem!1))), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4689, 112, 1181, 3888])).
% 1.13/1.38 tff(4691,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4690, 1738])).
% 1.13/1.38 tff(4692,plain,((~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4693,plain,
% 1.13/1.38 (~r(s(s(s(z))), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4692, 4683, 1181, 335])).
% 1.13/1.38 tff(4694,plain,
% 1.13/1.38 (b(s(s(s(z))), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[374, 4693, 4549])).
% 1.13/1.38 tff(4695,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4694, 4544])).
% 1.13/1.38 tff(4696,plain,
% 1.13/1.38 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4697,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4696])).
% 1.13/1.38 tff(4698,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4697, 4626])).
% 1.13/1.38 tff(4699,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4700,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 1.13/1.38 tff(4701,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4700, 224, 4598, 4599, 4695, 4674])).
% 1.13/1.38 tff(4702,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4703,plain,
% 1.13/1.38 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4702, 335, 1181, 1391, 543, 1390])).
% 1.13/1.38 tff(4704,plain,
% 1.13/1.38 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4703, 4557])).
% 1.13/1.38 tff(4705,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1884, 4704])).
% 1.13/1.38 tff(4706,plain,
% 1.13/1.38 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[335])).
% 1.13/1.38 tff(4707,plain,
% 1.13/1.38 (b(elem!1, s(s(elem!1)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1180, 4706])).
% 1.13/1.38 tff(4708,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4709,plain,
% 1.13/1.38 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4710,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4709])).
% 1.13/1.38 tff(4711,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4710, 4708])).
% 1.13/1.38 tff(4712,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4713,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4712, 4711])).
% 1.13/1.38 tff(4714,plain,
% 1.13/1.38 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4713, 224, 1488, 4707, 4598, 1390])).
% 1.13/1.38 tff(4715,plain,
% 1.13/1.38 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1869, 4714, 1683])).
% 1.13/1.38 tff(4716,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.38 tff(4717,plain,
% 1.13/1.38 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1617])).
% 1.13/1.38 tff(4718,plain,
% 1.13/1.38 (r(s(elem!1), s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[178, 4717])).
% 1.13/1.38 tff(4719,plain,
% 1.13/1.38 (r(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4718, 1948])).
% 1.13/1.38 tff(4720,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[1621])).
% 1.13/1.38 tff(4721,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4720])).
% 1.13/1.38 tff(4722,plain,
% 1.13/1.38 (~r(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1028, 178, 993])).
% 1.13/1.38 tff(4723,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[388, 4722, 4561])).
% 1.13/1.38 tff(4724,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[685, 4559])).
% 1.13/1.38 tff(4725,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4726,plain,
% 1.13/1.38 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4727,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4726])).
% 1.13/1.38 tff(4728,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4727, 4725])).
% 1.13/1.38 tff(4729,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4730,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 1.13/1.38 tff(4731,plain,
% 1.13/1.38 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4730, 224, 1488, 3919, 1409])).
% 1.13/1.38 tff(4732,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4731, 4724, 4599])).
% 1.13/1.39 tff(4733,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4734,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4733, 4723, 3919, 1409, 1488, 335])).
% 1.13/1.39 tff(4735,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4734, 4557])).
% 1.13/1.39 tff(4736,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1884, 4735])).
% 1.13/1.39 tff(4737,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4736, 4721])).
% 1.13/1.39 tff(4738,plain,
% 1.13/1.39 (((~![X0: $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(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4739,plain,
% 1.13/1.39 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4740,plain,
% 1.13/1.39 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4739])).
% 1.13/1.39 tff(4741,plain,
% 1.13/1.39 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4740, 4738])).
% 1.13/1.39 tff(4742,plain,
% 1.13/1.39 ((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4743,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4742, 4741])).
% 1.13/1.39 tff(4744,plain,
% 1.13/1.39 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4743, 112, 4716])).
% 1.13/1.39 tff(4745,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4744, 4737, 4719])).
% 1.13/1.39 tff(4746,plain,((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4747,plain,
% 1.13/1.39 (~r(s(z), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4746, 1409, 335, 3919, 4716, 1488, 993])).
% 1.13/1.39 tff(4748,plain,
% 1.13/1.39 (b(s(z), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[175, 4747])).
% 1.13/1.39 tff(4749,plain,
% 1.13/1.39 (b(s(elem!1), s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4748, 4645])).
% 1.13/1.39 tff(4750,plain,
% 1.13/1.39 (b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4749, 4644])).
% 1.13/1.39 tff(4751,plain,
% 1.13/1.39 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[1629])).
% 1.13/1.39 tff(4752,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4556])).
% 1.13/1.39 tff(4753,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.13/1.39 tff(4754,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4753, 4752])).
% 1.13/1.39 tff(4755,plain,
% 1.13/1.39 (~b(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4733, 4754, 3919, 1409, 1488, 335])).
% 1.13/1.39 tff(4756,plain,
% 1.13/1.39 (r(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[388, 4755, 4561])).
% 1.13/1.39 tff(4757,plain,
% 1.13/1.39 (r(z, s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4756, 4751])).
% 1.13/1.39 tff(4758,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1687, 1617])).
% 1.13/1.39 tff(4759,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4758])).
% 1.13/1.39 tff(4760,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1409, 4759])).
% 1.13/1.39 tff(4761,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[1687])).
% 1.13/1.39 tff(4762,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4761])).
% 1.13/1.39 tff(4763,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4753, 4762])).
% 1.13/1.39 tff(4764,plain,
% 1.13/1.39 (~b(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1579, 4763, 4760, 1090])).
% 1.13/1.39 tff(4765,plain,
% 1.13/1.39 (r(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[925, 4764])).
% 1.13/1.39 tff(4766,plain,
% 1.13/1.39 (~r(z, s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4621, 4765, 4569])).
% 1.13/1.39 tff(4767,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4766, 4757])).
% 1.13/1.39 tff(4768,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(z = elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4769,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4768, 4748, 4569, 335, 3919, 1409, 1488])).
% 1.13/1.39 tff(4770,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1884, 4769])).
% 1.13/1.39 tff(4771,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4772,plain,
% 1.13/1.39 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4773,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4772])).
% 1.13/1.39 tff(4774,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4773, 4771])).
% 1.13/1.39 tff(4775,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4776,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 1.13/1.39 tff(4777,plain,
% 1.13/1.39 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4776, 224, 1488, 3919, 1391])).
% 1.13/1.39 tff(4778,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4777, 1409])).
% 1.13/1.39 tff(4779,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1401, 68, 4778, 1694])).
% 1.13/1.39 tff(4780,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[560, 4555])).
% 1.13/1.39 tff(4781,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.13/1.39 tff(4782,plain,
% 1.13/1.39 (b(s(elem!1), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4781, 4644])).
% 1.13/1.39 tff(4783,plain,
% 1.13/1.39 ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4657, 224, 1391])).
% 1.13/1.39 tff(4784,plain,
% 1.13/1.39 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4783, 4782, 4780])).
% 1.13/1.39 tff(4785,plain,
% 1.13/1.39 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4784, 4643])).
% 1.13/1.39 tff(4786,plain,
% 1.13/1.39 (r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[147, 4785, 4642])).
% 1.13/1.39 tff(4787,plain,
% 1.13/1.39 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4786, 4639])).
% 1.13/1.39 tff(4788,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[1787, 4721])).
% 1.13/1.39 tff(4789,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.39 tff(4790,plain,
% 1.13/1.39 (((~![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(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4791,plain,
% 1.13/1.39 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4792,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4791])).
% 1.13/1.39 tff(4793,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4792, 4790])).
% 1.13/1.39 tff(4794,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4795,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4794, 4793])).
% 1.13/1.39 tff(4796,plain,
% 1.13/1.39 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4795, 112, 4789, 4788])).
% 1.13/1.39 tff(4797,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4796, 4787])).
% 1.13/1.39 tff(4798,plain,((~b(s(s(s(z))), s(z))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4799,plain,
% 1.13/1.39 (~b(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4798, 4779, 335, 1391, 4749, 4770])).
% 1.13/1.39 tff(4800,plain,
% 1.13/1.39 (r(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[925, 4799])).
% 1.13/1.39 tff(4801,plain,
% 1.13/1.39 (~r(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4608, 4800, 4569])).
% 1.13/1.39 tff(4802,plain,
% 1.13/1.39 (b(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[72, 4801])).
% 1.13/1.39 tff(4803,plain,
% 1.13/1.39 (b(s(s(s(z))), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4802, 4600])).
% 1.13/1.39 tff(4804,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4803, 4544])).
% 1.13/1.39 tff(4805,plain,
% 1.13/1.39 (~r(z, s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4621, 4800, 4569])).
% 1.13/1.39 tff(4806,plain,
% 1.13/1.39 (b(z, s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[100, 4805])).
% 1.13/1.39 tff(4807,plain,
% 1.13/1.39 (b(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4806, 4613])).
% 1.13/1.39 tff(4808,plain,
% 1.13/1.39 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4807, 4559])).
% 1.13/1.39 tff(4809,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4810,plain,
% 1.13/1.39 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4811,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4810])).
% 1.13/1.39 tff(4812,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4811, 4809])).
% 1.13/1.39 tff(4813,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4814,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4813, 4812])).
% 1.13/1.39 tff(4815,plain,
% 1.13/1.39 ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4814, 224, 1488])).
% 1.13/1.39 tff(4816,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4815, 4808, 4804, 4750])).
% 1.13/1.39 tff(4817,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4818,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4817, 335, 1488, 4567, 1391, 4598, 4715, 4646])).
% 1.13/1.39 tff(4819,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1345, 4818, 1832])).
% 1.13/1.39 tff(4820,plain,
% 1.13/1.39 (r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[3188, 1623])).
% 1.13/1.39 tff(4821,plain,
% 1.13/1.39 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4822,plain,
% 1.13/1.39 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4823,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4822])).
% 1.13/1.39 tff(4824,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4823, 4821])).
% 1.13/1.39 tff(4825,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4826,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.13/1.39 tff(4827,plain,
% 1.13/1.39 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4826, 112, 1289])).
% 1.13/1.39 tff(4828,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4827, 4820, 4788])).
% 1.13/1.39 tff(4829,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4830,plain,
% 1.13/1.39 (~r(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4829, 4819, 335, 4705])).
% 1.13/1.39 tff(4831,plain,
% 1.13/1.39 (b(s(s(s(z))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[925, 4830])).
% 1.13/1.39 tff(4832,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4831, 4555])).
% 1.13/1.39 tff(4833,plain,
% 1.13/1.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4679, 224, 1391, 1390, 4832])).
% 1.13/1.39 tff(4834,plain,
% 1.13/1.39 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3903, 68, 4833])).
% 1.13/1.39 tff(4835,plain,
% 1.13/1.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4834, 4553])).
% 1.13/1.39 tff(4836,plain,
% 1.13/1.39 (~r(s(s(s(z))), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4692, 4835, 1181, 335])).
% 1.13/1.39 tff(4837,plain,
% 1.13/1.39 (b(s(s(s(z))), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[374, 4836, 4549])).
% 1.13/1.39 tff(4838,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4837, 4544])).
% 1.13/1.39 tff(4839,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4840,plain,
% 1.13/1.39 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4841,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4840])).
% 1.23/1.40 tff(4842,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4841, 4839])).
% 1.23/1.40 tff(4843,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4844,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4843, 4842])).
% 1.23/1.40 tff(4845,plain,
% 1.23/1.40 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4844, 224, 1488, 4707, 1390, 4838])).
% 1.23/1.40 tff(4846,plain,
% 1.23/1.40 (~b(s(elem!1), s(s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4845, 1953])).
% 1.23/1.40 tff(4847,plain,
% 1.23/1.40 (r(s(elem!1), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1534, 4846, 4542])).
% 1.23/1.40 tff(4848,plain,
% 1.23/1.40 (r(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4847, 1948])).
% 1.23/1.40 tff(4849,plain,
% 1.23/1.40 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4705, 4721])).
% 1.23/1.40 tff(4850,plain,
% 1.23/1.40 (((~![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(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4851,plain,
% 1.23/1.40 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4852,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4851])).
% 1.23/1.40 tff(4853,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4852, 4850])).
% 1.23/1.40 tff(4854,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4855,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 1.23/1.40 tff(4856,plain,
% 1.23/1.40 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4855, 112, 4819])).
% 1.23/1.40 tff(4857,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4856, 4849, 4848])).
% 1.23/1.40 tff(4858,plain,((~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4859,plain,
% 1.23/1.40 (~(z = elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4858, 1180, 1390, 1181, 1391, 543, 1488])).
% 1.23/1.40 tff(4860,plain,
% 1.23/1.40 (r(z, elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[289, 4859, 4538])).
% 1.23/1.40 tff(4861,plain,
% 1.23/1.40 (((~![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(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4862,plain,
% 1.23/1.40 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4863,plain,
% 1.23/1.40 (((~![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(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4862])).
% 1.23/1.40 tff(4864,plain,
% 1.23/1.40 (((~![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(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4863, 4861])).
% 1.23/1.40 tff(4865,plain,
% 1.23/1.40 ((~![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(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4866,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4865, 4864])).
% 1.23/1.40 tff(4867,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4866, 112, 543, 4860, 4537])).
% 1.23/1.40 tff(4868,plain,((~b(z, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | b(z, elem!1) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4869,plain,
% 1.23/1.40 (~r(elem!1, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4868, 4533, 4476, 3340, 4469, 4535, 4472])).
% 1.23/1.40 tff(4870,plain,
% 1.23/1.40 (b(elem!1, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[515, 4869, 327])).
% 1.23/1.40 tff(4871,plain,
% 1.23/1.40 (~b(elem!1, s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3570, 4870, 4535, 4533])).
% 1.23/1.40 tff(4872,plain,
% 1.23/1.40 (r(elem!1, s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[558, 4871, 3])).
% 1.23/1.40 tff(4873,plain,
% 1.23/1.40 (~r(s(s(z)), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2388, 112, 4872, 267])).
% 1.23/1.40 tff(4874,plain,
% 1.23/1.40 (~r(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2993, 4531, 267])).
% 1.23/1.40 tff(4875,plain,
% 1.23/1.40 (b(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2726, 4874])).
% 1.23/1.40 tff(4876,plain,
% 1.23/1.40 (~b(s(s(z)), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4521, 224, 4468, 4458, 4875])).
% 1.23/1.40 tff(4877,plain,
% 1.23/1.40 (s(s(z)) = elem!1),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1135, 4876, 4873])).
% 1.23/1.40 tff(4878,plain,
% 1.23/1.40 (s(s(s(z))) = s(elem!1)),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4877])).
% 1.23/1.40 tff(4879,plain,
% 1.23/1.40 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4878])).
% 1.23/1.40 tff(4880,plain,
% 1.23/1.40 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4879, 1143])).
% 1.23/1.40 tff(4881,plain,
% 1.23/1.40 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4880])).
% 1.23/1.40 tff(4882,plain,
% 1.23/1.40 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[1165, 4881])).
% 1.23/1.40 tff(4883,plain,
% 1.23/1.40 (~b(s(z), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4221, 4870, 4468, 4472])).
% 1.23/1.40 tff(4884,plain,
% 1.23/1.40 (r(s(z), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[670, 4883, 4204])).
% 1.23/1.40 tff(4885,plain,
% 1.23/1.40 (~b(z, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4124, 4533, 4535, 4476])).
% 1.23/1.40 tff(4886,plain,
% 1.23/1.40 (r(z, s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[625, 4885])).
% 1.23/1.40 tff(4887,plain,
% 1.23/1.40 (((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4888,plain,
% 1.23/1.40 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4889,plain,
% 1.23/1.40 (((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4888])).
% 1.23/1.40 tff(4890,plain,
% 1.23/1.40 (((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4889, 4887])).
% 1.23/1.40 tff(4891,plain,
% 1.23/1.40 ((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4892,plain,
% 1.23/1.40 ((~![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(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4891, 4890])).
% 1.23/1.40 tff(4893,plain,
% 1.23/1.40 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4892, 112, 655, 1289])).
% 1.23/1.40 tff(4894,plain,
% 1.23/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4895,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4896,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4895, 4894])).
% 1.23/1.40 tff(4897,plain,
% 1.23/1.40 (b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4896, 68, 1364, 4893])).
% 1.23/1.40 tff(4898,plain,
% 1.23/1.40 (~r(z, s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4402, 112, 568, 1289])).
% 1.23/1.40 tff(4899,plain,
% 1.23/1.40 (b(z, s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4412, 4898])).
% 1.23/1.40 tff(4900,plain,
% 1.23/1.40 (~r(s(s(s(s(elem!1)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4419, 112, 688, 568, 1289])).
% 1.23/1.40 tff(4901,plain,
% 1.23/1.40 (b(s(s(s(s(elem!1)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1338, 4900])).
% 1.23/1.40 tff(4902,plain,
% 1.23/1.40 (~r(s(z), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4231, 655, 568])).
% 1.23/1.40 tff(4903,plain,
% 1.23/1.40 (b(s(z), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[194, 4902])).
% 1.23/1.40 tff(4904,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4905,plain,
% 1.23/1.40 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4906,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4905])).
% 1.23/1.40 tff(4907,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4906, 4904])).
% 1.23/1.40 tff(4908,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4909,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4908, 4907])).
% 1.23/1.40 tff(4910,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4909, 224, 4903, 4901, 4899, 4897])).
% 1.23/1.40 tff(4911,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4912,plain,
% 1.23/1.40 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4911, 4470, 4886, 4884])).
% 1.23/1.40 tff(4913,plain,
% 1.23/1.40 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1345, 4912, 4882])).
% 1.23/1.40 tff(4914,plain,
% 1.23/1.40 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4382, 224, 4870, 4472, 4913])).
% 1.23/1.40 tff(4915,plain,
% 1.23/1.40 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1397, 224, 4535, 4533, 4913])).
% 1.23/1.40 tff(4916,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.23/1.40 tff(4917,plain,
% 1.23/1.40 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1401, 68, 4916])).
% 1.23/1.40 tff(4918,plain,
% 1.23/1.40 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4917, 1389])).
% 1.23/1.40 tff(4919,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2022, 112, 1295, 1181, 4918])).
% 1.23/1.40 tff(4920,plain,((s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4921,plain,
% 1.23/1.40 (s(s(s(s(elem!1)))) = elem!1),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4920, 3340, 4915, 4914])).
% 1.23/1.40 tff(4922,plain,
% 1.23/1.40 (elem!1 = s(s(s(s(elem!1))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[4921])).
% 1.23/1.40 tff(4923,plain,
% 1.23/1.40 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4877, 4922])).
% 1.23/1.40 tff(4924,plain,
% 1.23/1.40 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4923])).
% 1.23/1.40 tff(4925,plain,
% 1.23/1.40 (s(z) = s(s(s(elem!1)))),
% 1.23/1.40 inference(transitivity,[status(thm)],[50, 4924, 989])).
% 1.23/1.40 tff(4926,plain,
% 1.23/1.40 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4925])).
% 1.23/1.40 tff(4927,plain,
% 1.23/1.40 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.23/1.40 inference(symmetry,[status(thm)],[4926])).
% 1.23/1.40 tff(4928,plain,
% 1.23/1.40 (s(s(elem!1)) = z),
% 1.23/1.40 inference(transitivity,[status(thm)],[1376, 4927, 27])).
% 1.23/1.40 tff(4929,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[566, 4928])).
% 1.23/1.40 tff(4930,plain,(b(s(s(elem!1)), elem!1) | (~r(s(s(z)), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4931,plain,
% 1.23/1.40 (b(s(s(elem!1)), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4930, 267, 3, 77, 689, 1240, 4, 2, 12])).
% 1.23/1.40 tff(4932,plain,
% 1.23/1.40 (~b(z, elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4026, 1180, 77, 11, 1240, 3, 4931, 83])).
% 1.23/1.40 tff(4933,plain,
% 1.23/1.40 (r(z, elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[289, 4932, 4])).
% 1.23/1.40 tff(4934,plain,
% 1.23/1.40 (~r(s(s(s(z))), elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2431, 4933, 73])).
% 1.23/1.40 tff(4935,plain,
% 1.23/1.40 (~r(elem!1, s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2420, 4933, 689])).
% 1.23/1.40 tff(4936,plain,
% 1.23/1.40 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.23/1.40 inference(commutativity,[status(thm)],[])).
% 1.23/1.40 tff(4937,plain,
% 1.23/1.40 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.23/1.40 inference(symmetry,[status(thm)],[4936])).
% 1.23/1.40 tff(4938,plain,
% 1.23/1.40 ((~(s(s(z)) = s(elem!1))) <=> (~(s(elem!1) = s(s(z))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4937])).
% 1.23/1.40 tff(4939,plain,
% 1.23/1.40 (~(s(s(z)) = s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2528, 91])).
% 1.23/1.40 tff(4940,plain,
% 1.23/1.40 (~(s(elem!1) = s(s(z)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4939, 4938])).
% 1.23/1.40 tff(4941,plain,
% 1.23/1.40 (~r(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2993, 3673, 267])).
% 1.23/1.40 tff(4942,plain,
% 1.23/1.40 (b(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2726, 4941])).
% 1.23/1.40 tff(4943,plain,
% 1.23/1.40 (~b(s(s(z)), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2846, 4942, 77, 3656])).
% 1.23/1.40 tff(4944,plain,
% 1.23/1.40 (r(s(s(z)), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[281, 4943])).
% 1.23/1.40 tff(4945,plain,
% 1.23/1.40 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3531, 4944, 177])).
% 1.23/1.40 tff(4946,plain,
% 1.23/1.40 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3535, 68, 4945])).
% 1.23/1.40 tff(4947,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4946, 56])).
% 1.23/1.40 tff(4948,plain,
% 1.23/1.40 (~b(s(z), s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4051, 3656, 1180, 1240])).
% 1.23/1.40 tff(4949,plain,
% 1.23/1.40 (r(s(z), s(s(elem!1)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[653, 4948])).
% 1.23/1.40 tff(4950,plain,
% 1.23/1.40 (~r(s(z), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3697, 112, 4949, 267])).
% 1.23/1.40 tff(4951,plain,
% 1.23/1.40 (b(s(z), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1071, 4950])).
% 1.23/1.40 tff(4952,plain,
% 1.23/1.40 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3455, 4944, 689])).
% 1.23/1.40 tff(4953,plain,
% 1.23/1.40 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[249, 4952])).
% 1.23/1.40 tff(4954,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4955,plain,
% 1.23/1.40 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4956,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4955])).
% 1.23/1.40 tff(4957,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4956, 4954])).
% 1.23/1.40 tff(4958,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4959,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 1.23/1.40 tff(4960,plain,
% 1.23/1.40 (~b(s(z), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4959, 224, 4953, 4951, 4947])).
% 1.23/1.40 tff(4961,plain,
% 1.23/1.40 (r(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[175, 4960])).
% 1.23/1.41 tff(4962,plain,
% 1.23/1.41 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4039, 4961, 3673])).
% 1.23/1.41 tff(4963,plain,
% 1.23/1.41 (b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[147, 4962, 2])).
% 1.23/1.41 tff(4964,plain,
% 1.23/1.41 (s(s(s(z))) = elem!1),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4045, 4963, 1240, 157, 390, 177, 3334])).
% 1.23/1.41 tff(4965,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4964])).
% 1.23/1.41 tff(4966,plain,
% 1.23/1.41 (b(s(s(z)), elem!1)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4953, 4965])).
% 1.23/1.41 tff(4967,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4964])).
% 1.23/1.41 tff(4968,plain,
% 1.23/1.41 (b(elem!1, s(s(z)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4947, 4967])).
% 1.23/1.41 tff(4969,plain,
% 1.23/1.41 (~r(s(elem!1), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2502, 416, 409, 688, 77])).
% 1.23/1.41 tff(4970,plain,
% 1.23/1.41 (b(s(elem!1), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[939, 4969, 303])).
% 1.23/1.41 tff(4971,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4972,plain,
% 1.23/1.41 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4973,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4972])).
% 1.23/1.41 tff(4974,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4973, 4971])).
% 1.23/1.41 tff(4975,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4976,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4975, 4974])).
% 1.23/1.41 tff(4977,plain,
% 1.23/1.41 (~b(s(elem!1), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4976, 224, 4970, 4968, 4966])).
% 1.23/1.41 tff(4978,plain,
% 1.23/1.41 (((~![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))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4979,plain,
% 1.23/1.41 ((~![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))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4980,plain,
% 1.23/1.41 ((~![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)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4979, 4978])).
% 1.23/1.41 tff(4981,plain,
% 1.23/1.41 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4980, 68, 4977])).
% 1.23/1.41 tff(4982,plain,
% 1.23/1.41 (r(s(elem!1), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4981, 4940])).
% 1.23/1.41 tff(4983,plain,
% 1.23/1.41 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4964])).
% 1.23/1.41 tff(4984,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4985,plain,
% 1.23/1.41 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4986,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4985])).
% 1.23/1.41 tff(4987,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4986, 4984])).
% 1.23/1.41 tff(4988,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4989,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 1.23/1.41 tff(4990,plain,
% 1.23/1.41 (~b(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4989, 224, 4951, 4942, 4947])).
% 1.23/1.41 tff(4991,plain,
% 1.23/1.41 (r(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[925, 4990])).
% 1.23/1.41 tff(4992,plain,
% 1.23/1.41 (r(elem!1, s(z))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4991, 4983])).
% 1.23/1.41 tff(4993,plain,
% 1.23/1.41 (~r(elem!1, s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[999, 112, 3673, 4992])).
% 1.23/1.41 tff(4994,plain,
% 1.23/1.41 (b(elem!1, s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[558, 4993, 3])).
% 1.23/1.41 tff(4995,plain,
% 1.23/1.41 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2541, 224, 4970, 4994, 390])).
% 1.23/1.41 tff(4996,plain,
% 1.23/1.41 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1521, 4995, 319])).
% 1.23/1.41 tff(4997,plain,
% 1.23/1.41 (((~![X0: $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(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4998,plain,
% 1.23/1.41 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4999,plain,
% 1.23/1.41 (((~![X0: $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(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4998])).
% 1.23/1.41 tff(5000,plain,
% 1.23/1.41 (((~![X0: $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(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4999, 4997])).
% 1.23/1.41 tff(5001,plain,
% 1.23/1.41 ((~![X0: $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(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(5002,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[5001, 5000])).
% 1.23/1.41 tff(5003,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5002, 112, 4996, 4944, 267, 4982])).
% 1.23/1.41 tff(5004,plain,((~r(s(z), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(5005,plain,
% 1.23/1.41 (~r(s(z), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5004, 1180, 4931, 3, 1240, 11, 73, 2, 689, 77, 267, 4933])).
% 1.23/1.41 tff(5006,plain,
% 1.23/1.41 (b(s(z), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[454, 5005, 91])).
% 1.23/1.41 tff(5007,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(5008,plain,
% 1.23/1.41 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(5009,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[5008])).
% 1.23/1.41 tff(5010,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[5009, 5007])).
% 1.23/1.41 tff(5011,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(5012,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[5011, 5010])).
% 1.23/1.41 tff(5013,plain,
% 1.23/1.41 (~b(s(s(elem!1)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5012, 224, 77, 1240, 5006, 4931])).
% 1.23/1.41 tff(5014,plain,
% 1.23/1.41 (r(s(s(elem!1)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[901, 5013])).
% 1.23/1.41 tff(5015,plain,
% 1.23/1.41 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4045, 362, 1240, 157, 390, 177, 2932])).
% 1.23/1.41 tff(5016,plain,
% 1.23/1.41 (r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[147, 5015, 2])).
% 1.23/1.41 tff(5017,plain,
% 1.23/1.41 (~b(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4200, 362, 684, 2440, 2932])).
% 1.23/1.41 tff(5018,plain,
% 1.23/1.41 (r(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[175, 5017])).
% 1.23/1.41 tff(5019,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4039, 5018, 5016, 887])).
% 1.23/1.41 tff(5020,plain,((s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(5021,plain,
% 1.23/1.41 (s(s(s(z))) = elem!1),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5020, 5014, 2, 5006, 4935, 4934, 1240, 11, 4931, 73])).
% 1.23/1.41 tff(5022,plain,
% 1.23/1.41 (~r(s(s(z)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2993, 5014, 267])).
% 1.23/1.41 tff(5023,plain,
% 1.23/1.41 (b(s(s(z)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2726, 5022])).
% 1.23/1.41 tff(5024,plain,
% 1.23/1.41 (~b(elem!1, z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2437, 5021, 12])).
% 1.23/1.41 tff(5025,plain,
% 1.23/1.41 (r(elem!1, z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[403, 5024, 11])).
% 1.23/1.41 tff(5026,plain,
% 1.23/1.41 (~r(z, s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4248, 5025, 160, 3, 4931, 4933, 5006])).
% 1.23/1.41 tff(5027,plain,
% 1.23/1.41 (b(z, s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[625, 5026])).
% 1.23/1.41 tff(5028,plain,
% 1.23/1.41 (~r(elem!1, s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1259, 179, 363])).
% 1.23/1.41 tff(5029,plain,
% 1.23/1.41 (b(elem!1, s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1277, 5028, 88])).
% 1.23/1.41 tff(5030,plain,
% 1.23/1.41 (elem!1 = s(s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2487, 341])).
% 1.23/1.41 tff(5031,plain,
% 1.23/1.41 (b(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2477, 5030, 684])).
% 1.23/1.41 tff(5032,plain,
% 1.23/1.41 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[341])).
% 1.23/1.41 tff(5033,plain,
% 1.23/1.41 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.23/1.41 inference(symmetry,[status(thm)],[5032])).
% 1.23/1.41 tff(5034,plain,
% 1.23/1.41 ((~r(elem!1, s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[5033])).
% 1.23/1.41 tff(5035,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(z))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[5028, 5034])).
% 1.23/1.41 tff(5036,plain,
% 1.23/1.41 (b(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[925, 5035])).
% 1.23/1.41 tff(5037,plain,
% 1.23/1.41 (~r(s(s(z)), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3472, 5036, 179, 5031, 689])).
% 1.23/1.41 tff(5038,plain,
% 1.23/1.41 (b(s(s(z)), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[281, 5037])).
% 1.23/1.41 tff(5039,plain,
% 1.23/1.41 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.23/1.41 inference(monotonicity,[status(thm)],[341])).
% 1.23/1.41 tff(5040,plain,
% 1.23/1.41 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[5039, 2587])).
% 1.23/1.41 tff(5041,plain,
% 1.23/1.41 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.23/1.41 inference(transitivity,[status(thm)],[5040, 2588])).
% 1.23/1.41 tff(5042,plain,
% 1.23/1.41 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[5041])).
% 1.23/1.41 tff(5043,plain,
% 1.23/1.41 (~(s(s(z)) = elem!1)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[55, 5042])).
% 1.23/1.41 tff(5044,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2721, 224, 77, 684, 1109, 1118, 2844])).
% 1.23/1.41 tff(5045,plain,((~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(5046,plain,
% 1.23/1.41 (~b(s(s(z)), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5045, 5038, 684, 77, 2844])).
% 1.23/1.41 tff(5047,plain,
% 1.23/1.41 (r(s(s(z)), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1135, 5046, 5043])).
% 1.23/1.41 tff(5048,plain,
% 1.23/1.41 (~r(s(elem!1), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2713, 5047, 2529, 407, 5038, 363])).
% 1.23/1.41 tff(5049,plain,
% 1.23/1.41 (b(s(elem!1), elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[939, 5048, 324])).
% 1.23/1.41 tff(5050,plain,
% 1.23/1.41 (~b(s(elem!1), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2662, 224, 5049, 684, 5029])).
% 1.23/1.41 tff(5051,plain,
% 1.23/1.41 (r(s(elem!1), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1476, 5050, 166])).
% 1.23/1.41 tff(5052,plain,
% 1.23/1.41 (~b(s(s(elem!1)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5012, 224, 77, 1240, 684, 390])).
% 1.23/1.41 tff(5053,plain,
% 1.23/1.41 (r(s(s(elem!1)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[901, 5052])).
% 1.23/1.41 tff(5054,plain,
% 1.23/1.41 (~b(s(s(elem!1)), s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4289, 224, 5049, 1240, 390, 407])).
% 1.23/1.41 tff(5055,plain,
% 1.23/1.41 (r(s(s(elem!1)), s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[530, 5054, 2505])).
% 1.23/1.41 tff(5056,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4173, 112, 5055, 5053, 5051])).
% 1.23/1.41 tff(5057,plain,((~r(s(z), z)) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~(s(s(s(z))) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(5058,plain,
% 1.23/1.41 (~r(s(z), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[5057, 5027, 160, 1240, 4931, 526, 5006, 303, 5025, 77, 5023, 689, 5021, 83])).
% 1.23/1.41 tff(5059,plain,
% 1.23/1.41 (b(s(z), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[194, 5058])).
% 1.23/1.41 tff(5060,plain,
% 1.23/1.41 (~b(s(z), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4051, 5059, 1180, 1240])).
% 1.23/1.41 tff(5061,plain,
% 1.23/1.41 (r(s(z), s(s(elem!1)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[653, 5060])).
% 1.23/1.41 tff(5062,plain,
% 1.23/1.41 (~r(s(z), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3697, 112, 5061, 267])).
% 1.23/1.41 tff(5063,plain,
% 1.23/1.41 (b(s(z), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1071, 5062])).
% 1.23/1.41 tff(5064,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.23/1.41 inference(monotonicity,[status(thm)],[5021])).
% 1.23/1.41 tff(5065,plain,
% 1.23/1.41 (~b(s(s(z)), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2846, 5059, 77, 5023])).
% 1.23/1.41 tff(5066,plain,
% 1.23/1.41 (r(s(s(z)), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[281, 5065])).
% 1.23/1.41 tff(5067,plain,
% 1.23/1.41 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3455, 5066, 689])).
% 1.23/1.41 tff(5068,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[249, 5067])).
% 1.23/1.41 tff(5069,plain,
% 1.23/1.41 (b(s(s(z)), elem!1)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[5068, 5064])).
% 1.23/1.42 tff(5070,plain,
% 1.23/1.42 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5021])).
% 1.23/1.42 tff(5071,plain,
% 1.23/1.42 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5070, 2587])).
% 1.23/1.42 tff(5072,plain,
% 1.23/1.42 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(z))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5071])).
% 1.23/1.42 tff(5073,plain,
% 1.23/1.42 (~(elem!1 = s(s(z)))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[55, 5072])).
% 1.23/1.42 tff(5074,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5075,plain,
% 1.23/1.42 (((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5076,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(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(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5075])).
% 1.23/1.42 tff(5077,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(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(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5076, 5074])).
% 1.23/1.42 tff(5078,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5079,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5078, 5077])).
% 1.23/1.42 tff(5080,plain,
% 1.23/1.42 (~r(elem!1, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5079, 112, 5025, 5066])).
% 1.23/1.42 tff(5081,plain,
% 1.23/1.42 (b(elem!1, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2874, 5080, 5073])).
% 1.23/1.42 tff(5082,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5083,plain,
% 1.23/1.42 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5084,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5083])).
% 1.23/1.42 tff(5085,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.23/1.42 tff(5086,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5087,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.23/1.42 tff(5088,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5087, 224, 5006, 5081, 5069, 5063])).
% 1.23/1.42 tff(5089,plain,((~b(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5090,plain,
% 1.23/1.42 (~b(z, s(s(elem!1)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5089, 4448, 101, 77, 3330, 3, 12, 2, 4])).
% 1.23/1.42 tff(5091,plain,
% 1.23/1.42 (r(s(s(elem!1)), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3865, 5090, 4, 77, 3330, 83, 12, 74])).
% 1.23/1.42 tff(5092,plain,
% 1.23/1.42 (~r(s(z), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4466, 5091, 4, 3330, 77, 3, 2, 12, 101])).
% 1.23/1.42 tff(5093,plain,
% 1.23/1.42 (b(s(z), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[454, 5092, 91])).
% 1.23/1.42 tff(5094,plain,
% 1.23/1.42 (~r(elem!1, s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4456, 5091, 4, 3330, 77, 3, 2, 12, 101])).
% 1.23/1.42 tff(5095,plain,
% 1.23/1.42 (b(elem!1, s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1277, 5094, 83])).
% 1.23/1.42 tff(5096,plain,
% 1.23/1.42 (r(z, s(s(elem!1)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[752, 5090])).
% 1.23/1.42 tff(5097,plain,
% 1.23/1.42 (~r(z, elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3500, 5091, 5096])).
% 1.23/1.42 tff(5098,plain,
% 1.23/1.42 (b(z, elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[289, 5097, 4])).
% 1.23/1.42 tff(5099,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2904, 5098, 5095, 77, 5093])).
% 1.23/1.42 tff(5100,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5101,plain,
% 1.23/1.42 (elem!1 = s(s(elem!1))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5100, 77, 4, 2, 12, 74])).
% 1.23/1.42 tff(5102,plain,
% 1.23/1.42 (s(s(elem!1)) = elem!1),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5101, 76])).
% 1.23/1.42 tff(5103,plain,
% 1.23/1.42 (s(s(s(s(elem!1)))) = elem!1),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1306, 5101])).
% 1.23/1.42 tff(5104,plain,
% 1.23/1.42 (~(elem!1 = s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2783, 5103, 5101])).
% 1.23/1.42 tff(5105,plain,
% 1.23/1.42 (~(s(s(z)) = elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2788, 5104])).
% 1.23/1.42 tff(5106,plain,
% 1.23/1.42 (b(elem!1, z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3641, 5101, 3330])).
% 1.23/1.42 tff(5107,plain,
% 1.23/1.42 (~(s(s(s(z))) = elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2437, 5106, 12])).
% 1.23/1.42 tff(5108,plain,
% 1.23/1.42 (b(elem!1, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[388, 3335, 4197])).
% 1.23/1.42 tff(5109,plain,
% 1.23/1.42 (b(s(s(s(z))), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[374, 3334, 362])).
% 1.23/1.42 tff(5110,plain,
% 1.23/1.42 (~r(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3337, 688, 362, 2930, 689, 177])).
% 1.23/1.42 tff(5111,plain,
% 1.23/1.42 (b(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[194, 5110])).
% 1.23/1.42 tff(5112,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3859, 5111, 5109, 1240, 1296, 77, 177, 129, 689, 688, 5108])).
% 1.23/1.42 tff(5113,plain,((~r(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~(elem!1 = s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (s(z) = elem!1) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5114,plain,
% 1.23/1.42 (~r(z, elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5113, 3330, 5101, 77, 73, 91, 101, 5107])).
% 1.23/1.42 tff(5115,plain,
% 1.23/1.42 (b(z, elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[289, 5114, 4])).
% 1.23/1.42 tff(5116,plain,
% 1.23/1.42 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5101])).
% 1.23/1.42 tff(5117,plain,
% 1.23/1.42 (r(s(s(elem!1)), s(s(elem!1))) <=> r(s(s(elem!1)), elem!1)),
% 1.23/1.42 inference(symmetry,[status(thm)],[5116])).
% 1.23/1.42 tff(5118,plain,
% 1.23/1.42 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(s(s(elem!1)), elem!1))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5117])).
% 1.23/1.42 tff(5119,plain,
% 1.23/1.42 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.23/1.42 inference(bind,[status(th)],[])).
% 1.23/1.42 tff(5120,plain,
% 1.23/1.42 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.23/1.42 inference(quant_intro,[status(thm)],[5119])).
% 1.23/1.42 tff(5121,plain,
% 1.23/1.42 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5122,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.23/1.42 tff(5123,plain,
% 1.23/1.42 (![X: $i] : (~r(X, X))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5122, 5121])).
% 1.23/1.42 tff(5124,plain,(
% 1.23/1.42 ![X: $i] : (~r(X, X))),
% 1.23/1.42 inference(skolemize,[status(sab)],[5123])).
% 1.23/1.42 tff(5125,plain,
% 1.23/1.42 (![X: $i] : (~r(X, X))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5124, 5120])).
% 1.23/1.42 tff(5126,plain,
% 1.23/1.42 ((~![X: $i] : (~r(X, X))) | (~r(s(s(elem!1)), s(s(elem!1))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5127,plain,
% 1.23/1.42 (~r(s(s(elem!1)), s(s(elem!1)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5126, 5125])).
% 1.23/1.42 tff(5128,plain,
% 1.23/1.42 (~r(s(s(elem!1)), elem!1)),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5127, 5118])).
% 1.23/1.42 tff(5129,plain,
% 1.23/1.42 (b(z, s(s(elem!1)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4020, 5128, 77, 3330, 83, 12, 74])).
% 1.23/1.42 tff(5130,plain,
% 1.23/1.42 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5101])).
% 1.23/1.42 tff(5131,plain,
% 1.23/1.42 (~r(s(s(z)), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1106, 3001, 77, 689, 416, 2083])).
% 1.23/1.42 tff(5132,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5133,plain,
% 1.23/1.42 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5134,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5133])).
% 1.23/1.42 tff(5135,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5134, 5132])).
% 1.23/1.42 tff(5136,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5137,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 1.23/1.42 tff(5138,plain,
% 1.23/1.42 (~r(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5137, 112, 179, 268])).
% 1.23/1.42 tff(5139,plain,
% 1.23/1.42 (b(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1071, 5138])).
% 1.23/1.42 tff(5140,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5141,plain,
% 1.23/1.42 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5142,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5141])).
% 1.23/1.42 tff(5143,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5142, 5140])).
% 1.23/1.42 tff(5144,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5145,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 1.23/1.42 tff(5146,plain,
% 1.23/1.42 (~b(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5145, 224, 77, 344, 1109, 5139])).
% 1.23/1.42 tff(5147,plain,
% 1.23/1.42 (r(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1088, 5146])).
% 1.23/1.42 tff(5148,plain,
% 1.23/1.42 (~r(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3470, 112, 179, 268])).
% 1.23/1.42 tff(5149,plain,
% 1.23/1.42 (b(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[213, 68, 210, 5148])).
% 1.23/1.42 tff(5150,plain,
% 1.23/1.42 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1096, 224, 1090, 560, 5149])).
% 1.23/1.42 tff(5151,plain,
% 1.23/1.42 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[249, 5150])).
% 1.23/1.42 tff(5152,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1104, 112, 5151, 689, 5147])).
% 1.23/1.42 tff(5153,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5154,plain,
% 1.23/1.42 (~r(s(s(z)), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5153, 179, 1090, 560, 77, 344, 1109, 689])).
% 1.23/1.42 tff(5155,plain,
% 1.23/1.42 (b(s(s(z)), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[234, 68, 42, 5154])).
% 1.23/1.42 tff(5156,plain,
% 1.23/1.42 (~b(elem!1, z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1126, 5155, 1109, 344])).
% 1.23/1.42 tff(5157,plain,
% 1.23/1.42 (r(elem!1, z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[403, 5156, 157])).
% 1.23/1.42 tff(5158,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2639, 112, 5157, 179, 416])).
% 1.23/1.42 tff(5159,plain,((~r(s(z), z)) | (~r(s(z), elem!1)) | (elem!1 = z) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5160,plain,
% 1.23/1.42 (~b(s(s(z)), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5159, 3001, 77, 416, 157, 179, 2083, 344, 689])).
% 1.23/1.42 tff(5161,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1135, 5160, 5131, 2796])).
% 1.23/1.42 tff(5162,plain,((~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (elem!1 = z) | (~b(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5163,plain,
% 1.23/1.42 (~r(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5162, 344, 77, 416, 157, 2833, 689, 177])).
% 1.23/1.42 tff(5164,plain,
% 1.23/1.42 (b(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[194, 5163])).
% 1.23/1.42 tff(5165,plain,
% 1.23/1.42 (~b(s(s(elem!1)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1249, 5164, 77, 1240])).
% 1.23/1.42 tff(5166,plain,
% 1.23/1.42 (r(s(s(elem!1)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[901, 5165])).
% 1.23/1.42 tff(5167,plain,
% 1.23/1.42 (b(elem!1, z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3641, 1296, 1240])).
% 1.23/1.42 tff(5168,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1296])).
% 1.23/1.42 tff(5169,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.23/1.42 inference(symmetry,[status(thm)],[5168])).
% 1.23/1.42 tff(5170,plain,
% 1.23/1.42 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5169])).
% 1.23/1.42 tff(5171,plain,
% 1.23/1.42 (~r(s(s(s(z))), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2374, 178, 416])).
% 1.23/1.42 tff(5172,plain,
% 1.23/1.42 (b(s(s(s(z))), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[374, 5171, 362])).
% 1.23/1.42 tff(5173,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[243, 178, 77, 1, 177])).
% 1.23/1.42 tff(5174,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[249, 5173])).
% 1.23/1.42 tff(5175,plain,
% 1.23/1.42 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.23/1.42 inference(symmetry,[status(thm)],[2825])).
% 1.23/1.42 tff(5176,plain,
% 1.23/1.42 (r(elem!1, s(z))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[887, 5175])).
% 1.23/1.42 tff(5177,plain,
% 1.23/1.42 (~r(elem!1, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1028, 178, 5176])).
% 1.23/1.42 tff(5178,plain,
% 1.23/1.42 (b(elem!1, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[388, 5177, 4197])).
% 1.23/1.42 tff(5179,plain,
% 1.23/1.42 (~b(s(s(z)), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2412, 5178, 5174, 5172])).
% 1.23/1.42 tff(5180,plain,
% 1.23/1.42 (r(s(s(z)), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1135, 5179, 2833])).
% 1.23/1.42 tff(5181,plain,
% 1.23/1.42 (r(s(s(z)), s(s(elem!1)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2801, 5180, 2834])).
% 1.23/1.42 tff(5182,plain,
% 1.23/1.42 (~r(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2853, 5181, 2850])).
% 1.23/1.42 tff(5183,plain,
% 1.23/1.42 (b(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2726, 5182])).
% 1.23/1.42 tff(5184,plain,
% 1.23/1.42 (~r(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3697, 112, 2850, 5181])).
% 1.23/1.42 tff(5185,plain,
% 1.23/1.42 (b(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1071, 5184])).
% 1.23/1.42 tff(5186,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3175, 224, 77, 1, 1570])).
% 1.23/1.42 tff(5187,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.23/1.42 tff(5188,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.23/1.42 tff(5189,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5190,plain,
% 1.23/1.42 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5191,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5190])).
% 1.23/1.42 tff(5192,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[5191, 5189])).
% 1.23/1.42 tff(5193,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(5194,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[5193, 5192])).
% 1.23/1.42 tff(5195,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5194, 224, 5187, 1570, 5188, 2844])).
% 1.23/1.42 tff(5196,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(5197,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[5196, 1570, 5187, 2844])).
% 1.23/1.42 tff(5198,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 5197])).
% 1.23/1.42 tff(5199,plain,
% 1.23/1.42 (~b(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1078, 224, 77, 5187, 2844])).
% 1.23/1.42 tff(5200,plain,
% 1.23/1.42 (r(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1088, 5199])).
% 1.23/1.42 tff(5201,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5202,plain,
% 1.23/1.42 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(5203,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[5202])).
% 1.23/1.42 tff(5204,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5203, 5201])).
% 1.23/1.43 tff(5205,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5206,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5205, 5204])).
% 1.23/1.43 tff(5207,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5206, 112, 689, 5200, 5198])).
% 1.23/1.43 tff(5208,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 5207, 5186])).
% 1.23/1.43 tff(5209,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5210,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5209, 5185, 77, 1, 689, 5183])).
% 1.23/1.43 tff(5211,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3168, 5210])).
% 1.23/1.43 tff(5212,plain,
% 1.23/1.43 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5213,plain,
% 1.23/1.43 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5214,plain,
% 1.23/1.43 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5213])).
% 1.23/1.43 tff(5215,plain,
% 1.23/1.43 (((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5214, 5212])).
% 1.23/1.43 tff(5216,plain,
% 1.23/1.43 ((~![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(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)))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5217,plain,
% 1.23/1.43 ((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5216, 5215])).
% 1.23/1.43 tff(5218,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5217, 112, 887, 5211])).
% 1.23/1.43 tff(5219,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), elem!1)),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5218, 5170])).
% 1.23/1.43 tff(5220,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3183, 5219, 3121])).
% 1.23/1.43 tff(5221,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5220, 3102])).
% 1.23/1.43 tff(5222,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5172, 2826])).
% 1.23/1.43 tff(5223,plain,
% 1.23/1.43 (~b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2846, 5183, 77, 1])).
% 1.23/1.43 tff(5224,plain,
% 1.23/1.43 (r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[281, 5223])).
% 1.23/1.43 tff(5225,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3531, 5224, 177])).
% 1.23/1.43 tff(5226,plain,
% 1.23/1.43 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3535, 68, 5225])).
% 1.23/1.43 tff(5227,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5226, 56])).
% 1.23/1.43 tff(5228,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4989, 224, 5185, 5183, 5227])).
% 1.23/1.43 tff(5229,plain,
% 1.23/1.43 (r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[925, 5228])).
% 1.23/1.43 tff(5230,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3326, 5211, 5229])).
% 1.23/1.43 tff(5231,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3252, 5230])).
% 1.23/1.43 tff(5232,plain,
% 1.23/1.43 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4039, 178, 887])).
% 1.23/1.43 tff(5233,plain,
% 1.23/1.43 (b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[147, 5232, 2])).
% 1.23/1.43 tff(5234,plain,
% 1.23/1.43 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5235,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5234])).
% 1.23/1.43 tff(5236,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5235, 3232])).
% 1.23/1.43 tff(5237,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5238,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5237, 5236])).
% 1.23/1.43 tff(5239,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5238, 224, 5233, 5231, 5222, 5221])).
% 1.23/1.43 tff(5240,plain,((~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5241,plain,
% 1.23/1.43 (~r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5240, 5166, 1296, 77, 5164, 689, 177, 362, 2, 416])).
% 1.23/1.43 tff(5242,plain,
% 1.23/1.43 (b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[175, 5241])).
% 1.23/1.43 tff(5243,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2853, 2851, 656])).
% 1.23/1.43 tff(5244,plain,
% 1.23/1.43 (b(s(s(z)), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[265, 5243, 259])).
% 1.23/1.43 tff(5245,plain,
% 1.23/1.43 (~r(s(s(z)), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2801, 5243, 2834])).
% 1.23/1.43 tff(5246,plain,
% 1.23/1.43 (b(s(s(z)), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1135, 5245, 2833])).
% 1.23/1.43 tff(5247,plain,
% 1.23/1.43 (~b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1126, 5246, 405, 344])).
% 1.23/1.43 tff(5248,plain,
% 1.23/1.43 (r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[281, 5247])).
% 1.23/1.43 tff(5249,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3531, 5248, 177])).
% 1.23/1.43 tff(5250,plain,
% 1.23/1.43 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3535, 68, 5249])).
% 1.23/1.43 tff(5251,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5250, 56])).
% 1.23/1.43 tff(5252,plain,
% 1.23/1.43 (~r(s(s(elem!1)), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3679, 112, 887, 2851])).
% 1.23/1.43 tff(5253,plain,
% 1.23/1.43 (~r(elem!1, s(s(z)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5252, 3187])).
% 1.23/1.43 tff(5254,plain,
% 1.23/1.43 (b(elem!1, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2874, 5253, 2832])).
% 1.23/1.43 tff(5255,plain,
% 1.23/1.43 (b(s(s(elem!1)), s(s(z)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5254, 3186])).
% 1.23/1.43 tff(5256,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5257,plain,
% 1.23/1.43 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(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(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5258,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5257])).
% 1.23/1.43 tff(5259,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5258, 5256])).
% 1.23/1.43 tff(5260,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5261,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5260, 5259])).
% 1.23/1.43 tff(5262,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5261, 224, 968, 2211, 2596, 5255])).
% 1.23/1.43 tff(5263,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5264,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5263, 5251, 5244, 1296, 887, 2851])).
% 1.23/1.43 tff(5265,plain,
% 1.23/1.43 (r(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[135, 68, 308, 5264])).
% 1.23/1.43 tff(5266,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5267,plain,
% 1.23/1.43 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5268,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5267])).
% 1.23/1.43 tff(5269,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5268, 5266])).
% 1.23/1.43 tff(5270,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5271,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5270, 5269])).
% 1.23/1.43 tff(5272,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5271, 112, 656, 5265])).
% 1.23/1.43 tff(5273,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[925, 5272])).
% 1.23/1.43 tff(5274,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.23/1.43 tff(5275,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5276,plain,
% 1.23/1.43 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, 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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5277,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5276])).
% 1.23/1.43 tff(5278,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5277, 5275])).
% 1.23/1.43 tff(5279,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5280,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5279, 5278])).
% 1.23/1.43 tff(5281,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5280, 224, 2861, 1109, 5274])).
% 1.23/1.43 tff(5282,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 5281])).
% 1.23/1.43 tff(5283,plain,
% 1.23/1.43 (~b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1126, 405, 1109, 344])).
% 1.23/1.43 tff(5284,plain,
% 1.23/1.43 (r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[234, 68, 42, 5283])).
% 1.23/1.43 tff(5285,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5286,plain,
% 1.23/1.43 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5287,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5286])).
% 1.23/1.43 tff(5288,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5287, 5285])).
% 1.23/1.44 tff(5289,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5290,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5289, 5288])).
% 1.23/1.44 tff(5291,plain,
% 1.23/1.44 (~b(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5290, 224, 405, 344, 5274])).
% 1.23/1.44 tff(5292,plain,
% 1.23/1.44 (r(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 5291])).
% 1.23/1.44 tff(5293,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5294,plain,
% 1.23/1.44 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5295,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5294])).
% 1.23/1.44 tff(5296,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5295, 5293])).
% 1.23/1.44 tff(5297,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5298,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5297, 5296])).
% 1.23/1.44 tff(5299,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5298, 112, 5292, 5284, 5282])).
% 1.23/1.44 tff(5300,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5301,plain,
% 1.23/1.44 (~b(s(s(s(s(z)))), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5300, 5254, 405, 344, 5246])).
% 1.23/1.44 tff(5302,plain,
% 1.23/1.44 (r(s(s(s(s(z)))), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3183, 5301, 3121])).
% 1.23/1.44 tff(5303,plain,
% 1.23/1.44 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5302, 5168])).
% 1.23/1.44 tff(5304,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3154, 112, 656, 5303])).
% 1.23/1.44 tff(5305,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3168, 5304])).
% 1.23/1.44 tff(5306,plain,
% 1.23/1.44 (((~![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(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5307,plain,
% 1.23/1.44 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5308,plain,
% 1.23/1.44 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5307])).
% 1.23/1.44 tff(5309,plain,
% 1.23/1.44 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5308, 5306])).
% 1.23/1.44 tff(5310,plain,
% 1.23/1.44 ((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5311,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5310, 5309])).
% 1.23/1.44 tff(5312,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5311, 112, 177, 5265, 5303])).
% 1.23/1.44 tff(5313,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3252, 5312])).
% 1.23/1.44 tff(5314,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1579, 5313, 5305, 1090, 5273])).
% 1.23/1.44 tff(5315,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5316,plain,
% 1.23/1.44 (~r(s(s(z)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5315, 5242, 177, 2850, 1296, 5167, 344, 5166, 132, 1108])).
% 1.23/1.44 tff(5317,plain,
% 1.23/1.44 (b(s(s(z)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2726, 5316])).
% 1.23/1.44 tff(5318,plain,
% 1.23/1.44 (~b(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2846, 5317, 77, 5164])).
% 1.23/1.44 tff(5319,plain,
% 1.23/1.44 (r(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[281, 5318])).
% 1.23/1.44 tff(5320,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3455, 5319, 689])).
% 1.23/1.44 tff(5321,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[249, 5320])).
% 1.23/1.44 tff(5322,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3531, 5319, 177])).
% 1.23/1.44 tff(5323,plain,
% 1.23/1.44 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3535, 68, 5322])).
% 1.23/1.44 tff(5324,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5323, 56])).
% 1.23/1.44 tff(5325,plain,
% 1.23/1.44 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5326,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5325])).
% 1.23/1.44 tff(5327,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5326, 4954])).
% 1.23/1.44 tff(5328,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5329,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.23/1.44 tff(5330,plain,
% 1.23/1.44 (~b(s(z), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5329, 224, 5321, 5242, 5324])).
% 1.23/1.44 tff(5331,plain,
% 1.23/1.44 (r(s(z), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1071, 5330])).
% 1.23/1.44 tff(5332,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3697, 112, 656, 2303, 267])).
% 1.23/1.44 tff(5333,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5334,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(elem!1)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5333, 5331, 2850])).
% 1.23/1.44 tff(5335,plain,
% 1.23/1.44 (~r(s(s(z)), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2801, 5334, 2834])).
% 1.23/1.44 tff(5336,plain,
% 1.23/1.44 (b(s(s(z)), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1135, 5335, 2833])).
% 1.23/1.44 tff(5337,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5338,plain,
% 1.23/1.44 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5339,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5338])).
% 1.23/1.44 tff(5340,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5339, 5337])).
% 1.23/1.44 tff(5341,plain,
% 1.23/1.44 ((~![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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5342,plain,
% 1.23/1.44 ((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5341, 5340])).
% 1.23/1.44 tff(5343,plain,
% 1.23/1.44 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5342, 112, 887, 3188])).
% 1.23/1.44 tff(5344,plain,
% 1.23/1.44 (b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[147, 5343, 2])).
% 1.23/1.44 tff(5345,plain,
% 1.23/1.44 (b(elem!1, s(s(s(z))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5344, 3126])).
% 1.23/1.44 tff(5346,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5347,plain,
% 1.23/1.44 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5348,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5347])).
% 1.23/1.44 tff(5349,plain,
% 1.23/1.44 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5348, 5346])).
% 1.23/1.44 tff(5350,plain,
% 1.23/1.44 ((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5351,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.23/1.44 tff(5352,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5351, 112, 887, 3188])).
% 1.23/1.44 tff(5353,plain,
% 1.23/1.44 (~r(s(s(s(z))), elem!1)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5352, 2916])).
% 1.23/1.44 tff(5354,plain,
% 1.23/1.44 (b(s(s(s(z))), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[374, 5353, 362])).
% 1.23/1.44 tff(5355,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2412, 5354, 5345, 1109, 2212])).
% 1.23/1.44 tff(5356,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5357,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5356, 5336, 5321, 362, 1296, 2, 5166])).
% 1.23/1.44 tff(5358,plain,
% 1.23/1.44 (b(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[925, 5357])).
% 1.23/1.44 tff(5359,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3462, 224, 5321, 5242, 5358, 5317])).
% 1.23/1.44 tff(5360,plain,((~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5361,plain,
% 1.23/1.44 (~r(s(z), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5360, 5115, 5101, 2, 101, 73, 77, 5107, 3330, 11])).
% 1.23/1.44 tff(5362,plain,
% 1.23/1.44 (b(s(z), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[454, 5361, 91])).
% 1.23/1.44 tff(5363,plain,
% 1.23/1.44 (b(s(z), s(s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5362, 5130])).
% 1.23/1.44 tff(5364,plain,
% 1.23/1.44 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5365,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5364])).
% 1.23/1.44 tff(5366,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5365, 3503])).
% 1.23/1.44 tff(5367,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5368,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 1.23/1.44 tff(5369,plain,
% 1.23/1.44 (~b(s(z), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5368, 224, 3330, 5363, 5129])).
% 1.23/1.44 tff(5370,plain,
% 1.23/1.44 (r(s(z), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[194, 5369])).
% 1.23/1.44 tff(5371,plain,
% 1.23/1.44 (~r(s(z), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[187, 5370, 73])).
% 1.23/1.44 tff(5372,plain,
% 1.23/1.44 (b(s(z), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[175, 5371])).
% 1.23/1.44 tff(5373,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[932, 112, 5370, 73])).
% 1.23/1.44 tff(5374,plain,
% 1.23/1.44 (b(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[925, 5373])).
% 1.23/1.44 tff(5375,plain,
% 1.23/1.44 (~r(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3472, 5374, 5370, 5372, 101])).
% 1.23/1.44 tff(5376,plain,
% 1.23/1.44 (b(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[281, 5375])).
% 1.23/1.44 tff(5377,plain,
% 1.23/1.44 (~b(s(s(z)), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1126, 5376, 5106, 5115])).
% 1.23/1.44 tff(5378,plain,
% 1.23/1.44 (r(s(s(z)), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1135, 5377, 5105])).
% 1.23/1.44 tff(5379,plain,
% 1.23/1.44 (r(s(s(z)), s(s(elem!1)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2801, 5378, 5102])).
% 1.23/1.44 tff(5380,plain,
% 1.23/1.44 (~b(elem!1, s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2904, 5362, 77, 5115])).
% 1.23/1.44 tff(5381,plain,
% 1.23/1.44 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1296])).
% 1.23/1.44 tff(5382,plain,
% 1.23/1.44 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.23/1.44 inference(symmetry,[status(thm)],[5381])).
% 1.23/1.44 tff(5383,plain,
% 1.23/1.44 (b(elem!1, s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1241, 5382])).
% 1.23/1.44 tff(5384,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1272, 5383])).
% 1.23/1.44 tff(5385,plain,((~b(s(s(elem!1)), s(z))) | b(elem!1, s(z)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5386,plain,
% 1.23/1.44 (~b(s(s(elem!1)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5385, 5380, 5101])).
% 1.23/1.44 tff(5387,plain,
% 1.23/1.44 (r(s(s(elem!1)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[901, 5386])).
% 1.23/1.44 tff(5388,plain,
% 1.23/1.44 (~r(s(s(z)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2993, 5387, 5379])).
% 1.23/1.44 tff(5389,plain,
% 1.23/1.44 (b(s(s(z)), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2726, 5388])).
% 1.23/1.44 tff(5390,plain,
% 1.23/1.44 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5101])).
% 1.23/1.44 tff(5391,plain,
% 1.23/1.44 (~(elem!1 = s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3418, 5107])).
% 1.23/1.44 tff(5392,plain,
% 1.23/1.44 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5101])).
% 1.23/1.44 tff(5393,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.23/1.44 inference(symmetry,[status(thm)],[5392])).
% 1.23/1.44 tff(5394,plain,
% 1.23/1.44 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5103, 5101])).
% 1.23/1.44 tff(5395,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5394])).
% 1.23/1.44 tff(5396,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.23/1.44 inference(transitivity,[status(thm)],[5395, 5393])).
% 1.23/1.44 tff(5397,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(5398,plain,
% 1.23/1.44 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), elem!1)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[2767])).
% 1.23/1.44 tff(5399,plain,
% 1.23/1.44 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(symmetry,[status(thm)],[5398])).
% 1.23/1.44 tff(5400,plain,
% 1.23/1.44 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1047, 5399])).
% 1.23/1.44 tff(5401,assumption,(~r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(5402,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5401, 5400])).
% 1.23/1.44 tff(5403,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5404,plain,
% 1.23/1.44 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5403, 1047, 2767])).
% 1.23/1.44 tff(5405,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(5406,plain,
% 1.23/1.44 (((~![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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5407,plain,
% 1.23/1.44 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5408,plain,
% 1.23/1.44 (((~![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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5407])).
% 1.23/1.44 tff(5409,plain,
% 1.23/1.45 (((~![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(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5408, 5406])).
% 1.23/1.45 tff(5410,plain,
% 1.23/1.45 ((~![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(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5411,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 1.23/1.45 tff(5412,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5411, 112, 196, 5397, 5405])).
% 1.23/1.45 tff(5413,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5414,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5413, 5404, 5397])).
% 1.23/1.45 tff(5415,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[249, 5414])).
% 1.23/1.45 tff(5416,plain,
% 1.23/1.45 (~b(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3462, 224, 5415, 1090, 560])).
% 1.23/1.45 tff(5417,plain,
% 1.23/1.45 (r(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[213, 68, 210, 5416])).
% 1.23/1.45 tff(5418,plain,
% 1.23/1.45 (r(s(s(z)), s(s(elem!1)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2801, 1047, 349])).
% 1.23/1.45 tff(5419,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2991, 112, 887, 5418, 5417])).
% 1.23/1.45 tff(5420,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5421,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5420, 5387, 5102, 5374, 5372, 5103, 5378])).
% 1.23/1.45 tff(5422,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5423,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5424,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 1.23/1.45 tff(5425,plain,
% 1.23/1.45 ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5424, 68])).
% 1.23/1.45 tff(5426,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5425, 1165])).
% 1.23/1.45 tff(5427,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5426, 5421])).
% 1.23/1.45 tff(5428,plain,
% 1.23/1.45 (b(s(s(s(z))), elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5427, 5396])).
% 1.23/1.45 tff(5429,plain,
% 1.23/1.45 (~b(elem!1, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2941, 5428, 5362, 5372])).
% 1.23/1.45 tff(5430,plain,
% 1.23/1.45 (r(elem!1, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[388, 5429, 5391])).
% 1.23/1.45 tff(5431,plain,
% 1.23/1.45 (r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5430, 5390])).
% 1.23/1.45 tff(5432,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5433,plain,
% 1.23/1.45 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5434,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5433])).
% 1.23/1.45 tff(5435,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5434, 5432])).
% 1.23/1.45 tff(5436,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5437,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5436, 5435])).
% 1.23/1.45 tff(5438,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5437, 112, 887, 196, 827, 267])).
% 1.23/1.45 tff(5439,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5440,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5439, 5387, 5431, 5379])).
% 1.23/1.45 tff(5441,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[249, 5440])).
% 1.23/1.45 tff(5442,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5443,plain,
% 1.23/1.45 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5444,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5443])).
% 1.23/1.45 tff(5445,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5444, 5442])).
% 1.23/1.45 tff(5446,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5447,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5446, 5445])).
% 1.23/1.45 tff(5448,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5447, 224, 77, 5441, 5372, 5376, 5389])).
% 1.23/1.45 tff(5449,plain,((~b(z, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1) | b(s(s(s(z))), z) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5450,plain,
% 1.23/1.45 (~b(z, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5449, 74, 4, 12, 2])).
% 1.23/1.45 tff(5451,plain,
% 1.23/1.45 ((z = s(z)) <=> (s(z) = z)),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(5452,plain,
% 1.23/1.45 ((s(z) = z) <=> (z = s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[5451])).
% 1.23/1.45 tff(5453,plain,
% 1.23/1.45 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5452])).
% 1.23/1.45 tff(5454,plain,
% 1.23/1.45 (~(z = s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[190, 5453])).
% 1.23/1.45 tff(5455,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5456,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5457,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 1.23/1.45 tff(5458,plain,
% 1.23/1.45 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5457, 68])).
% 1.23/1.45 tff(5459,plain,
% 1.23/1.45 (b(z, s(z)) | r(z, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5458, 5454])).
% 1.23/1.45 tff(5460,plain,
% 1.23/1.45 (r(z, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5459, 5450])).
% 1.23/1.45 tff(5461,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[4608, 5460, 73])).
% 1.23/1.45 tff(5462,plain,
% 1.23/1.45 (b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[925, 5461])).
% 1.23/1.45 tff(5463,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5464,plain,
% 1.23/1.45 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5465,plain,
% 1.23/1.45 (((~![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(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5464])).
% 1.23/1.45 tff(5466,plain,
% 1.23/1.45 (((~![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(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5465, 5463])).
% 1.23/1.45 tff(5467,plain,
% 1.23/1.45 ((~![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(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5468,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 1.23/1.45 tff(5469,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5468, 112, 4569, 178, 689])).
% 1.23/1.45 tff(5470,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5471,plain,
% 1.23/1.45 (~r(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5470, 5460, 101])).
% 1.23/1.45 tff(5472,plain,
% 1.23/1.45 (b(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[175, 5471])).
% 1.23/1.45 tff(5473,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5474,plain,
% 1.23/1.45 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5475,plain,
% 1.23/1.45 (((~![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(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5474])).
% 1.23/1.45 tff(5476,plain,
% 1.23/1.45 (((~![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(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5475, 5473])).
% 1.23/1.45 tff(5477,plain,
% 1.23/1.45 ((~![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(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5478,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5477, 5476])).
% 1.23/1.45 tff(5479,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5478, 112, 4569, 416, 688])).
% 1.23/1.45 tff(5480,plain,((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5481,plain,
% 1.23/1.45 (~r(s(z), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5480, 688, 4569])).
% 1.23/1.45 tff(5482,plain,
% 1.23/1.45 (b(s(z), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[454, 5481, 91])).
% 1.23/1.45 tff(5483,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5484,plain,
% 1.23/1.45 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5485,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5484])).
% 1.23/1.45 tff(5486,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.23/1.45 tff(5487,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5488,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 1.23/1.45 tff(5489,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5488, 112, 4569, 688, 993])).
% 1.23/1.45 tff(5490,plain,((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5491,plain,
% 1.23/1.45 (~r(elem!1, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5490, 688, 4569])).
% 1.23/1.45 tff(5492,plain,
% 1.23/1.45 (b(elem!1, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1277, 5491, 83])).
% 1.23/1.45 tff(5493,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[4608, 177, 4569])).
% 1.23/1.45 tff(5494,plain,
% 1.23/1.45 (b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[925, 5493])).
% 1.23/1.45 tff(5495,plain,
% 1.23/1.45 (~r(s(s(s(z))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2431, 177, 688])).
% 1.23/1.45 tff(5496,plain,
% 1.23/1.45 (b(s(s(s(z))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[374, 5495, 362])).
% 1.23/1.45 tff(5497,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5498,plain,
% 1.23/1.45 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5499,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5498])).
% 1.23/1.45 tff(5500,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5499, 5497])).
% 1.23/1.46 tff(5501,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5502,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5501, 5500])).
% 1.23/1.46 tff(5503,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5502, 224, 684, 2896, 5496, 5494])).
% 1.23/1.46 tff(5504,plain,((~r(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5505,plain,
% 1.23/1.46 (s(s(s(z))) = elem!1),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5504, 177, 2896, 684, 688, 4569])).
% 1.23/1.46 tff(5506,plain,
% 1.23/1.46 (s(s(s(s(z)))) = s(elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.46 tff(5507,plain,
% 1.23/1.46 (s(elem!1) = s(s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5506])).
% 1.23/1.46 tff(5508,plain,
% 1.23/1.46 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5507])).
% 1.23/1.46 tff(5509,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5508])).
% 1.23/1.46 tff(5510,plain,
% 1.23/1.46 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5509])).
% 1.23/1.46 tff(5511,plain,
% 1.23/1.46 (~(s(elem!1) = s(s(z)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1229, 5510])).
% 1.23/1.46 tff(5512,plain,
% 1.23/1.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.46 tff(5513,plain,
% 1.23/1.46 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5512, 2587])).
% 1.23/1.46 tff(5514,plain,
% 1.23/1.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.23/1.46 inference(transitivity,[status(thm)],[5513, 2588])).
% 1.23/1.46 tff(5515,plain,
% 1.23/1.46 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5514])).
% 1.23/1.46 tff(5516,plain,
% 1.23/1.46 (~(s(s(z)) = elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[55, 5515])).
% 1.23/1.46 tff(5517,plain,
% 1.23/1.46 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.46 tff(5518,plain,
% 1.23/1.46 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5517, 75])).
% 1.23/1.46 tff(5519,plain,
% 1.23/1.46 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.23/1.46 inference(transitivity,[status(thm)],[5518, 76])).
% 1.23/1.46 tff(5520,plain,
% 1.23/1.46 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5519])).
% 1.23/1.46 tff(5521,plain,
% 1.23/1.46 (~(s(s(elem!1)) = elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2, 5520])).
% 1.23/1.46 tff(5522,plain,
% 1.23/1.46 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5518])).
% 1.23/1.46 tff(5523,plain,
% 1.23/1.46 (~(elem!1 = s(s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2, 5522])).
% 1.23/1.46 tff(5524,plain,
% 1.23/1.46 (~(s(elem!1) = s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[318, 5523])).
% 1.23/1.46 tff(5525,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5506])).
% 1.23/1.46 tff(5526,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5525, 320])).
% 1.23/1.46 tff(5527,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.23/1.46 inference(transitivity,[status(thm)],[5526, 321])).
% 1.23/1.46 tff(5528,plain,
% 1.23/1.46 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5527])).
% 1.23/1.46 tff(5529,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.46 tff(5530,plain,
% 1.23/1.46 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5529])).
% 1.23/1.46 tff(5531,plain,
% 1.23/1.46 (~(s(s(s(s(z)))) = elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[3246, 5530])).
% 1.23/1.46 tff(5532,plain,
% 1.23/1.46 (~(s(elem!1) = elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5531, 5528])).
% 1.23/1.46 tff(5533,plain,
% 1.23/1.46 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.46 tff(5534,plain,
% 1.23/1.46 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5533])).
% 1.23/1.46 tff(5535,plain,
% 1.23/1.46 (~(elem!1 = z)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[58, 5534])).
% 1.23/1.46 tff(5536,plain,
% 1.23/1.46 (~(s(elem!1) = s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[159, 5535])).
% 1.23/1.46 tff(5537,plain,
% 1.23/1.46 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.23/1.46 inference(commutativity,[status(thm)],[])).
% 1.23/1.46 tff(5538,plain,
% 1.23/1.46 (s(elem!1) = s(s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[4131])).
% 1.23/1.46 tff(5539,plain,
% 1.23/1.46 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5538])).
% 1.23/1.46 tff(5540,plain,
% 1.23/1.46 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5539, 5537])).
% 1.23/1.46 tff(5541,plain,
% 1.23/1.46 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5540])).
% 1.23/1.46 tff(5542,plain,
% 1.23/1.46 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5541])).
% 1.23/1.46 tff(5543,plain,
% 1.23/1.46 (~(s(s(z)) = s(elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1229, 5542])).
% 1.23/1.46 tff(5544,plain,
% 1.23/1.46 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[341])).
% 1.23/1.46 tff(5545,plain,
% 1.23/1.46 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5544])).
% 1.23/1.46 tff(5546,plain,
% 1.23/1.46 (~(elem!1 = z)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[58, 5545])).
% 1.23/1.46 tff(5547,plain,
% 1.23/1.46 (~(s(elem!1) = s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[159, 5546])).
% 1.23/1.46 tff(5548,plain,
% 1.23/1.46 (~(s(s(z)) = s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[168, 5547])).
% 1.23/1.46 tff(5549,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(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(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5550,plain,
% 1.23/1.46 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5551,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5550])).
% 1.23/1.46 tff(5552,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5551, 5549])).
% 1.23/1.46 tff(5553,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5554,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5553, 5552])).
% 1.23/1.46 tff(5555,plain,
% 1.23/1.46 (~r(s(elem!1), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5554, 112, 887, 428])).
% 1.23/1.46 tff(5556,plain,
% 1.23/1.46 (b(s(elem!1), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1521, 5555, 523])).
% 1.23/1.46 tff(5557,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5558,plain,
% 1.23/1.46 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5559,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5558])).
% 1.23/1.46 tff(5560,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5559, 5557])).
% 1.23/1.46 tff(5561,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5562,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5561, 5560])).
% 1.23/1.46 tff(5563,plain,
% 1.23/1.46 (~r(z, s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5562, 112, 4569, 428])).
% 1.23/1.46 tff(5564,plain,
% 1.23/1.46 (b(z, s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[625, 5563])).
% 1.23/1.46 tff(5565,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5566,plain,
% 1.23/1.46 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5567,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5566])).
% 1.23/1.46 tff(5568,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5567, 5565])).
% 1.23/1.46 tff(5569,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5570,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 1.23/1.46 tff(5571,plain,
% 1.23/1.46 (~r(z, s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 887])).
% 1.23/1.46 tff(5572,plain,
% 1.23/1.46 (b(z, s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[752, 5571])).
% 1.23/1.46 tff(5573,plain,
% 1.23/1.46 (~r(s(s(elem!1)), s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4173, 112, 887, 428])).
% 1.23/1.46 tff(5574,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[530, 5573, 1923])).
% 1.23/1.46 tff(5575,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4124, 5574, 5572, 5564, 5556])).
% 1.23/1.46 tff(5576,plain,((~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5577,plain,
% 1.23/1.46 (~r(s(s(elem!1)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5576, 428, 319, 4569])).
% 1.23/1.46 tff(5578,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[901, 5577])).
% 1.23/1.46 tff(5579,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5580,plain,
% 1.23/1.46 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5581,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5580])).
% 1.23/1.46 tff(5582,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5581, 5579])).
% 1.23/1.46 tff(5583,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5584,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5583, 5582])).
% 1.23/1.46 tff(5585,plain,
% 1.23/1.46 (~b(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5584, 224, 684, 5578, 2896])).
% 1.23/1.46 tff(5586,plain,
% 1.23/1.46 (r(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[360, 5585, 355])).
% 1.23/1.46 tff(5587,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5588,plain,
% 1.23/1.46 (((~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)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5589,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5588])).
% 1.23/1.46 tff(5590,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5589, 5587])).
% 1.23/1.46 tff(5591,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5592,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5591, 5590])).
% 1.23/1.46 tff(5593,plain,
% 1.23/1.46 (~r(s(s(z)), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5592, 112, 1181, 1047])).
% 1.23/1.46 tff(5594,plain,
% 1.23/1.46 (b(s(s(z)), s(s(elem!1)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[263, 68, 5593, 259])).
% 1.23/1.46 tff(5595,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5596,plain,
% 1.23/1.46 (((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5597,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5598,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5597, 5595])).
% 1.23/1.47 tff(5599,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5600,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5599, 5598])).
% 1.23/1.47 tff(5601,plain,
% 1.23/1.47 (~r(s(s(z)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5600, 112, 4569, 688, 1047])).
% 1.23/1.47 tff(5602,plain,
% 1.23/1.47 (b(s(s(z)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[281, 5601])).
% 1.23/1.47 tff(5603,plain,
% 1.23/1.47 (~r(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2346, 1181, 688])).
% 1.23/1.47 tff(5604,plain,
% 1.23/1.47 (b(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[593, 5603])).
% 1.23/1.47 tff(5605,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4077, 224, 5604, 4106, 5602, 5594])).
% 1.23/1.47 tff(5606,plain,((~r(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5607,plain,
% 1.23/1.47 (~r(s(s(z)), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5606, 5586, 4569, 688, 5548])).
% 1.23/1.47 tff(5608,plain,
% 1.23/1.47 (b(s(s(z)), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1135, 5607, 5043])).
% 1.23/1.47 tff(5609,plain,
% 1.23/1.47 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5610,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5609])).
% 1.23/1.47 tff(5611,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5610, 4516])).
% 1.23/1.47 tff(5612,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5613,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5612, 5611])).
% 1.23/1.47 tff(5614,plain,
% 1.23/1.47 (~b(s(s(z)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5613, 224, 684, 2896, 5608])).
% 1.23/1.47 tff(5615,plain,
% 1.23/1.47 (r(s(s(z)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[213, 68, 210, 5614])).
% 1.23/1.47 tff(5616,plain,
% 1.23/1.47 (~r(z, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[3500, 5586, 688])).
% 1.23/1.47 tff(5617,plain,
% 1.23/1.47 (b(z, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[752, 5616])).
% 1.23/1.47 tff(5618,plain,
% 1.23/1.47 (~r(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2346, 5586, 688])).
% 1.23/1.47 tff(5619,plain,
% 1.23/1.47 (b(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[593, 5618])).
% 1.23/1.47 tff(5620,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5621,plain,
% 1.23/1.47 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5622,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5621])).
% 1.23/1.47 tff(5623,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5622, 5620])).
% 1.23/1.47 tff(5624,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5625,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5624, 5623])).
% 1.23/1.47 tff(5626,plain,
% 1.23/1.47 (~r(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5625, 112, 4569, 428])).
% 1.23/1.47 tff(5627,plain,
% 1.23/1.47 (b(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[498, 5626])).
% 1.23/1.47 tff(5628,plain,
% 1.23/1.47 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4154, 5627, 5619, 5617])).
% 1.23/1.47 tff(5629,plain,
% 1.23/1.47 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1521, 5628, 319])).
% 1.23/1.47 tff(5630,plain,
% 1.23/1.47 (((~![X0: $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(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5631,plain,
% 1.23/1.47 (((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~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(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5632,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(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(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5631])).
% 1.23/1.47 tff(5633,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(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(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5632, 5630])).
% 1.23/1.47 tff(5634,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5635,plain,
% 1.23/1.47 ((~![X0: $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(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5634, 5633])).
% 1.23/1.47 tff(5636,plain,
% 1.23/1.47 (~r(s(s(z)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5635, 112, 5629, 428, 5615])).
% 1.23/1.47 tff(5637,plain,
% 1.23/1.47 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[4131])).
% 1.23/1.47 tff(5638,plain,
% 1.23/1.47 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5637, 320])).
% 1.23/1.47 tff(5639,plain,
% 1.23/1.47 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.23/1.47 inference(transitivity,[status(thm)],[5638, 321])).
% 1.23/1.47 tff(5640,plain,
% 1.23/1.47 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5639])).
% 1.23/1.47 tff(5641,plain,
% 1.23/1.47 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[341])).
% 1.23/1.47 tff(5642,plain,
% 1.23/1.47 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5641])).
% 1.23/1.47 tff(5643,plain,
% 1.23/1.47 (~(s(s(s(s(z)))) = elem!1)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[3246, 5642])).
% 1.23/1.47 tff(5644,plain,
% 1.23/1.47 (~(s(elem!1) = elem!1)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5643, 5640])).
% 1.23/1.47 tff(5645,plain,
% 1.23/1.47 (~r(s(elem!1), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4126, 5586, 319, 688])).
% 1.23/1.47 tff(5646,plain,
% 1.23/1.47 (b(s(elem!1), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[939, 5645, 5644])).
% 1.23/1.47 tff(5647,plain,
% 1.23/1.47 (~b(s(s(elem!1)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4320, 5564, 5619, 5627])).
% 1.23/1.47 tff(5648,plain,
% 1.23/1.47 (b(elem!1, s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[541, 5647, 3, 5585])).
% 1.23/1.47 tff(5649,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5650,plain,
% 1.23/1.47 (((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5651,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5650])).
% 1.23/1.47 tff(5652,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5651, 5649])).
% 1.23/1.47 tff(5653,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5654,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 1.23/1.47 tff(5655,plain,
% 1.23/1.47 (~b(s(s(z)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5654, 224, 5648, 5646, 5608])).
% 1.23/1.47 tff(5656,plain,
% 1.23/1.47 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2532, 68, 5655])).
% 1.23/1.47 tff(5657,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5656, 5636, 5543])).
% 1.23/1.47 tff(5658,plain,((~r(s(elem!1), s(z))) | (~(s(s(s(z))) = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5659,plain,
% 1.23/1.47 (~r(s(elem!1), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5658, 5505, 684, 2896, 4569, 688, 5523, 5521])).
% 1.23/1.47 tff(5660,plain,
% 1.23/1.47 (b(s(elem!1), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1476, 5659, 5536])).
% 1.23/1.47 tff(5661,plain,
% 1.23/1.47 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5662,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5661])).
% 1.23/1.47 tff(5663,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5662, 2657])).
% 1.23/1.47 tff(5664,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5665,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5664, 5663])).
% 1.23/1.47 tff(5666,plain,
% 1.23/1.47 (~b(s(elem!1), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5665, 224, 684, 2896, 5660])).
% 1.23/1.47 tff(5667,plain,
% 1.23/1.47 (r(s(elem!1), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[939, 5666, 5532])).
% 1.23/1.47 tff(5668,plain,
% 1.23/1.47 (~r(s(s(elem!1)), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4126, 5667, 5524, 688])).
% 1.23/1.47 tff(5669,plain,
% 1.23/1.47 (b(s(s(elem!1)), elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[360, 5668, 5521])).
% 1.23/1.47 tff(5670,plain,
% 1.23/1.47 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(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)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5671,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5670])).
% 1.23/1.47 tff(5672,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5671, 5579])).
% 1.23/1.47 tff(5673,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5674,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5673, 5672])).
% 1.23/1.47 tff(5675,plain,
% 1.23/1.47 (~b(s(s(elem!1)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5674, 224, 684, 2896, 5669])).
% 1.23/1.47 tff(5676,plain,
% 1.23/1.47 (r(s(s(elem!1)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[901, 5675])).
% 1.23/1.47 tff(5677,plain,
% 1.23/1.47 (~r(z, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 5676])).
% 1.23/1.47 tff(5678,plain,
% 1.23/1.47 (b(z, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[752, 5677])).
% 1.23/1.47 tff(5679,plain,
% 1.23/1.47 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5505])).
% 1.23/1.47 tff(5680,plain,
% 1.23/1.47 (r(elem!1, z)),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[177, 5679])).
% 1.23/1.47 tff(5681,plain,
% 1.23/1.47 (~r(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2694, 5667, 5680])).
% 1.23/1.47 tff(5682,plain,
% 1.23/1.47 (b(s(elem!1), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[498, 5681])).
% 1.23/1.47 tff(5683,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5684,plain,
% 1.23/1.47 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5685,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5684])).
% 1.23/1.47 tff(5686,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5685, 5683])).
% 1.23/1.47 tff(5687,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5688,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.23/1.47 tff(5689,plain,
% 1.23/1.47 (~r(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5688, 112, 4569, 5676])).
% 1.23/1.47 tff(5690,plain,
% 1.23/1.47 (b(s(s(elem!1)), z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[593, 5689])).
% 1.23/1.47 tff(5691,plain,
% 1.23/1.47 (~b(s(elem!1), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4154, 5690, 5682, 5678])).
% 1.23/1.47 tff(5692,plain,
% 1.23/1.47 (r(s(elem!1), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1521, 5691, 5524])).
% 1.23/1.47 tff(5693,plain,
% 1.23/1.47 (~r(elem!1, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4010, 5692, 5667])).
% 1.23/1.47 tff(5694,plain,
% 1.23/1.47 (b(elem!1, s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[558, 5693, 5523])).
% 1.23/1.47 tff(5695,plain,
% 1.23/1.47 (~(s(s(z)) = s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[168, 5536])).
% 1.23/1.47 tff(5696,plain,
% 1.23/1.47 (~(s(s(elem!1)) = s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[525, 5524])).
% 1.23/1.47 tff(5697,plain,
% 1.23/1.47 (~r(z, s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[2499, 5667, 688])).
% 1.23/1.47 tff(5698,plain,
% 1.23/1.47 (b(z, s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[625, 5697])).
% 1.23/1.47 tff(5699,plain,
% 1.23/1.47 (~b(s(s(elem!1)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4320, 5690, 5698, 5682])).
% 1.23/1.47 tff(5700,plain,
% 1.23/1.47 (r(s(s(elem!1)), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[530, 5699, 5696])).
% 1.23/1.47 tff(5701,plain,
% 1.23/1.47 (~b(s(s(z)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5613, 224, 684, 2896, 1109])).
% 1.23/1.47 tff(5702,plain,
% 1.23/1.47 (r(s(s(z)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[213, 68, 210, 5701])).
% 1.23/1.47 tff(5703,plain,
% 1.23/1.47 (~b(s(s(elem!1)), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5674, 224, 684, 2896, 390])).
% 1.23/1.48 tff(5704,plain,
% 1.23/1.48 (r(s(s(elem!1)), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[901, 5703])).
% 1.23/1.48 tff(5705,plain,
% 1.23/1.48 (((~![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(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5706,plain,
% 1.23/1.48 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5707,plain,
% 1.23/1.48 (((~![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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(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(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5706])).
% 1.23/1.48 tff(5708,plain,
% 1.23/1.48 (((~![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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(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(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5707, 5705])).
% 1.23/1.48 tff(5709,plain,
% 1.23/1.48 ((~![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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5710,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5709, 5708])).
% 1.23/1.48 tff(5711,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5710, 112, 544, 5704, 1117, 5702])).
% 1.23/1.48 tff(5712,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5713,plain,
% 1.23/1.48 (~b(s(s(z)), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5712, 5700, 5695, 5694, 5669, 684, 2896])).
% 1.23/1.48 tff(5714,plain,
% 1.23/1.48 (r(s(s(z)), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1135, 5713, 5516])).
% 1.23/1.48 tff(5715,plain,
% 1.23/1.48 (~r(s(s(z)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5600, 112, 4569, 688, 5714])).
% 1.23/1.48 tff(5716,plain,
% 1.23/1.48 (b(s(s(z)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[281, 5715])).
% 1.23/1.48 tff(5717,plain,
% 1.23/1.48 (~r(z, s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3758, 5714, 688])).
% 1.23/1.48 tff(5718,plain,
% 1.23/1.48 (b(z, s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1088, 5717])).
% 1.23/1.48 tff(5719,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5720,plain,
% 1.23/1.48 (((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5721,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5720])).
% 1.23/1.48 tff(5722,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5721, 5719])).
% 1.23/1.48 tff(5723,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5724,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5723, 5722])).
% 1.23/1.48 tff(5725,plain,
% 1.23/1.48 (~b(s(elem!1), s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5724, 224, 5682, 5718, 5716])).
% 1.23/1.48 tff(5726,plain,
% 1.23/1.48 (((~![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(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(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5727,plain,
% 1.23/1.48 (((~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(elem!1), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5728,plain,
% 1.23/1.48 (((~![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(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(elem!1), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5727])).
% 1.23/1.48 tff(5729,plain,
% 1.23/1.48 (((~![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(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(elem!1), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5728, 5726])).
% 1.23/1.48 tff(5730,plain,
% 1.23/1.48 ((~![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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5731,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5730, 5729])).
% 1.23/1.48 tff(5732,plain,
% 1.23/1.48 (~r(s(elem!1), s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5731, 112, 5667, 5714])).
% 1.23/1.48 tff(5733,plain,
% 1.23/1.48 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[4980, 68, 5732])).
% 1.23/1.48 tff(5734,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5733, 5725, 5511])).
% 1.23/1.48 tff(5735,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5736,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5735, 5492, 5482, 177, 4569, 688, 2])).
% 1.23/1.48 tff(5737,plain,((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5738,plain,
% 1.23/1.48 (~r(z, elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5737, 4569, 177, 2])).
% 1.23/1.48 tff(5739,plain,
% 1.23/1.48 (b(z, elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[289, 5738, 4])).
% 1.23/1.48 tff(5740,plain,
% 1.23/1.48 (~(s(s(s(z))) = elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[347, 5739, 74])).
% 1.23/1.48 tff(5741,plain,
% 1.23/1.48 (~(elem!1 = s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3418, 5740])).
% 1.23/1.48 tff(5742,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5743,plain,
% 1.23/1.48 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5744,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5743])).
% 1.23/1.48 tff(5745,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5744, 5742])).
% 1.23/1.48 tff(5746,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5747,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5746, 5745])).
% 1.23/1.48 tff(5748,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5747, 112, 4569, 363, 993])).
% 1.23/1.48 tff(5749,plain,((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5750,plain,
% 1.23/1.48 (~r(elem!1, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5749, 363, 4569])).
% 1.23/1.48 tff(5751,plain,
% 1.23/1.48 (~r(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5470, 689, 4569])).
% 1.23/1.48 tff(5752,plain,
% 1.23/1.48 (b(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[175, 5751])).
% 1.23/1.48 tff(5753,plain,
% 1.23/1.48 (~r(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[4621, 689, 4569])).
% 1.23/1.48 tff(5754,plain,
% 1.23/1.48 (b(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[925, 5753])).
% 1.23/1.48 tff(5755,plain,
% 1.23/1.48 (~b(elem!1, s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3008, 224, 2896, 1090, 5754])).
% 1.23/1.48 tff(5756,plain,
% 1.23/1.48 (r(elem!1, s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[388, 5755, 680])).
% 1.23/1.48 tff(5757,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5758,plain,
% 1.23/1.48 (((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5759,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5758])).
% 1.23/1.48 tff(5760,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5759, 5757])).
% 1.23/1.48 tff(5761,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5762,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 1.23/1.48 tff(5763,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5762, 112, 4569, 363, 5756, 689])).
% 1.23/1.48 tff(5764,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5765,plain,
% 1.23/1.48 (~b(elem!1, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5764, 363, 689, 5752, 680, 4569])).
% 1.23/1.48 tff(5766,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1277, 5765, 5750, 88])).
% 1.23/1.48 tff(5767,plain,((~r(elem!1, z)) | (elem!1 = s(z)) | (~r(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5768,plain,
% 1.23/1.48 (~r(elem!1, z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5767, 5741, 83, 101, 4569])).
% 1.23/1.48 tff(5769,plain,
% 1.23/1.48 (b(elem!1, z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[403, 5768, 11])).
% 1.23/1.48 tff(5770,plain,
% 1.23/1.48 (~r(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5470, 4569, 101])).
% 1.23/1.48 tff(5771,plain,
% 1.23/1.48 (b(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[175, 5770])).
% 1.23/1.48 tff(5772,plain,
% 1.23/1.48 (~r(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[4608, 4569, 177])).
% 1.23/1.48 tff(5773,plain,
% 1.23/1.48 (b(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[925, 5772])).
% 1.23/1.48 tff(5774,plain,
% 1.23/1.48 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3206, 1241, 5773, 5771])).
% 1.23/1.48 tff(5775,plain,
% 1.23/1.48 (r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[147, 5774, 2])).
% 1.23/1.48 tff(5776,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5777,plain,
% 1.23/1.48 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5778,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5777])).
% 1.23/1.48 tff(5779,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5778, 5776])).
% 1.23/1.48 tff(5780,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5781,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5780, 5779])).
% 1.23/1.48 tff(5782,plain,
% 1.23/1.48 (~r(s(s(elem!1)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5781, 112, 4569, 5775, 101])).
% 1.23/1.48 tff(5783,plain,
% 1.23/1.48 (b(s(s(elem!1)), z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[593, 5782])).
% 1.23/1.48 tff(5784,plain,
% 1.23/1.48 (~r(elem!1, z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5767, 680, 83, 101, 4569])).
% 1.23/1.48 tff(5785,plain,
% 1.23/1.48 (b(elem!1, z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[403, 5784, 11])).
% 1.23/1.48 tff(5786,plain,
% 1.23/1.48 (~r(elem!1, s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3368, 5785, 3, 5775, 5783, 101])).
% 1.23/1.48 tff(5787,plain,
% 1.23/1.48 (b(elem!1, s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[388, 5786, 680])).
% 1.23/1.48 tff(5788,plain,
% 1.23/1.48 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5789,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5788])).
% 1.23/1.48 tff(5790,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5789, 3003])).
% 1.23/1.48 tff(5791,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5792,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 1.23/1.48 tff(5793,plain,
% 1.23/1.48 (~b(elem!1, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5792, 224, 5787, 5771, 5773])).
% 1.23/1.48 tff(5794,plain,
% 1.23/1.48 (r(elem!1, s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1277, 5793, 83])).
% 1.23/1.48 tff(5795,plain,
% 1.23/1.48 (~r(z, elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5490, 5794, 4569])).
% 1.23/1.48 tff(5796,plain,
% 1.23/1.48 (b(z, elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[289, 5795, 4])).
% 1.23/1.48 tff(5797,plain,
% 1.23/1.48 (~b(s(s(elem!1)), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3407, 5796, 5783, 5785])).
% 1.23/1.48 tff(5798,plain,
% 1.23/1.48 (r(s(s(elem!1)), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[360, 5797, 353])).
% 1.23/1.48 tff(5799,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(5800,plain,
% 1.23/1.48 (~(s(s(s(z))) = elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[347, 74, 344])).
% 1.23/1.48 tff(5801,plain,
% 1.23/1.48 (r(s(s(s(z))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[374, 5800, 5799])).
% 1.23/1.48 tff(5802,plain,
% 1.23/1.48 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[3387, 112, 1181, 5801])).
% 1.23/1.48 tff(5803,plain,
% 1.23/1.48 (~r(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[4621, 101, 4569])).
% 1.23/1.48 tff(5804,plain,
% 1.23/1.48 (b(s(s(s(z))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[925, 5803])).
% 1.23/1.48 tff(5805,plain,
% 1.23/1.48 (~r(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5470, 101, 4569])).
% 1.23/1.48 tff(5806,plain,
% 1.23/1.48 (b(s(z), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[175, 5805])).
% 1.23/1.48 tff(5807,plain,
% 1.23/1.48 (((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5808,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5807])).
% 1.23/1.49 tff(5809,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5808, 3199])).
% 1.23/1.49 tff(5810,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5811,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 1.23/1.49 tff(5812,plain,
% 1.23/1.49 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5811, 224, 1241, 5806, 5804])).
% 1.23/1.49 tff(5813,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[147, 5812, 5802, 2])).
% 1.23/1.49 tff(5814,plain,(b(z, s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(z))), elem!1) | (~r(z, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(5815,plain,
% 1.23/1.49 (b(s(s(s(z))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5814, 5798, 74, 2, 4569, 1241, 5796])).
% 1.23/1.49 tff(5816,plain,
% 1.23/1.49 (~b(s(z), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2941, 5815, 5787, 5771])).
% 1.23/1.49 tff(5817,plain,
% 1.23/1.49 (r(s(z), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[454, 5816, 91])).
% 1.23/1.49 tff(5818,plain,
% 1.23/1.49 (~r(z, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[3074, 5775, 101])).
% 1.23/1.49 tff(5819,plain,
% 1.23/1.49 (b(z, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[752, 5818])).
% 1.23/1.49 tff(5820,plain,
% 1.23/1.49 (~r(s(z), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1195, 112, 5798, 5817])).
% 1.23/1.49 tff(5821,plain,
% 1.23/1.49 (b(s(z), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[653, 5820])).
% 1.23/1.49 tff(5822,plain,
% 1.23/1.49 (~b(s(z), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[4051, 5821, 5819, 5783])).
% 1.23/1.49 tff(5823,plain,
% 1.23/1.49 (r(s(z), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[194, 5822])).
% 1.23/1.49 tff(5824,plain,
% 1.23/1.49 (~r(s(s(z)), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[3472, 5823, 5773, 5771, 101])).
% 1.23/1.49 tff(5825,plain,
% 1.23/1.49 (b(s(s(z)), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[281, 5824])).
% 1.23/1.49 tff(5826,plain,
% 1.23/1.49 (~b(s(s(z)), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1126, 5825, 5785, 5796])).
% 1.23/1.49 tff(5827,plain,
% 1.23/1.49 (~b(elem!1, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[613, 5785, 5819, 5783])).
% 1.23/1.49 tff(5828,plain,
% 1.23/1.49 (r(elem!1, s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[558, 5827, 3])).
% 1.23/1.49 tff(5829,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.23/1.49 tff(5830,plain,
% 1.23/1.49 (r(s(s(z)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1169])).
% 1.23/1.49 tff(5831,plain,
% 1.23/1.49 (r(elem!1, s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.23/1.49 inference(symmetry,[status(thm)],[5830])).
% 1.23/1.49 tff(5832,plain,
% 1.23/1.49 (r(s(s(z)), s(s(elem!1)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[545, 5831])).
% 1.23/1.49 tff(5833,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[260, 5832])).
% 1.23/1.49 tff(5834,plain,((~(s(s(z)) = elem!1)) | r(s(s(z)), s(s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(5835,plain,
% 1.23/1.49 (~(s(s(z)) = elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5834, 260, 545])).
% 1.23/1.49 tff(5836,plain,
% 1.23/1.49 (r(s(s(z)), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1135, 5835, 5829])).
% 1.23/1.49 tff(5837,plain,
% 1.23/1.49 (((~![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), z)) | (~r(s(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), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5838,plain,
% 1.23/1.49 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5839,plain,
% 1.23/1.49 (((~![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), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5838])).
% 1.23/1.49 tff(5840,plain,
% 1.23/1.49 (((~![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), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5839, 5837])).
% 1.23/1.49 tff(5841,plain,
% 1.23/1.49 ((~![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), z)) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5842,plain,
% 1.23/1.49 ((~![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), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5841, 5840])).
% 1.23/1.49 tff(5843,plain,
% 1.23/1.49 (~r(s(s(z)), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5842, 112, 179, 416, 5836])).
% 1.23/1.49 tff(5844,plain,
% 1.23/1.49 (b(s(s(z)), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2726, 5843])).
% 1.23/1.49 tff(5845,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5846,plain,
% 1.23/1.49 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5847,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5846])).
% 1.23/1.49 tff(5848,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5847, 5845])).
% 1.23/1.49 tff(5849,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5850,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5849, 5848])).
% 1.23/1.49 tff(5851,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 1241, 5844, 3219])).
% 1.23/1.49 tff(5852,plain,(r(s(s(z)), s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | b(s(s(z)), elem!1) | (~r(elem!1, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(5853,plain,
% 1.23/1.49 (r(s(s(z)), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5852, 5821, 1241, 5823, 5817, 5826, 5828, 169])).
% 1.23/1.49 tff(5854,plain,
% 1.23/1.49 (~r(s(s(z)), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2388, 112, 5828, 5853])).
% 1.23/1.49 tff(5855,plain,
% 1.23/1.49 (s(s(z)) = elem!1),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1135, 5854, 5826])).
% 1.23/1.49 tff(5856,plain,
% 1.23/1.49 (b(z, s(s(z))) <=> b(z, elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5855])).
% 1.23/1.49 tff(5857,plain,
% 1.23/1.49 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.23/1.49 inference(symmetry,[status(thm)],[5856])).
% 1.23/1.49 tff(5858,plain,
% 1.23/1.49 (b(z, s(s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5796, 5857])).
% 1.23/1.49 tff(5859,plain,
% 1.23/1.49 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5855])).
% 1.23/1.49 tff(5860,plain,
% 1.23/1.49 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 1.23/1.49 inference(symmetry,[status(thm)],[5859])).
% 1.23/1.49 tff(5861,plain,
% 1.23/1.49 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5815, 5860])).
% 1.23/1.49 tff(5862,plain,
% 1.23/1.49 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5863,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5862])).
% 1.23/1.49 tff(5864,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5863, 2153])).
% 1.23/1.49 tff(5865,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5866,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 1.23/1.49 tff(5867,plain,
% 1.23/1.49 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5866, 224, 5821, 1241, 5773])).
% 1.23/1.49 tff(5868,plain,
% 1.23/1.49 (r(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[135, 68, 132, 5867])).
% 1.23/1.49 tff(5869,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), 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(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5870,plain,
% 1.23/1.49 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5871,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5870])).
% 1.23/1.49 tff(5872,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5871, 5869])).
% 1.23/1.49 tff(5873,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5874,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 1.23/1.49 tff(5875,plain,
% 1.23/1.49 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5874, 112, 177, 5853, 5868])).
% 1.23/1.49 tff(5876,plain,
% 1.23/1.49 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[249, 5875])).
% 1.23/1.49 tff(5877,plain,
% 1.23/1.49 (s(s(s(z))) = s(elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5855])).
% 1.23/1.49 tff(5878,plain,
% 1.23/1.49 (s(elem!1) = s(s(s(z)))),
% 1.23/1.49 inference(symmetry,[status(thm)],[5877])).
% 1.23/1.49 tff(5879,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[2240, 5878, 5825, 5876, 5861, 5858, 177])).
% 1.23/1.49 tff(5880,plain,
% 1.23/1.49 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1216])).
% 1.23/1.49 tff(5881,plain,
% 1.23/1.49 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5880])).
% 1.23/1.49 tff(5882,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5881, 1169])).
% 1.23/1.49 tff(5883,plain,
% 1.23/1.49 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5882])).
% 1.23/1.49 tff(5884,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.23/1.49 tff(5885,plain,
% 1.23/1.49 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 1.23/1.49 tff(5886,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[3919, 5885])).
% 1.23/1.49 tff(5887,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(s(s(z)))))), s(s(z))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(5888,plain,
% 1.23/1.49 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5887, 5879, 5855])).
% 1.23/1.49 tff(5889,plain,
% 1.23/1.49 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1294, 1290, 1288])).
% 1.23/1.49 tff(5890,plain,
% 1.23/1.49 (((~![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(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5891,plain,
% 1.23/1.49 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5892,plain,
% 1.23/1.49 (((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5891])).
% 1.23/1.49 tff(5893,plain,
% 1.23/1.49 (((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5892, 5890])).
% 1.23/1.49 tff(5894,plain,
% 1.23/1.49 ((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(5895,plain,
% 1.23/1.49 ((~![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(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5894, 5893])).
% 1.23/1.49 tff(5896,plain,
% 1.23/1.49 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5895, 112, 5889, 416])).
% 1.23/1.49 tff(5897,plain,
% 1.23/1.49 (b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[4896, 68, 1364, 5896])).
% 1.23/1.49 tff(5898,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5899,plain,
% 1.23/1.49 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(5900,plain,
% 1.23/1.50 (((~![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(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[5899])).
% 1.23/1.50 tff(5901,plain,
% 1.23/1.50 (((~![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(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.23/1.50 inference(transitivity,[status(thm)],[5900, 5898])).
% 1.23/1.50 tff(5902,plain,
% 1.23/1.50 ((~![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(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.23/1.50 inference(quant_inst,[status(thm)],[])).
% 1.23/1.50 tff(5903,plain,
% 1.23/1.50 ((~![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)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[5902, 5901])).
% 1.23/1.50 tff(5904,plain,
% 1.23/1.50 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[5903, 112, 5889, 1181])).
% 1.23/1.50 tff(5905,plain,
% 1.23/1.50 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[1422, 68, 5904, 1381])).
% 1.23/1.50 tff(5906,plain,
% 1.23/1.50 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[4920, 1290, 1181, 1288])).
% 1.23/1.50 tff(5907,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(5908,plain,
% 1.23/1.50 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(5909,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[5908])).
% 1.23/1.50 tff(5910,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[5909, 5907])).
% 1.33/1.50 tff(5911,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(5912,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.33/1.50 tff(5913,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5912, 224, 1197, 5906, 5905, 5897])).
% 1.33/1.50 tff(5914,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(5915,plain,
% 1.33/1.50 (s(s(s(s(elem!1)))) = elem!1),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5914, 5888, 5798, 5817])).
% 1.33/1.50 tff(5916,plain,
% 1.33/1.50 (elem!1 = s(s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[5915])).
% 1.33/1.50 tff(5917,plain,
% 1.33/1.50 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[5855, 5916])).
% 1.33/1.50 tff(5918,plain,
% 1.33/1.50 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5917])).
% 1.33/1.50 tff(5919,plain,
% 1.33/1.50 (s(z) = s(s(s(elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[50, 5918, 989])).
% 1.33/1.50 tff(5920,plain,
% 1.33/1.50 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5919])).
% 1.33/1.50 tff(5921,plain,
% 1.33/1.50 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.33/1.50 inference(symmetry,[status(thm)],[5920])).
% 1.33/1.50 tff(5922,plain,
% 1.33/1.50 (s(s(elem!1)) = z),
% 1.33/1.50 inference(transitivity,[status(thm)],[1376, 5921, 27])).
% 1.33/1.50 tff(5923,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[566, 5922])).
% 1.33/1.50 tff(5924,plain,((elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(z))) | (z = elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(5925,plain,
% 1.33/1.50 (~b(s(s(elem!1)), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5924, 3, 177, 74, 2, 4569, 4, 5741])).
% 1.33/1.50 tff(5926,plain,
% 1.33/1.50 (r(s(s(elem!1)), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[901, 5925])).
% 1.33/1.50 tff(5927,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5688, 112, 4569, 102, 887])).
% 1.33/1.50 tff(5928,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(5929,plain,
% 1.33/1.50 (~r(s(s(elem!1)), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5928, 5926, 4569])).
% 1.33/1.50 tff(5930,plain,
% 1.33/1.50 (b(s(s(elem!1)), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[593, 5929])).
% 1.33/1.50 tff(5931,plain,
% 1.33/1.50 (~b(s(z), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[461, 224, 5769, 684, 5739])).
% 1.33/1.50 tff(5932,plain,
% 1.33/1.50 (r(s(z), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[194, 5931])).
% 1.33/1.50 tff(5933,plain,
% 1.33/1.50 (~r(s(s(z)), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3472, 5932, 5773, 5771, 101])).
% 1.33/1.50 tff(5934,plain,
% 1.33/1.50 (b(s(s(z)), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[281, 5933])).
% 1.33/1.50 tff(5935,plain,
% 1.33/1.50 (~b(s(s(z)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1126, 5934, 5769, 5739])).
% 1.33/1.50 tff(5936,plain,
% 1.33/1.50 (~r(z, s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 5926])).
% 1.33/1.50 tff(5937,plain,
% 1.33/1.50 (b(z, s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[752, 5936])).
% 1.33/1.50 tff(5938,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[4077, 224, 1240, 1180, 1118, 2596])).
% 1.33/1.50 tff(5939,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(5940,plain,
% 1.33/1.50 (~b(s(s(z)), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5939, 5930, 5937, 5934])).
% 1.33/1.50 tff(5941,plain,
% 1.33/1.50 (r(s(s(z)), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[265, 5940, 169])).
% 1.33/1.50 tff(5942,plain,
% 1.33/1.50 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[613, 5937, 5769, 5930])).
% 1.33/1.50 tff(5943,plain,
% 1.33/1.50 (r(elem!1, s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[558, 5942, 3])).
% 1.33/1.50 tff(5944,plain,
% 1.33/1.50 (~r(s(s(z)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2388, 112, 5943, 5941])).
% 1.33/1.50 tff(5945,plain,
% 1.33/1.50 (s(s(z)) = elem!1),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1135, 5944, 5935])).
% 1.33/1.50 tff(5946,plain,
% 1.33/1.50 (s(s(s(z))) = s(elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5945])).
% 1.33/1.50 tff(5947,plain,
% 1.33/1.50 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5946])).
% 1.33/1.50 tff(5948,plain,
% 1.33/1.50 (r(z, s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[101, 5947])).
% 1.33/1.50 tff(5949,plain,
% 1.33/1.50 (~r(s(elem!1), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5576, 5926, 4569, 319])).
% 1.33/1.50 tff(5950,plain,
% 1.33/1.50 (b(s(elem!1), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1476, 5949, 160])).
% 1.33/1.50 tff(5951,plain,
% 1.33/1.50 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3407, 5930, 5739, 5769])).
% 1.33/1.50 tff(5952,plain,
% 1.33/1.50 (r(s(s(elem!1)), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[360, 5951, 353])).
% 1.33/1.50 tff(5953,plain,
% 1.33/1.50 (~r(elem!1, s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3588, 5952, 5926])).
% 1.33/1.50 tff(5954,plain,
% 1.33/1.50 (b(elem!1, s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1277, 5953, 83])).
% 1.33/1.50 tff(5955,plain,
% 1.33/1.50 (~b(s(elem!1), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5665, 224, 684, 5954, 5950])).
% 1.33/1.50 tff(5956,plain,
% 1.33/1.50 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5946])).
% 1.33/1.50 tff(5957,plain,
% 1.33/1.50 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.33/1.50 inference(transitivity,[status(thm)],[5956, 1143])).
% 1.33/1.50 tff(5958,plain,
% 1.33/1.50 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5957])).
% 1.33/1.50 tff(5959,plain,
% 1.33/1.50 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1165, 5958])).
% 1.33/1.50 tff(5960,plain,
% 1.33/1.50 (r(s(elem!1), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[939, 5955, 303])).
% 1.33/1.50 tff(5961,plain,
% 1.33/1.50 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[4010, 5960, 5943])).
% 1.33/1.50 tff(5962,plain,
% 1.33/1.50 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1521, 5961, 319])).
% 1.33/1.50 tff(5963,plain,
% 1.33/1.50 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5946])).
% 1.33/1.50 tff(5964,plain,
% 1.33/1.50 (b(s(z), s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5771, 5963])).
% 1.33/1.50 tff(5965,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(5966,plain,
% 1.33/1.50 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(5967,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5966])).
% 1.33/1.50 tff(5968,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[5967, 5965])).
% 1.33/1.50 tff(5969,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(5970,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 1.33/1.50 tff(5971,plain,
% 1.33/1.50 (~b(elem!1, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5970, 224, 5954, 5950, 5964])).
% 1.33/1.50 tff(5972,plain,
% 1.33/1.50 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[541, 5971, 3, 5951])).
% 1.33/1.50 tff(5973,plain,
% 1.33/1.50 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1170])).
% 1.33/1.50 tff(5974,plain,
% 1.33/1.50 (b(s(z), s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1090, 5973])).
% 1.33/1.50 tff(5975,plain,
% 1.33/1.50 (((~![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)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(5976,plain,
% 1.33/1.50 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(5977,plain,
% 1.33/1.50 (((~![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)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5976])).
% 1.33/1.50 tff(5978,plain,
% 1.33/1.50 (((~![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)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[5977, 5975])).
% 1.33/1.50 tff(5979,plain,
% 1.33/1.50 ((~![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)), 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)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(5980,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5979, 5978])).
% 1.33/1.50 tff(5981,plain,
% 1.33/1.50 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5980, 112, 1181, 690])).
% 1.33/1.50 tff(5982,plain,
% 1.33/1.50 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[305])).
% 1.33/1.50 tff(5983,plain,
% 1.33/1.50 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2, 5982])).
% 1.33/1.50 tff(5984,plain,
% 1.33/1.50 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[135, 68, 5983, 5981])).
% 1.33/1.50 tff(5985,plain,
% 1.33/1.50 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3387, 112, 1181, 690])).
% 1.33/1.50 tff(5986,plain,
% 1.33/1.50 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[147, 5985, 2])).
% 1.33/1.50 tff(5987,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2089, 224, 2252, 1090, 5986, 5984])).
% 1.33/1.50 tff(5988,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(5989,plain,
% 1.33/1.50 (~r(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5988, 2252, 1181, 2, 1090])).
% 1.33/1.50 tff(5990,plain,
% 1.33/1.50 (r(elem!1, s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[4200, 5989, 362, 684, 1090])).
% 1.33/1.50 tff(5991,plain,
% 1.33/1.50 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3368, 5990, 405, 3, 1240, 689])).
% 1.33/1.50 tff(5992,plain,
% 1.33/1.50 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[147, 5991, 2])).
% 1.33/1.50 tff(5993,plain,
% 1.33/1.50 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5992, 3558])).
% 1.33/1.50 tff(5994,plain,
% 1.33/1.50 (s(elem!1) = s(s(s(z)))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1170])).
% 1.33/1.50 tff(5995,plain,
% 1.33/1.50 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5994])).
% 1.33/1.50 tff(5996,plain,
% 1.33/1.50 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.33/1.50 inference(symmetry,[status(thm)],[5995])).
% 1.33/1.50 tff(5997,plain,
% 1.33/1.50 (b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[374, 5989, 362])).
% 1.33/1.50 tff(5998,plain,
% 1.33/1.50 (b(s(elem!1), elem!1)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[5997, 5996])).
% 1.33/1.50 tff(5999,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6000,plain,
% 1.33/1.50 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6001,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6000])).
% 1.33/1.50 tff(6002,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6001, 5999])).
% 1.33/1.50 tff(6003,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6004,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6003, 6002])).
% 1.33/1.50 tff(6005,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6004, 224, 5998, 5993, 2252, 684, 5974])).
% 1.33/1.50 tff(6006,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~(s(s(z)) = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6007,plain,
% 1.33/1.50 (~b(s(z), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6006, 5945, 684, 2, 5769, 3, 5930, 101, 5740, 5771, 5952])).
% 1.33/1.50 tff(6008,plain,
% 1.33/1.50 (r(s(z), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[653, 6007])).
% 1.33/1.50 tff(6009,plain,
% 1.33/1.50 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1340, 1288, 405, 344, 1287, 568])).
% 1.33/1.50 tff(6010,plain,
% 1.33/1.50 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1345, 6009, 1286])).
% 1.33/1.50 tff(6011,plain,
% 1.33/1.50 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1353, 224, 1347, 683, 6010])).
% 1.33/1.50 tff(6012,plain,
% 1.33/1.50 (r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 6011])).
% 1.33/1.50 tff(6013,plain,
% 1.33/1.50 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 1390, 6010])).
% 1.33/1.50 tff(6014,plain,
% 1.33/1.50 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1401, 68, 6013, 1389])).
% 1.33/1.50 tff(6015,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6016,plain,
% 1.33/1.50 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6017,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6016])).
% 1.33/1.50 tff(6018,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6017, 6015])).
% 1.33/1.50 tff(6019,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6020,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6019, 6018])).
% 1.33/1.51 tff(6021,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6020, 112, 179, 656, 6014, 6012])).
% 1.33/1.51 tff(6022,plain,((s(s(s(s(elem!1)))) = elem!1) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | b(s(elem!1), elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6023,plain,
% 1.33/1.51 (s(s(s(s(elem!1)))) = elem!1),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6022, 6008, 5932, 5950, 5964, 5972, 5962, 5959, 5769, 5739, 5955, 5948])).
% 1.33/1.51 tff(6024,plain,
% 1.33/1.51 (elem!1 = s(s(s(s(elem!1))))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6023])).
% 1.33/1.51 tff(6025,plain,
% 1.33/1.51 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[5945, 6024])).
% 1.33/1.51 tff(6026,plain,
% 1.33/1.51 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6025])).
% 1.33/1.51 tff(6027,plain,
% 1.33/1.51 (s(z) = s(s(s(elem!1)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[50, 6026, 989])).
% 1.33/1.51 tff(6028,plain,
% 1.33/1.51 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6027])).
% 1.33/1.51 tff(6029,plain,
% 1.33/1.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6028])).
% 1.33/1.51 tff(6030,plain,
% 1.33/1.51 (s(s(elem!1)) = z),
% 1.33/1.51 inference(transitivity,[status(thm)],[1376, 6029, 27])).
% 1.33/1.51 tff(6031,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[566, 6030])).
% 1.33/1.51 tff(6032,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6033,plain,
% 1.33/1.51 (elem!1 = s(s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6032, 684, 2, 4569, 177, 74, 4])).
% 1.33/1.51 tff(6034,plain,
% 1.33/1.51 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6033])).
% 1.33/1.51 tff(6035,plain,
% 1.33/1.51 (s(s(s(s(elem!1)))) = elem!1),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1306, 6033])).
% 1.33/1.51 tff(6036,plain,
% 1.33/1.51 (~(elem!1 = s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2783, 6035, 6033])).
% 1.33/1.51 tff(6037,plain,
% 1.33/1.51 (~(s(s(z)) = elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2788, 6036])).
% 1.33/1.51 tff(6038,plain,
% 1.33/1.51 (r(s(s(z)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1135, 6037, 5935])).
% 1.33/1.51 tff(6039,plain,
% 1.33/1.51 (r(s(s(z)), s(s(elem!1)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6038, 6034])).
% 1.33/1.51 tff(6040,plain,
% 1.33/1.51 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5403, 6038, 6035])).
% 1.33/1.51 tff(6041,plain,
% 1.33/1.51 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6033])).
% 1.33/1.51 tff(6042,plain,
% 1.33/1.51 (b(s(z), s(s(elem!1)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[684, 6041])).
% 1.33/1.51 tff(6043,plain,
% 1.33/1.51 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[3101])).
% 1.33/1.51 tff(6044,plain,
% 1.33/1.51 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5866, 224, 2252, 1241, 560])).
% 1.33/1.51 tff(6045,plain,
% 1.33/1.51 (r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[135, 68, 132, 6044])).
% 1.33/1.51 tff(6046,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(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(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6047,plain,
% 1.33/1.51 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(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(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6048,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(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(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6047])).
% 1.33/1.51 tff(6049,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(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(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6048, 6046])).
% 1.33/1.51 tff(6050,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6051,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6050, 6049])).
% 1.33/1.51 tff(6052,plain,
% 1.33/1.51 (~r(s(s(s(z))), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6051, 112, 267, 6045])).
% 1.33/1.51 tff(6053,plain,
% 1.33/1.51 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3535, 68, 6052])).
% 1.33/1.51 tff(6054,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6053, 56])).
% 1.33/1.51 tff(6055,plain,
% 1.33/1.51 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2831, 1296])).
% 1.33/1.51 tff(6056,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6055])).
% 1.33/1.51 tff(6057,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6056])).
% 1.33/1.51 tff(6058,plain,
% 1.33/1.51 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6057])).
% 1.33/1.51 tff(6059,plain,
% 1.33/1.51 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6044, 6058])).
% 1.33/1.51 tff(6060,plain,
% 1.33/1.51 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5426, 6059])).
% 1.33/1.51 tff(6061,plain,
% 1.33/1.51 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5413, 6060, 5405])).
% 1.33/1.51 tff(6062,plain,
% 1.33/1.51 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[249, 6061])).
% 1.33/1.51 tff(6063,plain,
% 1.33/1.51 (~b(s(z), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5329, 224, 6062, 1090, 6054])).
% 1.33/1.51 tff(6064,plain,
% 1.33/1.51 (r(s(z), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1071, 6063])).
% 1.33/1.51 tff(6065,plain,
% 1.33/1.51 (~b(s(s(z)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3462, 224, 6062, 1090, 560])).
% 1.33/1.51 tff(6066,plain,
% 1.33/1.51 (r(s(s(z)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2726, 6065])).
% 1.33/1.51 tff(6067,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6068,plain,
% 1.33/1.51 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6069,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6068])).
% 1.33/1.51 tff(6070,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6069, 6067])).
% 1.33/1.51 tff(6071,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6072,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6071, 6070])).
% 1.33/1.51 tff(6073,plain,
% 1.33/1.51 (~r(z, s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6072, 112, 4569, 6066])).
% 1.33/1.51 tff(6074,plain,
% 1.33/1.51 (b(z, s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1088, 6073])).
% 1.33/1.51 tff(6075,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.33/1.51 tff(6076,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(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(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6077,plain,
% 1.33/1.51 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6078,plain,
% 1.33/1.51 (((~![X0: $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), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6077])).
% 1.33/1.51 tff(6079,plain,
% 1.33/1.51 (((~![X0: $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), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6078, 6076])).
% 1.33/1.51 tff(6080,plain,
% 1.33/1.51 ((~![X0: $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), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6081,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6080, 6079])).
% 1.33/1.51 tff(6082,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6081, 112, 179, 2303, 3317, 6075])).
% 1.33/1.51 tff(6083,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6084,plain,
% 1.33/1.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6083, 3317, 2303, 179])).
% 1.33/1.51 tff(6085,plain,
% 1.33/1.51 (b(s(s(s(s(z)))), s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 6084])).
% 1.33/1.51 tff(6086,plain,
% 1.33/1.51 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6087,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6086])).
% 1.33/1.51 tff(6088,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6087, 3293])).
% 1.33/1.51 tff(6089,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6090,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6089, 6088])).
% 1.33/1.51 tff(6091,plain,
% 1.33/1.51 (~b(s(s(s(s(z)))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6090, 224, 2191, 1118, 6085])).
% 1.33/1.51 tff(6092,plain,
% 1.33/1.51 (~r(s(s(s(s(z)))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4589, 112, 4569, 3317])).
% 1.33/1.51 tff(6093,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 6092, 6091])).
% 1.33/1.51 tff(6094,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6095,plain,
% 1.33/1.51 (~r(s(s(s(s(z)))), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6094, 6074, 1118, 4569, 6064, 179])).
% 1.33/1.51 tff(6096,plain,
% 1.33/1.51 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3168, 6095])).
% 1.33/1.51 tff(6097,plain,
% 1.33/1.51 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6098,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6097])).
% 1.33/1.51 tff(6099,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6098, 3305])).
% 1.33/1.51 tff(6100,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6101,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6100, 6099])).
% 1.33/1.51 tff(6102,plain,
% 1.33/1.51 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6101, 224, 2252, 1241, 6096])).
% 1.33/1.51 tff(6103,plain,
% 1.33/1.51 (~b(s(s(s(s(z)))), elem!1)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6102, 6043])).
% 1.33/1.51 tff(6104,plain,
% 1.33/1.51 (r(s(s(s(s(z)))), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3183, 6103, 3121])).
% 1.33/1.51 tff(6105,plain,
% 1.33/1.51 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6104, 5168])).
% 1.33/1.51 tff(6106,plain,
% 1.33/1.51 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1579, 6096, 1090, 560])).
% 1.33/1.51 tff(6107,plain,
% 1.33/1.51 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3252, 6106])).
% 1.33/1.51 tff(6108,plain,
% 1.33/1.51 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3206, 1241, 560, 1090])).
% 1.33/1.51 tff(6109,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[147, 6108, 2])).
% 1.33/1.51 tff(6110,plain,
% 1.33/1.51 (((~![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(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6111,plain,
% 1.33/1.51 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6112,plain,
% 1.33/1.51 (((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6111])).
% 1.33/1.51 tff(6113,plain,
% 1.33/1.51 (((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6112, 6110])).
% 1.33/1.51 tff(6114,plain,
% 1.33/1.51 ((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6115,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 1.33/1.51 tff(6116,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6115, 112, 6109, 6107, 6105])).
% 1.33/1.51 tff(6117,plain,((~b(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6118,plain,
% 1.33/1.51 (~b(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6117, 6033, 6042, 5771, 5773, 5934, 4569, 5932, 6039, 6040, 2])).
% 1.33/1.51 tff(6119,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[901, 6118])).
% 1.33/1.51 tff(6120,plain,
% 1.33/1.51 (~r(s(s(z)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2993, 6119, 6039])).
% 1.33/1.51 tff(6121,plain,
% 1.33/1.51 (b(s(s(z)), s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2726, 6120])).
% 1.33/1.51 tff(6122,plain,
% 1.33/1.51 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6033])).
% 1.33/1.51 tff(6123,plain,
% 1.33/1.51 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6033])).
% 1.33/1.51 tff(6124,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.51 inference(symmetry,[status(thm)],[6123])).
% 1.33/1.51 tff(6125,plain,
% 1.33/1.51 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6035, 6033])).
% 1.33/1.51 tff(6126,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6125])).
% 1.33/1.51 tff(6127,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.51 inference(transitivity,[status(thm)],[6126, 6124])).
% 1.33/1.51 tff(6128,plain,
% 1.33/1.51 (s(s(elem!1)) = elem!1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6033, 76])).
% 1.33/1.51 tff(6129,plain,
% 1.33/1.51 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5420, 6119, 6128, 5773, 5771, 6035, 6038])).
% 1.33/1.51 tff(6130,plain,
% 1.33/1.51 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5426, 6129])).
% 1.33/1.51 tff(6131,plain,
% 1.33/1.51 (b(s(s(s(z))), elem!1)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6130, 6127])).
% 1.33/1.51 tff(6132,plain,
% 1.33/1.51 (~b(elem!1, s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2941, 6131, 684, 5771])).
% 1.33/1.51 tff(6133,plain,
% 1.33/1.51 (r(elem!1, s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[388, 6132, 5741])).
% 1.33/1.51 tff(6134,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6133, 6122])).
% 1.33/1.51 tff(6135,plain,
% 1.33/1.51 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[5439, 6134, 6119, 6039])).
% 1.33/1.51 tff(6136,plain,
% 1.33/1.51 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[249, 6135])).
% 1.33/1.51 tff(6137,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3462, 224, 6136, 5771, 5773, 6121])).
% 1.33/1.51 tff(6138,plain,((~b(s(z), elem!1)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6139,plain,
% 1.33/1.51 (~b(s(z), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6138, 4569, 2, 177, 74, 4])).
% 1.33/1.51 tff(6140,plain,
% 1.33/1.51 (r(s(z), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[454, 6139, 91])).
% 1.33/1.51 tff(6141,plain,
% 1.33/1.51 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4065, 5926, 6140])).
% 1.33/1.51 tff(6142,plain,
% 1.33/1.51 (b(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[360, 6141, 353])).
% 1.33/1.51 tff(6143,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3407, 6142, 5930, 5739, 5769])).
% 1.33/1.51 tff(6144,plain,((elem!1 = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | b(z, s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6145,plain,
% 1.33/1.51 (elem!1 = s(s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6144, 5460, 73, 74, 2, 4])).
% 1.33/1.52 tff(6146,plain,
% 1.33/1.52 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6145])).
% 1.33/1.52 tff(6147,plain,
% 1.33/1.52 (~b(s(z), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6138, 5460, 2, 73, 74, 4])).
% 1.33/1.52 tff(6148,plain,
% 1.33/1.52 (r(s(z), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[454, 6147, 91])).
% 1.33/1.52 tff(6149,plain,
% 1.33/1.52 (r(s(z), s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6148, 6146])).
% 1.33/1.52 tff(6150,plain,
% 1.33/1.52 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6145])).
% 1.33/1.52 tff(6151,plain,
% 1.33/1.52 (~r(z, elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[5737, 5460, 73, 2])).
% 1.33/1.52 tff(6152,plain,
% 1.33/1.52 (b(z, elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[289, 6151, 4])).
% 1.33/1.52 tff(6153,plain,
% 1.33/1.52 (~(s(s(s(z))) = elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[347, 6152, 74])).
% 1.33/1.52 tff(6154,plain,
% 1.33/1.52 (~(elem!1 = s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3418, 6153])).
% 1.33/1.52 tff(6155,plain,
% 1.33/1.52 (~r(elem!1, z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[5767, 6154, 83, 101, 5460])).
% 1.33/1.52 tff(6156,plain,
% 1.33/1.52 (b(elem!1, z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[403, 6155, 11])).
% 1.33/1.52 tff(6157,plain,
% 1.33/1.52 (b(s(s(elem!1)), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6156, 6150])).
% 1.33/1.52 tff(6158,plain,
% 1.33/1.52 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6145])).
% 1.33/1.52 tff(6159,plain,
% 1.33/1.52 (b(z, s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6152, 6158])).
% 1.33/1.52 tff(6160,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6161,plain,
% 1.33/1.52 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6162,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6161])).
% 1.33/1.52 tff(6163,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6162, 6160])).
% 1.33/1.52 tff(6164,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6165,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6164, 6163])).
% 1.33/1.52 tff(6166,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6165, 112, 4569, 268, 2851])).
% 1.33/1.52 tff(6167,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6168,plain,
% 1.33/1.52 (~r(s(s(z)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6167, 268, 4569])).
% 1.33/1.52 tff(6169,plain,
% 1.33/1.52 (b(s(s(z)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2726, 6168])).
% 1.33/1.52 tff(6170,plain,
% 1.33/1.52 (~r(s(z), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[5470, 4569, 689])).
% 1.33/1.52 tff(6171,plain,
% 1.33/1.52 (b(s(z), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[175, 6170])).
% 1.33/1.52 tff(6172,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3462, 224, 3457, 6171, 560, 6169])).
% 1.33/1.52 tff(6173,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6174,plain,
% 1.33/1.52 (~r(s(s(z)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6173, 5462, 5460, 101])).
% 1.33/1.52 tff(6175,plain,
% 1.33/1.52 (b(s(s(z)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[281, 6174])).
% 1.33/1.52 tff(6176,plain,
% 1.33/1.52 (~b(s(s(z)), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[5939, 6175, 6159, 6157])).
% 1.33/1.52 tff(6177,plain,
% 1.33/1.52 (r(s(s(z)), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[265, 6176, 169])).
% 1.33/1.52 tff(6178,plain,
% 1.33/1.52 (~r(s(s(z)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2853, 6177, 6149])).
% 1.33/1.52 tff(6179,plain,
% 1.33/1.52 (b(s(s(z)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2726, 6178])).
% 1.33/1.52 tff(6180,plain,
% 1.33/1.52 (~r(s(z), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[5333, 6177, 6149])).
% 1.33/1.52 tff(6181,plain,
% 1.33/1.52 (b(s(z), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1071, 6180])).
% 1.33/1.52 tff(6182,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.33/1.52 tff(6183,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.33/1.52 tff(6184,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 6183, 6182])).
% 1.33/1.52 tff(6185,plain,(r(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6186,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6185, 5197])).
% 1.33/1.52 tff(6187,plain,
% 1.33/1.52 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6188,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6187])).
% 1.33/1.52 tff(6189,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6188, 4984])).
% 1.33/1.52 tff(6190,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6191,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 1.33/1.52 tff(6192,plain,
% 1.33/1.52 (~b(s(s(s(z))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6191, 224, 5187, 560, 2844])).
% 1.33/1.52 tff(6193,plain,
% 1.33/1.52 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3535, 68, 6192])).
% 1.33/1.52 tff(6194,plain,
% 1.33/1.52 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6193, 56])).
% 1.33/1.52 tff(6195,plain,
% 1.33/1.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1579, 1570, 1090, 560])).
% 1.33/1.52 tff(6196,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3252, 6195])).
% 1.33/1.52 tff(6197,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6198,plain,
% 1.33/1.52 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6199,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6198])).
% 1.33/1.52 tff(6200,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6199, 6197])).
% 1.33/1.52 tff(6201,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6202,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 1.33/1.52 tff(6203,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6202, 112, 177, 6196, 6194, 6186])).
% 1.33/1.52 tff(6204,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6205,plain,
% 1.33/1.52 (~b(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6204, 6181, 73, 6179, 5472, 5462])).
% 1.33/1.52 tff(6206,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3168, 6205])).
% 1.33/1.52 tff(6207,plain,
% 1.33/1.52 (s(s(elem!1)) = elem!1),
% 1.33/1.52 inference(symmetry,[status(thm)],[6145])).
% 1.33/1.52 tff(6208,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6207])).
% 1.33/1.52 tff(6209,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6208])).
% 1.33/1.52 tff(6210,plain,
% 1.33/1.52 (s(s(elem!1)) = elem!1),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6145, 76])).
% 1.33/1.52 tff(6211,plain,
% 1.33/1.52 (~(s(s(s(s(z)))) = elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3120, 6210])).
% 1.33/1.52 tff(6212,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6145])).
% 1.33/1.52 tff(6213,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.33/1.52 inference(symmetry,[status(thm)],[6212])).
% 1.33/1.52 tff(6214,plain,
% 1.33/1.52 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6213])).
% 1.33/1.52 tff(6215,plain,
% 1.33/1.52 (~b(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1096, 224, 5472, 5462, 6179])).
% 1.33/1.52 tff(6216,plain,
% 1.33/1.52 (r(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[249, 6215])).
% 1.33/1.52 tff(6217,plain,
% 1.33/1.52 (~r(z, s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1104, 112, 6216, 101])).
% 1.33/1.52 tff(6218,plain,
% 1.33/1.52 (b(z, s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1088, 6217])).
% 1.33/1.52 tff(6219,plain,
% 1.33/1.52 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6220,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6219])).
% 1.33/1.52 tff(6221,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6220, 2877])).
% 1.33/1.52 tff(6222,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6223,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6222, 6221])).
% 1.33/1.52 tff(6224,plain,
% 1.33/1.52 (~b(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6223, 224, 6218, 6181, 6175])).
% 1.33/1.52 tff(6225,plain,
% 1.33/1.52 (r(s(z), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[194, 6224])).
% 1.33/1.52 tff(6226,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6227,plain,
% 1.33/1.52 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6228,plain,
% 1.33/1.52 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6227])).
% 1.33/1.52 tff(6229,plain,
% 1.33/1.52 (((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6228, 6226])).
% 1.33/1.52 tff(6230,plain,
% 1.33/1.52 ((~![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(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6231,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6230, 6229])).
% 1.33/1.52 tff(6232,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6231, 112, 179, 656, 3317, 3136])).
% 1.33/1.52 tff(6233,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6234,plain,
% 1.33/1.52 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6233, 6225, 6149, 6206])).
% 1.33/1.52 tff(6235,plain,
% 1.33/1.52 (~r(s(s(s(s(z)))), elem!1)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6234, 6214])).
% 1.33/1.52 tff(6236,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3183, 6235, 6211])).
% 1.33/1.52 tff(6237,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6236, 6209])).
% 1.33/1.52 tff(6238,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6239,plain,
% 1.33/1.52 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6240,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6239])).
% 1.33/1.52 tff(6241,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6240, 6238])).
% 1.33/1.52 tff(6242,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6243,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.33/1.52 tff(6244,plain,
% 1.33/1.52 (~b(s(s(s(s(z)))), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6243, 224, 6157, 6159, 6237])).
% 1.33/1.52 tff(6245,plain,
% 1.33/1.52 (r(s(s(s(s(z)))), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 6244])).
% 1.33/1.52 tff(6246,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6247,plain,
% 1.33/1.53 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6248,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6247])).
% 1.33/1.53 tff(6249,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6248, 6246])).
% 1.33/1.53 tff(6250,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6251,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.33/1.53 tff(6252,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6251, 112, 6225, 6245, 6206])).
% 1.33/1.53 tff(6253,plain,(b(z, s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6254,plain,
% 1.33/1.53 (b(z, s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6253, 2, 4, 12])).
% 1.33/1.53 tff(6255,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.33/1.53 tff(6256,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[202, 112, 196, 178, 2851])).
% 1.33/1.53 tff(6257,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6258,plain,
% 1.33/1.53 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6257, 2851, 178])).
% 1.33/1.53 tff(6259,plain,
% 1.33/1.53 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[249, 6258])).
% 1.33/1.53 tff(6260,plain,
% 1.33/1.53 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[135, 68, 132, 294])).
% 1.33/1.53 tff(6261,plain,
% 1.33/1.53 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[147, 312, 2])).
% 1.33/1.53 tff(6262,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[256, 224, 2212, 6261, 6260, 2596])).
% 1.33/1.53 tff(6263,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6264,plain,
% 1.33/1.53 (~r(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6263, 6259, 2596, 2, 177])).
% 1.33/1.53 tff(6265,plain,
% 1.33/1.53 (b(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[593, 6264])).
% 1.33/1.53 tff(6266,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6267,plain,
% 1.33/1.53 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6268,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6267])).
% 1.33/1.53 tff(6269,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6268, 6266])).
% 1.33/1.53 tff(6270,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6271,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6270, 6269])).
% 1.33/1.53 tff(6272,plain,
% 1.33/1.53 (~b(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6271, 224, 6265, 6259, 6255, 2596])).
% 1.33/1.53 tff(6273,plain,
% 1.33/1.53 (r(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[281, 6272])).
% 1.33/1.53 tff(6274,plain,
% 1.33/1.53 (~r(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6167, 6273, 2851])).
% 1.33/1.53 tff(6275,plain,
% 1.33/1.53 (b(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[5459, 6274])).
% 1.33/1.53 tff(6276,plain,
% 1.33/1.53 (~b(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1249, 6275, 1, 6265])).
% 1.33/1.53 tff(6277,plain,
% 1.33/1.53 (r(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[901, 6276])).
% 1.33/1.53 tff(6278,plain,
% 1.33/1.53 (~r(s(s(elem!1)), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3679, 112, 6277, 2851])).
% 1.33/1.53 tff(6279,plain,
% 1.33/1.53 (b(s(s(elem!1)), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3547, 68, 3492, 6278])).
% 1.33/1.53 tff(6280,plain,
% 1.33/1.53 (~r(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3531, 6273, 177])).
% 1.33/1.53 tff(6281,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3535, 68, 6280])).
% 1.33/1.53 tff(6282,plain,
% 1.33/1.53 (b(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6281, 56])).
% 1.33/1.53 tff(6283,plain,
% 1.33/1.53 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4039, 6277, 178])).
% 1.33/1.53 tff(6284,plain,
% 1.33/1.53 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[147, 6283, 2])).
% 1.33/1.53 tff(6285,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3543, 224, 6259, 6284, 6282, 6279])).
% 1.33/1.53 tff(6286,plain,((~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6287,plain,
% 1.33/1.53 (~r(s(s(z)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6286, 178, 2, 3492, 1, 177, 6255, 2596])).
% 1.33/1.53 tff(6288,plain,
% 1.33/1.53 (b(s(s(z)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2726, 6287])).
% 1.33/1.53 tff(6289,plain,
% 1.33/1.53 (((~![X0: $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(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(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6290,plain,
% 1.33/1.53 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6291,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6290])).
% 1.33/1.53 tff(6292,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6291, 6289])).
% 1.33/1.53 tff(6293,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6294,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6293, 6292])).
% 1.33/1.53 tff(6295,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6294, 112, 196, 178, 2303])).
% 1.33/1.53 tff(6296,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6297,plain,
% 1.33/1.53 (~r(s(z), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6296, 196, 178])).
% 1.33/1.53 tff(6298,plain,
% 1.33/1.53 (b(s(z), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1071, 6297])).
% 1.33/1.53 tff(6299,plain,
% 1.33/1.53 (~b(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[243, 196, 178, 1, 177])).
% 1.33/1.53 tff(6300,plain,
% 1.33/1.53 (r(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[5459, 6299])).
% 1.33/1.53 tff(6301,plain,
% 1.33/1.53 (~r(s(s(s(z))), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4608, 6300, 177])).
% 1.33/1.53 tff(6302,plain,
% 1.33/1.53 (b(s(s(s(z))), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[925, 6301])).
% 1.33/1.53 tff(6303,plain,
% 1.33/1.53 (~b(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6191, 224, 6298, 6302, 2844])).
% 1.33/1.53 tff(6304,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3535, 68, 6303])).
% 1.33/1.53 tff(6305,plain,
% 1.33/1.53 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6304, 56])).
% 1.33/1.53 tff(6306,plain,
% 1.33/1.53 (~r(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3531, 6305, 177])).
% 1.33/1.53 tff(6307,plain,
% 1.33/1.53 (b(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[281, 6306])).
% 1.33/1.53 tff(6308,plain,
% 1.33/1.53 (~r(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[5928, 102, 4569])).
% 1.33/1.53 tff(6309,plain,
% 1.33/1.53 (b(s(s(elem!1)), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[901, 6308])).
% 1.33/1.53 tff(6310,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6311,plain,
% 1.33/1.53 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6312,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6311])).
% 1.33/1.53 tff(6313,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6312, 6310])).
% 1.33/1.53 tff(6314,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6315,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6314, 6313])).
% 1.33/1.53 tff(6316,plain,
% 1.33/1.53 (~b(z, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6315, 224, 6261, 6255, 6260])).
% 1.33/1.53 tff(6317,plain,
% 1.33/1.53 (r(z, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[752, 6316])).
% 1.33/1.53 tff(6318,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6319,plain,
% 1.33/1.53 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6320,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6319])).
% 1.33/1.53 tff(6321,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6320, 6318])).
% 1.33/1.53 tff(6322,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6323,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 1.33/1.53 tff(6324,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6323, 112, 4569, 656, 293])).
% 1.33/1.53 tff(6325,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6326,plain,
% 1.33/1.53 (~r(s(z), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6325, 6317, 4569])).
% 1.33/1.53 tff(6327,plain,
% 1.33/1.53 (b(s(z), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[653, 6326])).
% 1.33/1.53 tff(6328,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[5866, 224, 6327, 6309, 5773, 6260])).
% 1.33/1.53 tff(6329,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6330,plain,
% 1.33/1.53 (~r(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6329, 6300, 6255, 2, 177])).
% 1.33/1.53 tff(6331,plain,
% 1.33/1.53 (b(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[593, 6330])).
% 1.33/1.53 tff(6332,plain,
% 1.33/1.53 (~b(z, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[5939, 6331, 2596, 6307])).
% 1.33/1.53 tff(6333,plain,
% 1.33/1.53 (r(z, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[752, 6332])).
% 1.33/1.53 tff(6334,plain,
% 1.33/1.53 (~r(s(z), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6325, 6333, 6300])).
% 1.33/1.53 tff(6335,plain,
% 1.33/1.53 (b(s(z), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[653, 6334])).
% 1.33/1.53 tff(6336,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6337,plain,
% 1.33/1.53 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6338,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6337])).
% 1.33/1.53 tff(6339,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6338, 6336])).
% 1.33/1.53 tff(6340,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6341,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6340, 6339])).
% 1.33/1.54 tff(6342,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6341, 224, 6331, 1, 6335, 6298, 2596])).
% 1.33/1.54 tff(6343,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6344,plain,
% 1.33/1.54 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6343, 6288, 2596, 6255, 2, 177, 1, 178])).
% 1.33/1.54 tff(6345,plain,
% 1.33/1.54 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[249, 6344])).
% 1.33/1.54 tff(6346,plain,
% 1.33/1.54 (~r(s(s(elem!1)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6263, 6345, 2596, 2, 177])).
% 1.33/1.54 tff(6347,plain,
% 1.33/1.54 (b(s(s(elem!1)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[593, 6346])).
% 1.33/1.54 tff(6348,plain,
% 1.33/1.54 (~b(s(s(z)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6271, 224, 6347, 6345, 6255, 2596])).
% 1.33/1.54 tff(6349,plain,
% 1.33/1.54 (r(s(s(z)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[281, 6348])).
% 1.33/1.54 tff(6350,plain,
% 1.33/1.54 (~r(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3531, 6349, 177])).
% 1.33/1.54 tff(6351,plain,
% 1.33/1.54 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3535, 68, 6350])).
% 1.33/1.54 tff(6352,plain,
% 1.33/1.54 (b(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6351, 56])).
% 1.33/1.54 tff(6353,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6354,plain,
% 1.33/1.54 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6355,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6354])).
% 1.33/1.54 tff(6356,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6355, 6353])).
% 1.33/1.54 tff(6357,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6358,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6357, 6356])).
% 1.33/1.54 tff(6359,plain,
% 1.33/1.54 (~b(z, s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6358, 224, 6345, 6255, 6352])).
% 1.33/1.54 tff(6360,plain,
% 1.33/1.54 (r(z, s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1088, 6359])).
% 1.33/1.54 tff(6361,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[256, 224, 2212, 152, 968, 2596])).
% 1.33/1.54 tff(6362,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6363,plain,
% 1.33/1.54 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6362, 152, 2212, 2596])).
% 1.33/1.54 tff(6364,plain,
% 1.33/1.54 (r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[135, 68, 308, 6363])).
% 1.33/1.54 tff(6365,plain,
% 1.33/1.54 (~b(s(s(elem!1)), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3543, 224, 2212, 152, 2211])).
% 1.33/1.54 tff(6366,plain,
% 1.33/1.54 (r(s(s(elem!1)), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[3547, 68, 6365, 3492])).
% 1.33/1.54 tff(6367,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6368,plain,
% 1.33/1.54 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6369,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6368])).
% 1.33/1.54 tff(6370,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6369, 6367])).
% 1.33/1.54 tff(6371,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6372,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6371, 6370])).
% 1.33/1.54 tff(6373,plain,
% 1.33/1.54 (~r(z, s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6372, 112, 3750, 6366])).
% 1.33/1.54 tff(6374,plain,
% 1.33/1.54 (b(z, s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[752, 6373])).
% 1.33/1.54 tff(6375,plain,
% 1.33/1.54 (~b(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[4051, 6374, 1, 1240])).
% 1.33/1.54 tff(6376,plain,
% 1.33/1.54 (r(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[653, 6375])).
% 1.33/1.54 tff(6377,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6378,plain,
% 1.33/1.54 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6379,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6378])).
% 1.33/1.54 tff(6380,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6379, 6377])).
% 1.33/1.54 tff(6381,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6382,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6381, 6380])).
% 1.33/1.54 tff(6383,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6382, 112, 6376, 178, 6364])).
% 1.33/1.54 tff(6384,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6385,plain,
% 1.33/1.54 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6384, 178, 132, 6345, 2596, 1, 6347, 6360, 3492, 6352])).
% 1.33/1.54 tff(6386,plain,
% 1.33/1.54 (r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[147, 6385, 2])).
% 1.33/1.54 tff(6387,plain,
% 1.33/1.54 (~r(s(s(elem!1)), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[4039, 6386, 178])).
% 1.33/1.54 tff(6388,plain,
% 1.33/1.54 (b(s(s(elem!1)), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[901, 6387])).
% 1.33/1.54 tff(6389,plain,
% 1.33/1.54 (~r(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[835, 6386, 178])).
% 1.33/1.54 tff(6390,plain,
% 1.33/1.54 (b(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[653, 6389])).
% 1.33/1.54 tff(6391,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[5850, 224, 6390, 6388, 6288, 2596])).
% 1.33/1.54 tff(6392,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6393,plain,
% 1.33/1.54 (~r(s(z), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6392, 2596, 2, 1, 3491, 6254, 73])).
% 1.33/1.54 tff(6394,plain,
% 1.33/1.54 (b(s(z), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[175, 6393])).
% 1.33/1.54 tff(6395,plain,
% 1.33/1.54 (~r(z, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6329, 102, 6254, 2, 73])).
% 1.33/1.54 tff(6396,plain,
% 1.33/1.54 (b(z, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[5459, 6395])).
% 1.33/1.54 tff(6397,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6398,plain,
% 1.33/1.54 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6399,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6398])).
% 1.33/1.54 tff(6400,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6399, 6397])).
% 1.33/1.54 tff(6401,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6402,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 1.33/1.54 tff(6403,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6402, 224, 77, 1090, 6255, 560])).
% 1.33/1.54 tff(6404,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6405,plain,
% 1.33/1.54 (~b(s(s(s(z))), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6404, 6396, 6254, 1090])).
% 1.33/1.54 tff(6406,plain,
% 1.33/1.54 (r(s(s(s(z))), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[925, 6405])).
% 1.33/1.54 tff(6407,plain,
% 1.33/1.54 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2076, 363, 102])).
% 1.33/1.54 tff(6408,plain,
% 1.33/1.54 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[398, 363, 362, 152, 177])).
% 1.33/1.54 tff(6409,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[360, 6408, 6407, 355])).
% 1.33/1.54 tff(6410,plain,((~r(elem!1, z)) | (s(s(elem!1)) = elem!1) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6411,plain,
% 1.33/1.54 (~r(elem!1, z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6410, 362, 355, 152, 177, 102])).
% 1.33/1.54 tff(6412,plain,
% 1.33/1.54 (b(elem!1, z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[403, 6411, 11])).
% 1.33/1.54 tff(6413,plain,
% 1.33/1.54 (~b(elem!1, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1466, 224, 77, 6412, 1])).
% 1.33/1.54 tff(6414,plain,
% 1.33/1.54 (r(elem!1, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1277, 6413, 88])).
% 1.33/1.54 tff(6415,plain,
% 1.33/1.54 (~r(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2168, 112, 6414, 3188])).
% 1.33/1.54 tff(6416,plain,
% 1.33/1.54 (b(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[374, 6415, 362])).
% 1.33/1.54 tff(6417,plain,
% 1.33/1.54 (((~![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(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6418,plain,
% 1.33/1.54 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6419,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6418])).
% 1.33/1.54 tff(6420,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6419, 6417])).
% 1.33/1.54 tff(6421,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6422,plain,
% 1.33/1.54 ((~![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(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6421, 6420])).
% 1.33/1.54 tff(6423,plain,
% 1.33/1.54 (~r(elem!1, s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6422, 112, 6414, 177, 3188])).
% 1.33/1.54 tff(6424,plain,
% 1.33/1.54 (b(elem!1, s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[388, 6423, 4197])).
% 1.33/1.54 tff(6425,plain,
% 1.33/1.54 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[396, 224, 6424, 6416, 152])).
% 1.33/1.54 tff(6426,plain,
% 1.33/1.54 (r(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[360, 6425, 355])).
% 1.33/1.54 tff(6427,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6428,plain,
% 1.33/1.54 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6429,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6428])).
% 1.33/1.54 tff(6430,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6429, 6427])).
% 1.33/1.54 tff(6431,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6432,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6431, 6430])).
% 1.33/1.54 tff(6433,plain,
% 1.33/1.54 (~b(z, elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6432, 224, 6424, 6416, 6255])).
% 1.33/1.54 tff(6434,plain,
% 1.33/1.54 (r(z, elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[289, 6433, 4])).
% 1.33/1.54 tff(6435,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2346, 6434, 6426, 102])).
% 1.33/1.54 tff(6436,plain,((s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6437,plain,
% 1.33/1.54 (s(s(s(z))) = elem!1),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6436, 102, 4, 355, 6254, 148, 73, 6406, 83, 6396, 1])).
% 1.33/1.54 tff(6438,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6437])).
% 1.33/1.54 tff(6439,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6438])).
% 1.33/1.54 tff(6440,plain,
% 1.33/1.54 (s(s(s(s(z)))) = s(elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6437])).
% 1.33/1.54 tff(6441,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6440])).
% 1.33/1.54 tff(6442,plain,
% 1.33/1.54 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.33/1.54 inference(symmetry,[status(thm)],[6441])).
% 1.33/1.54 tff(6443,plain,
% 1.33/1.54 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6442, 6439])).
% 1.33/1.54 tff(6444,plain,
% 1.33/1.54 (~b(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2089, 224, 1090, 148, 136])).
% 1.33/1.54 tff(6445,plain,
% 1.33/1.54 (r(s(z), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[653, 6444])).
% 1.33/1.54 tff(6446,plain,
% 1.33/1.54 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6437])).
% 1.33/1.54 tff(6447,plain,
% 1.33/1.54 (b(elem!1, s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[136, 6446])).
% 1.33/1.54 tff(6448,plain,
% 1.33/1.54 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6437])).
% 1.33/1.54 tff(6449,plain,
% 1.33/1.54 (b(s(z), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[1090, 6448])).
% 1.33/1.54 tff(6450,plain,
% 1.33/1.54 (~b(elem!1, z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2437, 6437, 12])).
% 1.33/1.54 tff(6451,plain,
% 1.33/1.54 (r(elem!1, z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[403, 6450, 11])).
% 1.33/1.54 tff(6452,plain,
% 1.33/1.54 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2076, 6451, 102])).
% 1.33/1.54 tff(6453,plain,
% 1.33/1.54 (b(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[360, 6452, 355])).
% 1.33/1.54 tff(6454,plain,
% 1.33/1.54 (~b(z, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2684, 1488, 390, 684, 682, 363, 166, 129, 656, 523])).
% 1.33/1.54 tff(6455,plain,
% 1.33/1.54 (~r(z, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2512, 1488, 1923, 102, 363, 2506, 390])).
% 1.33/1.54 tff(6456,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[625, 6455, 6454])).
% 1.33/1.54 tff(6457,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6458,plain,
% 1.33/1.54 (~b(s(elem!1), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6457, 102, 6451, 2618, 6453, 6449, 6447, 160, 91, 6445, 523])).
% 1.33/1.54 tff(6459,plain,
% 1.33/1.54 (r(s(elem!1), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[939, 6458, 324])).
% 1.33/1.54 tff(6460,plain,
% 1.33/1.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6459, 6443])).
% 1.33/1.54 tff(6461,plain,
% 1.33/1.54 (~r(s(elem!1), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2694, 6459, 6451])).
% 1.33/1.55 tff(6462,plain,
% 1.33/1.55 (b(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[498, 6461])).
% 1.33/1.55 tff(6463,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6464,plain,
% 1.33/1.55 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6465,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6464])).
% 1.33/1.55 tff(6466,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6465, 6463])).
% 1.33/1.55 tff(6467,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6468,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6467, 6466])).
% 1.33/1.55 tff(6469,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6468, 224, 77, 1, 500, 1347])).
% 1.33/1.55 tff(6470,plain,((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6471,plain,
% 1.33/1.55 (~b(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6470, 6462, 1, 6396])).
% 1.33/1.55 tff(6472,plain,
% 1.33/1.55 (r(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1476, 6471, 160])).
% 1.33/1.55 tff(6473,plain,
% 1.33/1.55 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[4131])).
% 1.33/1.55 tff(6474,plain,
% 1.33/1.55 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.33/1.55 inference(symmetry,[status(thm)],[6473])).
% 1.33/1.55 tff(6475,plain,
% 1.33/1.55 (r(s(s(s(s(z)))), s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[428, 6474])).
% 1.33/1.55 tff(6476,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3162, 6475])).
% 1.33/1.55 tff(6477,plain,((~r(s(elem!1), s(z))) | r(s(s(s(s(z)))), s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6478,plain,
% 1.33/1.55 (r(s(s(s(s(z)))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6477, 6472, 6437])).
% 1.33/1.55 tff(6479,plain,
% 1.33/1.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3326, 6478, 6406])).
% 1.33/1.55 tff(6480,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6479, 6460])).
% 1.33/1.55 tff(6481,plain,((~r(s(s(elem!1)), z)) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = elem!1) | b(s(s(s(z))), z) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6482,plain,
% 1.33/1.55 (~r(s(s(elem!1)), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6481, 6394, 303, 319, 1, 353, 12, 4, 2])).
% 1.33/1.55 tff(6483,plain,
% 1.33/1.55 (b(s(s(elem!1)), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[593, 6482])).
% 1.33/1.55 tff(6484,assumption,(~b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.33/1.55 tff(6485,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6486,plain,
% 1.33/1.55 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6487,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6486])).
% 1.33/1.55 tff(6488,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6487, 6485])).
% 1.33/1.55 tff(6489,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6490,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6489, 6488])).
% 1.33/1.55 tff(6491,plain,
% 1.33/1.55 (~b(s(z), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6490, 224, 1240, 1, 1090, 6255])).
% 1.33/1.55 tff(6492,plain,
% 1.33/1.55 (r(s(z), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[653, 6491])).
% 1.33/1.55 tff(6493,plain,
% 1.33/1.55 (~r(z, s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6325, 4569, 6492])).
% 1.33/1.55 tff(6494,plain,
% 1.33/1.55 (b(z, s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[752, 6493])).
% 1.33/1.55 tff(6495,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1195, 112, 1181, 656, 416])).
% 1.33/1.55 tff(6496,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6497,plain,
% 1.33/1.55 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6496, 416, 656])).
% 1.33/1.55 tff(6498,plain,
% 1.33/1.55 (b(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[360, 6497, 353])).
% 1.33/1.55 tff(6499,plain,
% 1.33/1.55 (~b(elem!1, z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[3407, 6498, 344, 1240])).
% 1.33/1.55 tff(6500,plain,
% 1.33/1.55 (r(elem!1, z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[403, 6499, 157])).
% 1.33/1.55 tff(6501,plain,
% 1.33/1.55 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[743, 6498, 1180, 344])).
% 1.33/1.55 tff(6502,plain,
% 1.33/1.55 (r(elem!1, s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[558, 6501, 3])).
% 1.33/1.55 tff(6503,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6504,plain,
% 1.33/1.55 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6505,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6504])).
% 1.33/1.55 tff(6506,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6505, 6503])).
% 1.33/1.55 tff(6507,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6508,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6507, 6506])).
% 1.33/1.55 tff(6509,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6508, 112, 6502, 6500, 656, 416])).
% 1.33/1.55 tff(6510,plain,((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6511,plain,
% 1.33/1.55 (~r(s(z), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6510, 6494, 3, 11, 6492, 5739, 1240])).
% 1.33/1.55 tff(6512,plain,
% 1.33/1.55 (b(s(z), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[454, 6511, 91])).
% 1.33/1.55 tff(6513,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6514,plain,
% 1.33/1.55 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6515,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6514])).
% 1.33/1.55 tff(6516,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6515, 6513])).
% 1.33/1.55 tff(6517,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6518,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6517, 6516])).
% 1.33/1.55 tff(6519,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6518, 224, 405, 1, 684, 1090, 6255])).
% 1.33/1.55 tff(6520,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6521,plain,
% 1.33/1.55 (~b(elem!1, z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6520, 6512, 1, 1090, 6255])).
% 1.33/1.55 tff(6522,plain,
% 1.33/1.55 (r(elem!1, z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[403, 6521, 11])).
% 1.33/1.55 tff(6523,plain,
% 1.33/1.55 (~r(elem!1, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5749, 6522, 4569])).
% 1.33/1.55 tff(6524,plain,
% 1.33/1.55 (b(elem!1, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1277, 6523, 83])).
% 1.33/1.55 tff(6525,plain,
% 1.33/1.55 (~r(s(s(s(z))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[369, 112, 6522, 177])).
% 1.33/1.55 tff(6526,plain,
% 1.33/1.55 (~r(elem!1, s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[383, 112, 6522, 177])).
% 1.33/1.55 tff(6527,plain,
% 1.33/1.55 (s(s(s(z))) = elem!1),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4200, 6526, 6512, 6525, 1090])).
% 1.33/1.55 tff(6528,plain,
% 1.33/1.55 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6527])).
% 1.33/1.55 tff(6529,plain,
% 1.33/1.55 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6528])).
% 1.33/1.55 tff(6530,plain,
% 1.33/1.55 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6484, 6529])).
% 1.33/1.55 tff(6531,plain,
% 1.33/1.55 (~b(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2662, 224, 1488, 684, 2896])).
% 1.33/1.55 tff(6532,plain,
% 1.33/1.55 (r(s(elem!1), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1476, 6531, 166])).
% 1.33/1.55 tff(6533,plain,
% 1.33/1.55 (~r(z, s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5562, 112, 4569, 6532])).
% 1.33/1.55 tff(6534,plain,
% 1.33/1.55 (b(z, s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[625, 6533])).
% 1.33/1.55 tff(6535,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6536,plain,
% 1.33/1.55 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6537,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6536])).
% 1.33/1.55 tff(6538,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6537, 6535])).
% 1.33/1.55 tff(6539,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6540,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6539, 6538])).
% 1.33/1.55 tff(6541,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6540, 224, 501, 1488, 344, 407])).
% 1.33/1.55 tff(6542,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6543,plain,
% 1.33/1.55 (~b(elem!1, s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6542, 6534, 344, 1488])).
% 1.33/1.55 tff(6544,plain,
% 1.33/1.55 (~r(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5625, 112, 4569, 6532])).
% 1.33/1.55 tff(6545,plain,
% 1.33/1.55 (b(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[498, 6544])).
% 1.33/1.55 tff(6546,plain,
% 1.33/1.55 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4320, 6545, 1240, 6534])).
% 1.33/1.55 tff(6547,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[541, 6546, 6543, 3, 354])).
% 1.33/1.55 tff(6548,plain,((~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6549,plain,
% 1.33/1.55 (~b(s(elem!1), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6548, 6530, 3, 1240, 5739, 4569, 160, 6512, 6524])).
% 1.33/1.55 tff(6550,plain,
% 1.33/1.55 (r(s(elem!1), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[939, 6549, 303])).
% 1.33/1.55 tff(6551,plain,
% 1.33/1.55 (~r(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2694, 6550, 6522])).
% 1.33/1.55 tff(6552,plain,
% 1.33/1.55 (b(s(elem!1), z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[498, 6551])).
% 1.33/1.55 tff(6553,plain,
% 1.33/1.55 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6527])).
% 1.33/1.55 tff(6554,plain,
% 1.33/1.55 (r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[147, 6484, 2])).
% 1.33/1.55 tff(6555,plain,
% 1.33/1.55 (r(s(s(elem!1)), elem!1)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6554, 6553])).
% 1.33/1.55 tff(6556,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4102, 112, 408, 1700, 1181])).
% 1.33/1.55 tff(6557,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,[]))).
% 1.33/1.55 tff(6558,plain,
% 1.33/1.55 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6557, 6550, 6555])).
% 1.33/1.55 tff(6559,plain,
% 1.33/1.55 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1521, 6558, 319])).
% 1.33/1.55 tff(6560,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4154, 6559, 6552, 1240, 6494])).
% 1.33/1.55 tff(6561,plain,((~r(z, s(z))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6562,plain,
% 1.33/1.55 (~r(z, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6561, 6484, 3, 1240, 1090, 177, 1, 6255, 4, 2])).
% 1.33/1.55 tff(6563,plain,
% 1.33/1.55 (b(z, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5459, 6562])).
% 1.33/1.55 tff(6564,plain,
% 1.33/1.55 (~b(s(s(s(z))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6404, 6563, 6255, 1090])).
% 1.33/1.55 tff(6565,plain,
% 1.33/1.55 (r(s(s(s(z))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[925, 6564])).
% 1.33/1.55 tff(6566,plain,
% 1.33/1.55 (~b(s(s(elem!1)), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1249, 6563, 1, 1240])).
% 1.33/1.55 tff(6567,plain,
% 1.33/1.55 (r(s(s(elem!1)), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[901, 6566])).
% 1.33/1.55 tff(6568,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5342, 112, 6567, 6554, 6565])).
% 1.33/1.55 tff(6569,plain,(b(s(s(elem!1)), s(s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6570,plain,
% 1.33/1.55 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6569, 6483, 1, 6254, 6394, 3, 73, 4, 2])).
% 1.33/1.55 tff(6571,plain,
% 1.33/1.55 (~b(s(s(s(z))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6404, 77, 6255, 1090])).
% 1.33/1.55 tff(6572,plain,
% 1.33/1.55 (r(s(s(s(z))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[925, 6571])).
% 1.33/1.55 tff(6573,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6574,plain,
% 1.33/1.55 (((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6575,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6574])).
% 1.33/1.55 tff(6576,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6575, 6573])).
% 1.33/1.55 tff(6577,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6578,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6577, 6576])).
% 1.33/1.55 tff(6579,plain,
% 1.33/1.55 (~b(s(s(elem!1)), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6578, 224, 1240, 1, 152, 6255])).
% 1.33/1.55 tff(6580,plain,
% 1.33/1.55 (r(s(s(elem!1)), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[901, 6579])).
% 1.33/1.55 tff(6581,plain,
% 1.33/1.55 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[5351, 112, 6580, 6572])).
% 1.33/1.56 tff(6582,plain,
% 1.33/1.56 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[135, 68, 150, 6581])).
% 1.33/1.56 tff(6583,plain,
% 1.33/1.56 (~b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6315, 224, 152, 6255, 6582])).
% 1.33/1.56 tff(6584,plain,
% 1.33/1.56 (r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[752, 6583])).
% 1.33/1.56 tff(6585,plain,
% 1.33/1.56 (~r(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3500, 1181, 293])).
% 1.33/1.56 tff(6586,plain,
% 1.33/1.56 (b(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[289, 6585, 4])).
% 1.33/1.56 tff(6587,plain,
% 1.33/1.56 (~r(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6496, 1181, 656])).
% 1.33/1.56 tff(6588,plain,
% 1.33/1.56 (b(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[454, 6587, 149])).
% 1.33/1.56 tff(6589,plain,
% 1.33/1.56 (~r(elem!1, s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3588, 1181, 887])).
% 1.33/1.56 tff(6590,plain,
% 1.33/1.56 (b(elem!1, s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1277, 6589, 88])).
% 1.33/1.56 tff(6591,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2904, 6590, 6588, 77, 6586])).
% 1.33/1.56 tff(6592,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (z = elem!1) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6593,plain,
% 1.33/1.56 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6592, 77, 88, 4, 6580, 6492, 6584])).
% 1.33/1.56 tff(6594,plain,
% 1.33/1.56 (r(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[454, 2337, 129])).
% 1.33/1.56 tff(6595,plain,
% 1.33/1.56 (s(s(s(z))) = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4045, 2432, 1240, 157, 361, 73, 152])).
% 1.33/1.56 tff(6596,plain,
% 1.33/1.56 (~r(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3681, 688, 1240, 77, 152, 293, 1108, 416, 3, 73, 328])).
% 1.33/1.56 tff(6597,plain,
% 1.33/1.56 (b(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[403, 6596, 157])).
% 1.33/1.56 tff(6598,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2437, 6597, 6595, 12])).
% 1.33/1.56 tff(6599,plain,((~r(z, elem!1)) | b(s(s(s(z))), z) | (elem!1 = z) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6600,plain,
% 1.33/1.56 (~r(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6599, 6594, 11, 1240, 152, 77, 3596, 12, 3, 328])).
% 1.33/1.56 tff(6601,plain,
% 1.33/1.56 (b(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[289, 6600, 4])).
% 1.33/1.56 tff(6602,plain,
% 1.33/1.56 (~b(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3606, 6601, 750, 328, 1240])).
% 1.33/1.56 tff(6603,plain,
% 1.33/1.56 (r(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[403, 6602, 11])).
% 1.33/1.56 tff(6604,plain,
% 1.33/1.56 (s(s(s(z))) = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[398, 6603, 152, 361, 73])).
% 1.33/1.56 tff(6605,plain,
% 1.33/1.56 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6604])).
% 1.33/1.56 tff(6606,plain,
% 1.33/1.56 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[6605])).
% 1.33/1.56 tff(6607,plain,
% 1.33/1.56 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6606])).
% 1.33/1.56 tff(6608,plain,
% 1.33/1.56 (~b(s(z), s(s(s(z))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2337, 6607])).
% 1.33/1.56 tff(6609,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1090, 6608])).
% 1.33/1.56 tff(6610,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | b(z, s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), z)) | (z = elem!1) | (~b(z, s(z))) | b(s(s(s(z))), z) | (elem!1 = s(s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6611,plain,
% 1.33/1.56 (b(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6610, 6583, 152, 1090, 6593, 1240, 4, 77, 12, 3, 149])).
% 1.33/1.56 tff(6612,plain,
% 1.33/1.56 (~b(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6520, 6611, 1, 1090, 6255])).
% 1.33/1.56 tff(6613,plain,
% 1.33/1.56 (r(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[403, 6612, 11])).
% 1.33/1.56 tff(6614,plain,
% 1.33/1.56 (b(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[360, 6593, 353])).
% 1.33/1.56 tff(6615,plain,
% 1.33/1.56 (s(s(s(z))) = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[398, 6613, 152, 6614, 73])).
% 1.33/1.56 tff(6616,plain,
% 1.33/1.56 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[341])).
% 1.33/1.56 tff(6617,plain,
% 1.33/1.56 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[6616])).
% 1.33/1.56 tff(6618,plain,
% 1.33/1.56 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[4131])).
% 1.33/1.56 tff(6619,plain,
% 1.33/1.56 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.33/1.56 inference(symmetry,[status(thm)],[6618])).
% 1.33/1.56 tff(6620,plain,
% 1.33/1.56 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[6619, 6617])).
% 1.33/1.56 tff(6621,plain,
% 1.33/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[408, 6620])).
% 1.33/1.56 tff(6622,plain,
% 1.33/1.56 (~b(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6470, 2696, 1, 77])).
% 1.33/1.56 tff(6623,plain,
% 1.33/1.56 (r(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1476, 6622, 166])).
% 1.33/1.56 tff(6624,plain,
% 1.33/1.56 (r(s(s(s(s(z)))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6477, 6623, 341])).
% 1.33/1.56 tff(6625,plain,
% 1.33/1.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[3326, 6624, 3188])).
% 1.33/1.56 tff(6626,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6625, 6621])).
% 1.33/1.56 tff(6627,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6628,plain,
% 1.33/1.56 (~r(s(elem!1), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6627, 6615, 6572, 160, 1, 77, 6613])).
% 1.33/1.56 tff(6629,plain,
% 1.33/1.56 (b(s(elem!1), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[939, 6628, 303])).
% 1.33/1.56 tff(6630,plain,
% 1.33/1.56 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6615])).
% 1.33/1.56 tff(6631,plain,
% 1.33/1.56 (b(elem!1, s(s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6582, 6630])).
% 1.33/1.56 tff(6632,plain,
% 1.33/1.56 (~b(z, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2684, 6629, 6614, 6611, 6631, 6613, 160, 149, 6492, 319])).
% 1.33/1.56 tff(6633,plain,
% 1.33/1.56 (r(z, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[625, 6632])).
% 1.33/1.56 tff(6634,plain,
% 1.33/1.56 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[576, 6633, 6584])).
% 1.33/1.56 tff(6635,plain,
% 1.33/1.56 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[530, 6634, 526])).
% 1.33/1.56 tff(6636,plain,
% 1.33/1.56 (~r(elem!1, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[604, 6633, 6613])).
% 1.33/1.56 tff(6637,plain,
% 1.33/1.56 (b(elem!1, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[515, 6636, 327])).
% 1.33/1.56 tff(6638,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1496, 6637, 6635, 6614, 6629])).
% 1.33/1.56 tff(6639,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (z = elem!1) | b(s(s(s(z))), z) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6640,plain,
% 1.33/1.56 (~b(z, s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6639, 6570, 1, 6394, 6254, 6483, 4, 12, 3, 83])).
% 1.33/1.56 tff(6641,plain,
% 1.33/1.56 (r(z, s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5459, 6640])).
% 1.33/1.56 tff(6642,plain,
% 1.33/1.56 (~r(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4608, 6641, 73])).
% 1.33/1.56 tff(6643,plain,
% 1.33/1.56 (b(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[925, 6642])).
% 1.33/1.56 tff(6644,plain,
% 1.33/1.56 (~b(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6490, 224, 6483, 1, 6394, 6254])).
% 1.33/1.56 tff(6645,plain,
% 1.33/1.56 (r(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[653, 6644])).
% 1.33/1.56 tff(6646,plain,
% 1.33/1.56 (~r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6325, 6641, 6645])).
% 1.33/1.56 tff(6647,plain,
% 1.33/1.56 (b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[752, 6646])).
% 1.33/1.56 tff(6648,plain,
% 1.33/1.56 (~b(s(s(z)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5939, 6647, 2596, 6483])).
% 1.33/1.56 tff(6649,plain,
% 1.33/1.56 (r(s(s(z)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[281, 6648])).
% 1.33/1.56 tff(6650,plain,
% 1.33/1.56 (~r(s(s(z)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6167, 6649, 6641])).
% 1.33/1.56 tff(6651,plain,
% 1.33/1.56 (b(s(s(z)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2726, 6650])).
% 1.33/1.56 tff(6652,plain,
% 1.33/1.56 (~b(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6578, 224, 6483, 1, 6570, 6254])).
% 1.33/1.56 tff(6653,plain,
% 1.33/1.56 (r(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[901, 6652])).
% 1.33/1.56 tff(6654,plain,
% 1.33/1.56 (~r(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5576, 6641, 319, 6653])).
% 1.33/1.56 tff(6655,plain,
% 1.33/1.56 (b(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1476, 6654, 160])).
% 1.33/1.56 tff(6656,plain,
% 1.33/1.56 (~r(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5737, 6641, 73, 2])).
% 1.33/1.56 tff(6657,plain,
% 1.33/1.56 (b(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[289, 6656, 4])).
% 1.33/1.56 tff(6658,plain,
% 1.33/1.56 (~r(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6510, 6647, 3, 11, 6645, 6657, 6483])).
% 1.33/1.56 tff(6659,plain,
% 1.33/1.56 (b(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[454, 6658, 91])).
% 1.33/1.56 tff(6660,plain,
% 1.33/1.56 (~b(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6520, 6659, 1, 6394, 6254])).
% 1.33/1.56 tff(6661,plain,
% 1.33/1.56 (r(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[403, 6660, 11])).
% 1.33/1.56 tff(6662,plain,
% 1.33/1.56 (~r(s(s(s(z))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[369, 112, 6661, 73])).
% 1.33/1.56 tff(6663,plain,
% 1.33/1.56 (~r(elem!1, s(s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[383, 112, 6661, 73])).
% 1.33/1.56 tff(6664,plain,
% 1.33/1.56 (s(s(s(z))) = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4200, 6663, 6659, 6662, 6394])).
% 1.33/1.56 tff(6665,plain,
% 1.33/1.56 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4136, 6664, 6655])).
% 1.33/1.56 tff(6666,plain,
% 1.33/1.56 (~b(s(z), s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6204, 6665, 73, 6394, 6651, 6643])).
% 1.33/1.56 tff(6667,plain,
% 1.33/1.56 (r(s(z), s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1071, 6666])).
% 1.33/1.56 tff(6668,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6669,plain,
% 1.33/1.56 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6670,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6669])).
% 1.33/1.56 tff(6671,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[6670, 6668])).
% 1.33/1.56 tff(6672,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(6673,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6672, 6671])).
% 1.33/1.56 tff(6674,plain,
% 1.33/1.56 ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6673, 224, 6570, 6254, 2596])).
% 1.33/1.56 tff(6675,plain,
% 1.33/1.56 (~b(z, s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6674, 6647])).
% 1.33/1.56 tff(6676,plain,
% 1.33/1.56 (r(z, s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1088, 6675])).
% 1.33/1.56 tff(6677,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6678,plain,
% 1.33/1.56 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6679,plain,
% 1.33/1.56 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6678])).
% 1.33/1.56 tff(6680,plain,
% 1.33/1.56 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[6679, 6677])).
% 1.33/1.56 tff(6681,plain,
% 1.33/1.56 ((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(6682,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 1.33/1.56 tff(6683,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6682, 112, 6641, 6676, 6667])).
% 1.33/1.56 tff(6684,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6685,plain,
% 1.33/1.56 (~b(s(s(z)), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6684, 1, 3, 4, 2, 12])).
% 1.33/1.56 tff(6686,plain,
% 1.33/1.56 (r(s(s(z)), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[265, 6685, 169])).
% 1.33/1.56 tff(6687,plain,
% 1.33/1.56 (~r(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6329, 4569, 6255, 2, 177])).
% 1.33/1.56 tff(6688,plain,
% 1.33/1.56 (b(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[593, 6687])).
% 1.33/1.56 tff(6689,plain,
% 1.33/1.56 (~b(s(z), s(s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6561, 6484, 3, 4569, 6688, 177, 1, 6255, 4, 2])).
% 1.33/1.56 tff(6690,plain,
% 1.33/1.56 (r(s(z), s(s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[175, 6689])).
% 1.33/1.56 tff(6691,plain,
% 1.33/1.56 (~r(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4039, 6690, 6554])).
% 1.33/1.56 tff(6692,plain,
% 1.33/1.56 (b(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[901, 6691])).
% 1.33/1.56 tff(6693,plain,
% 1.33/1.56 (~r(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[835, 6690, 6554])).
% 1.33/1.56 tff(6694,plain,
% 1.33/1.56 (b(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[653, 6693])).
% 1.33/1.56 tff(6695,plain,
% 1.33/1.56 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5866, 224, 6694, 6692, 5773])).
% 1.33/1.56 tff(6696,plain,
% 1.33/1.56 (r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[135, 68, 132, 6695])).
% 1.33/1.56 tff(6697,plain,
% 1.33/1.56 (~b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4051, 6694, 1, 6688])).
% 1.33/1.56 tff(6698,plain,
% 1.33/1.56 (r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[752, 6697])).
% 1.33/1.56 tff(6699,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6700,plain,
% 1.33/1.56 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6701,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6700])).
% 1.33/1.56 tff(6702,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(transitivity,[status(thm)],[6701, 6699])).
% 1.33/1.56 tff(6703,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(6704,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6703, 6702])).
% 1.33/1.56 tff(6705,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6704, 112, 4569, 6698, 177, 6696])).
% 1.33/1.56 tff(6706,plain,(b(s(s(elem!1)), s(s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(z))))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6707,plain,
% 1.33/1.56 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6706, 4569, 177, 1, 3, 6255, 4, 2])).
% 1.33/1.56 tff(6708,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6709,plain,
% 1.33/1.56 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(6710,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6709])).
% 1.33/1.56 tff(6711,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[6710, 6708])).
% 1.33/1.56 tff(6712,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(6713,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6712, 6711])).
% 1.33/1.56 tff(6714,plain,
% 1.33/1.56 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6713, 224, 6688, 1, 5773])).
% 1.33/1.56 tff(6715,plain,
% 1.33/1.56 (~b(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6714, 6707])).
% 1.33/1.56 tff(6716,plain,
% 1.33/1.56 (r(s(s(elem!1)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[901, 6715])).
% 1.33/1.56 tff(6717,plain,
% 1.33/1.56 (~r(s(s(z)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2993, 6716, 267])).
% 1.33/1.56 tff(6718,plain,
% 1.33/1.56 (b(s(s(z)), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2726, 6717])).
% 1.33/1.56 tff(6719,plain,
% 1.33/1.56 (~r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 6716])).
% 1.33/1.56 tff(6720,plain,
% 1.33/1.56 (b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[752, 6719])).
% 1.33/1.56 tff(6721,plain,
% 1.33/1.56 (~b(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4051, 6720, 1, 6688])).
% 1.33/1.56 tff(6722,plain,
% 1.33/1.56 (r(s(z), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[653, 6721])).
% 1.33/1.56 tff(6723,plain,
% 1.33/1.56 (~r(s(z), s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5333, 6722, 267])).
% 1.33/1.56 tff(6724,plain,
% 1.33/1.56 (b(s(z), s(s(z)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1071, 6723])).
% 1.33/1.56 tff(6725,plain,
% 1.33/1.56 (~r(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[5576, 6716, 319, 4569])).
% 1.33/1.56 tff(6726,plain,
% 1.33/1.56 (b(s(elem!1), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1476, 6725, 160])).
% 1.33/1.56 tff(6727,plain,
% 1.33/1.56 (~r(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6510, 6722, 3, 11, 6720, 5739, 6688])).
% 1.33/1.56 tff(6728,plain,
% 1.33/1.56 (b(s(z), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[454, 6727, 91])).
% 1.33/1.56 tff(6729,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[461, 224, 405, 1, 684, 344])).
% 1.33/1.56 tff(6730,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(6731,plain,
% 1.33/1.56 (~b(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6730, 6728, 1, 5739])).
% 1.33/1.56 tff(6732,plain,
% 1.33/1.56 (r(elem!1, z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[403, 6731, 11])).
% 1.33/1.56 tff(6733,plain,
% 1.33/1.57 (~r(elem!1, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5749, 6732, 4569])).
% 1.33/1.57 tff(6734,plain,
% 1.33/1.57 (b(elem!1, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1277, 6733, 83])).
% 1.33/1.57 tff(6735,plain,
% 1.33/1.57 (~b(s(elem!1), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6548, 354, 3, 1240, 4569, 344, 166, 684, 2896])).
% 1.33/1.57 tff(6736,plain,
% 1.33/1.57 (r(s(elem!1), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[939, 6735, 303])).
% 1.33/1.57 tff(6737,plain,
% 1.33/1.57 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6557, 6736, 3340])).
% 1.33/1.57 tff(6738,plain,
% 1.33/1.57 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1521, 6737, 319])).
% 1.33/1.57 tff(6739,plain,
% 1.33/1.57 (~r(s(elem!1), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2694, 6736, 363])).
% 1.33/1.57 tff(6740,plain,
% 1.33/1.57 (b(s(elem!1), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[498, 6739])).
% 1.33/1.57 tff(6741,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4154, 6740, 6738, 1240, 1180])).
% 1.33/1.57 tff(6742,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~r(z, s(z))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6743,plain,
% 1.33/1.57 (b(s(s(elem!1)), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6742, 6688, 6720, 6732, 3, 4569, 5739, 160, 6728, 6734])).
% 1.33/1.57 tff(6744,plain,
% 1.33/1.57 (s(s(s(z))) = elem!1),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[398, 6743, 6707, 6732, 177])).
% 1.33/1.57 tff(6745,plain,
% 1.33/1.57 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4136, 6744, 6726])).
% 1.33/1.57 tff(6746,plain,
% 1.33/1.57 (elem!1 = s(s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2487, 6744])).
% 1.33/1.57 tff(6747,plain,
% 1.33/1.57 (b(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2477, 6746, 6728])).
% 1.33/1.57 tff(6748,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6204, 6747, 6745, 177, 6724, 6718, 5773])).
% 1.33/1.57 tff(6749,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6750,plain,
% 1.33/1.57 (~r(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6749, 1, 3, 73, 6686, 6254, 4, 2])).
% 1.33/1.57 tff(6751,plain,
% 1.33/1.57 (b(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5459, 6750])).
% 1.33/1.57 tff(6752,plain,
% 1.33/1.57 (~r(s(s(z)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[276, 102, 267])).
% 1.33/1.57 tff(6753,plain,
% 1.33/1.57 (b(s(s(z)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[281, 6752])).
% 1.33/1.57 tff(6754,plain,
% 1.33/1.57 (~b(s(s(z)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2846, 6753, 1, 77])).
% 1.33/1.57 tff(6755,plain,
% 1.33/1.57 (r(s(s(z)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2726, 6754])).
% 1.33/1.57 tff(6756,plain,
% 1.33/1.57 (~r(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2993, 6755, 267])).
% 1.33/1.57 tff(6757,plain,
% 1.33/1.57 (b(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[901, 6756])).
% 1.33/1.57 tff(6758,plain,
% 1.33/1.57 (~r(s(z), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2853, 6755, 267])).
% 1.33/1.57 tff(6759,plain,
% 1.33/1.57 (b(s(z), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[653, 6758])).
% 1.33/1.57 tff(6760,plain,
% 1.33/1.57 (~b(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2158, 224, 6759, 6757, 136])).
% 1.33/1.57 tff(6761,plain,
% 1.33/1.57 (r(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[925, 6760])).
% 1.33/1.57 tff(6762,plain,
% 1.33/1.57 (s(s(s(z))) = elem!1),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6436, 6761, 4, 355, 6254, 102, 73, 148, 83, 77, 1])).
% 1.33/1.57 tff(6763,plain,
% 1.33/1.57 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6762])).
% 1.33/1.57 tff(6764,plain,
% 1.33/1.57 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[6763, 2587])).
% 1.33/1.57 tff(6765,plain,
% 1.33/1.57 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(z))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6764])).
% 1.33/1.57 tff(6766,plain,
% 1.33/1.57 (~(elem!1 = s(s(z)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[55, 6765])).
% 1.33/1.57 tff(6767,plain,
% 1.33/1.57 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6762])).
% 1.33/1.57 tff(6768,plain,
% 1.33/1.57 (r(elem!1, s(z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6761, 6767])).
% 1.33/1.57 tff(6769,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6770,plain,
% 1.33/1.57 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6771,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6770])).
% 1.33/1.57 tff(6772,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[6771, 6769])).
% 1.33/1.57 tff(6773,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(6774,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6773, 6772])).
% 1.33/1.57 tff(6775,plain,
% 1.33/1.57 (~r(elem!1, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6774, 112, 6768, 267, 6755])).
% 1.33/1.57 tff(6776,plain,
% 1.33/1.57 (~b(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1203, 224, 77, 6759, 6757])).
% 1.33/1.57 tff(6777,plain,
% 1.33/1.57 (r(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[752, 6776])).
% 1.33/1.57 tff(6778,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6779,plain,
% 1.33/1.57 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6780,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6779])).
% 1.33/1.57 tff(6781,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[6780, 6778])).
% 1.33/1.57 tff(6782,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(6783,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 1.33/1.57 tff(6784,plain,
% 1.33/1.57 (~r(z, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6783, 112, 6777, 267, 6755])).
% 1.33/1.57 tff(6785,plain,
% 1.33/1.57 (b(z, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1088, 6784])).
% 1.33/1.57 tff(6786,plain,
% 1.33/1.57 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6762])).
% 1.33/1.57 tff(6787,plain,
% 1.33/1.57 (b(z, elem!1)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6254, 6786])).
% 1.33/1.57 tff(6788,plain,
% 1.33/1.57 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6762])).
% 1.33/1.57 tff(6789,plain,
% 1.33/1.57 (~b(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6481, 102, 324, 523, 1, 355, 12, 4, 2])).
% 1.33/1.57 tff(6790,plain,
% 1.33/1.57 (r(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[175, 6789])).
% 1.33/1.57 tff(6791,plain,
% 1.33/1.57 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[243, 6790, 77, 1, 73])).
% 1.33/1.57 tff(6792,plain,
% 1.33/1.57 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[249, 6791])).
% 1.33/1.57 tff(6793,plain,
% 1.33/1.57 (b(s(s(z)), elem!1)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6792, 6788])).
% 1.33/1.57 tff(6794,plain,
% 1.33/1.57 (~b(elem!1, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2869, 6793, 6787, 6785])).
% 1.33/1.57 tff(6795,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2874, 6794, 6775, 6766])).
% 1.33/1.57 tff(6796,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z)))) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(elem!1))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6797,plain,
% 1.33/1.57 (~r(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6796, 6686, 4, 353, 6751, 1, 2, 303, 319, 12])).
% 1.33/1.57 tff(6798,plain,
% 1.33/1.57 (b(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[593, 6797])).
% 1.33/1.57 tff(6799,plain,
% 1.33/1.57 (~b(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1249, 6798, 1, 6751])).
% 1.33/1.57 tff(6800,plain,
% 1.33/1.57 (r(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[901, 6799])).
% 1.33/1.57 tff(6801,plain,
% 1.33/1.57 (~r(s(s(z)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2993, 6800, 6686])).
% 1.33/1.57 tff(6802,plain,
% 1.33/1.57 (b(s(s(z)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2726, 6801])).
% 1.33/1.57 tff(6803,plain,
% 1.33/1.57 (~b(s(s(z)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2846, 6802, 1, 6751])).
% 1.33/1.57 tff(6804,plain,
% 1.33/1.57 (r(s(s(z)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[281, 6803])).
% 1.33/1.57 tff(6805,plain,
% 1.33/1.57 (~r(s(s(s(z))), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3531, 6804, 73])).
% 1.33/1.57 tff(6806,plain,
% 1.33/1.57 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3535, 68, 6805])).
% 1.33/1.57 tff(6807,plain,
% 1.33/1.57 (b(s(s(s(z))), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6806, 56])).
% 1.33/1.57 tff(6808,plain,
% 1.33/1.57 (~b(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6569, 6484, 1, 6255, 1240, 3, 177, 4, 2])).
% 1.33/1.57 tff(6809,plain,
% 1.33/1.57 (~r(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4039, 6554, 887])).
% 1.33/1.57 tff(6810,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[175, 6809, 6808])).
% 1.33/1.57 tff(6811,plain,(b(s(s(elem!1)), s(s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (z = elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6812,plain,
% 1.33/1.57 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6811, 6800, 1, 6254, 6798, 3, 73, 4, 2])).
% 1.33/1.57 tff(6813,plain,
% 1.33/1.57 (~b(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6639, 6812, 1, 6751, 6254, 6798, 4, 12, 3, 83])).
% 1.33/1.57 tff(6814,plain,
% 1.33/1.57 (r(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[175, 6813])).
% 1.33/1.57 tff(6815,plain,
% 1.33/1.57 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[243, 6814, 6751, 1, 73])).
% 1.33/1.57 tff(6816,plain,
% 1.33/1.57 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[249, 6815])).
% 1.33/1.57 tff(6817,plain,
% 1.33/1.57 (~b(s(s(elem!1)), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3543, 224, 6816, 6812, 6807])).
% 1.33/1.57 tff(6818,plain,
% 1.33/1.57 (r(s(s(elem!1)), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3547, 68, 6817, 3491])).
% 1.33/1.57 tff(6819,plain,
% 1.33/1.57 (~b(z, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6358, 224, 6816, 6254, 6807])).
% 1.33/1.57 tff(6820,plain,
% 1.33/1.57 (r(z, s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1088, 6819])).
% 1.33/1.57 tff(6821,plain,
% 1.33/1.57 (~r(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6372, 112, 6820, 6818])).
% 1.33/1.57 tff(6822,plain,
% 1.33/1.57 (b(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[752, 6821])).
% 1.33/1.57 tff(6823,plain,
% 1.33/1.57 (~b(s(z), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4051, 6822, 1, 6798])).
% 1.33/1.57 tff(6824,plain,
% 1.33/1.57 (r(s(z), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[653, 6823])).
% 1.33/1.57 tff(6825,plain,
% 1.33/1.57 (~r(s(z), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5333, 6824, 6686])).
% 1.33/1.57 tff(6826,plain,
% 1.33/1.57 (b(s(z), s(s(z)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1071, 6825])).
% 1.33/1.57 tff(6827,plain,
% 1.33/1.57 (~b(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4989, 224, 6826, 6802, 6807])).
% 1.33/1.57 tff(6828,plain,
% 1.33/1.57 (r(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[925, 6827])).
% 1.33/1.57 tff(6829,plain,
% 1.33/1.57 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5351, 112, 6800, 6828])).
% 1.33/1.57 tff(6830,plain,
% 1.33/1.57 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[135, 68, 132, 6829])).
% 1.33/1.57 tff(6831,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6315, 224, 6822, 6812, 6254, 6830])).
% 1.33/1.57 tff(6832,plain,((~b(s(z), z)) | (z = elem!1) | b(s(s(s(z))), z) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6833,plain,
% 1.33/1.57 (~b(s(z), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6832, 3, 12, 4, 2])).
% 1.33/1.57 tff(6834,plain,
% 1.33/1.57 (r(s(z), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[194, 6833])).
% 1.33/1.57 tff(6835,plain,
% 1.33/1.57 (~r(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[187, 6834, 73])).
% 1.33/1.57 tff(6836,plain,
% 1.33/1.57 (b(s(z), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[175, 6835])).
% 1.33/1.57 tff(6837,plain,
% 1.33/1.57 (~r(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[932, 112, 6834, 73])).
% 1.33/1.57 tff(6838,plain,
% 1.33/1.57 (b(s(s(s(z))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[925, 6837])).
% 1.33/1.57 tff(6839,plain,
% 1.33/1.57 (~b(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6404, 6838, 6254, 6836])).
% 1.33/1.57 tff(6840,plain,
% 1.33/1.57 (r(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5459, 6839])).
% 1.33/1.57 tff(6841,plain,
% 1.33/1.57 (~r(z, elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5737, 6840, 73, 2])).
% 1.33/1.57 tff(6842,plain,
% 1.33/1.57 (b(z, elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[289, 6841, 4])).
% 1.33/1.57 tff(6843,plain,
% 1.33/1.57 (~r(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6329, 6840, 6254, 2, 73])).
% 1.33/1.57 tff(6844,plain,
% 1.33/1.57 (b(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[593, 6843])).
% 1.33/1.57 tff(6845,plain,
% 1.33/1.57 (~b(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6404, 3434, 6255, 3413])).
% 1.33/1.57 tff(6846,plain,
% 1.33/1.57 (r(z, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5459, 6845])).
% 1.33/1.57 tff(6847,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.57 tff(6848,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6704, 112, 4569, 293, 177, 6847])).
% 1.33/1.57 tff(6849,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6850,plain,
% 1.33/1.57 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6849, 293, 4569, 177])).
% 1.33/1.57 tff(6851,plain,
% 1.33/1.57 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[135, 68, 308, 6850])).
% 1.33/1.57 tff(6852,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2158, 224, 2252, 1241, 560, 968])).
% 1.33/1.57 tff(6853,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6854,plain,
% 1.33/1.57 (~b(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6853, 6851, 560, 2252])).
% 1.33/1.57 tff(6855,plain,
% 1.33/1.57 (r(s(s(elem!1)), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[901, 6854])).
% 1.33/1.57 tff(6856,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 6855, 293])).
% 1.33/1.57 tff(6857,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6858,plain,
% 1.33/1.57 (~r(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6857, 2252, 3434, 6846, 132, 73])).
% 1.33/1.57 tff(6859,plain,
% 1.33/1.57 (b(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[752, 6858])).
% 1.33/1.57 tff(6860,plain,
% 1.33/1.57 (~r(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6329, 6846, 6255, 2, 73])).
% 1.33/1.57 tff(6861,plain,
% 1.33/1.57 (b(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[593, 6860])).
% 1.33/1.57 tff(6862,plain,
% 1.33/1.57 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[3407, 405, 344, 1240])).
% 1.33/1.57 tff(6863,plain,
% 1.33/1.57 (r(s(s(elem!1)), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[360, 6862, 353])).
% 1.33/1.57 tff(6864,plain,
% 1.33/1.57 (~r(s(s(s(z))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[5988, 6863, 2252, 2, 1090])).
% 1.33/1.57 tff(6865,plain,
% 1.33/1.57 (b(s(s(s(z))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[374, 6864, 2438])).
% 1.33/1.57 tff(6866,plain,
% 1.33/1.57 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[613, 405, 1180, 1240])).
% 1.33/1.57 tff(6867,plain,
% 1.33/1.57 (r(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[558, 6866, 3])).
% 1.33/1.57 tff(6868,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6869,plain,
% 1.33/1.57 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6870,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6869])).
% 1.33/1.57 tff(6871,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[6870, 6868])).
% 1.33/1.57 tff(6872,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(6873,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6872, 6871])).
% 1.33/1.57 tff(6874,plain,
% 1.33/1.57 (~r(elem!1, s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6873, 112, 6867, 73, 6847])).
% 1.33/1.57 tff(6875,plain,
% 1.33/1.57 (b(elem!1, s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[388, 6874, 3419])).
% 1.33/1.57 tff(6876,plain,
% 1.33/1.57 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(6877,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[6876])).
% 1.33/1.57 tff(6878,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[6877, 6427])).
% 1.33/1.57 tff(6879,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(6880,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[6879, 6878])).
% 1.33/1.57 tff(6881,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6880, 224, 344, 6875, 6865, 6255])).
% 1.33/1.57 tff(6882,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(6883,plain,
% 1.33/1.57 (~b(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6882, 6847, 6255, 344, 2252, 2, 3413, 3, 6861, 6859, 12])).
% 1.33/1.57 tff(6884,plain,
% 1.33/1.57 (r(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[403, 6883, 157])).
% 1.33/1.57 tff(6885,plain,
% 1.33/1.57 (~r(elem!1, s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[383, 112, 6884, 73])).
% 1.33/1.57 tff(6886,plain,
% 1.33/1.57 (~r(s(z), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2841, 6884, 179])).
% 1.33/1.57 tff(6887,plain,
% 1.33/1.57 (b(s(z), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[454, 6886, 91])).
% 1.33/1.57 tff(6888,plain,
% 1.33/1.57 (~r(elem!1, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1259, 6884, 179])).
% 1.33/1.57 tff(6889,plain,
% 1.33/1.57 (b(elem!1, s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1277, 6888, 83])).
% 1.33/1.58 tff(6890,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6742, 6887, 6861, 6859, 3, 6846, 344, 409, 6884, 6889])).
% 1.33/1.58 tff(6891,plain,
% 1.33/1.58 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[743, 6890, 6859, 344])).
% 1.33/1.58 tff(6892,plain,
% 1.33/1.58 (r(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[558, 6891, 3])).
% 1.33/1.58 tff(6893,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6894,plain,
% 1.33/1.58 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6895,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6894])).
% 1.33/1.58 tff(6896,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.58 inference(transitivity,[status(thm)],[6895, 6893])).
% 1.33/1.58 tff(6897,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(6898,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6897, 6896])).
% 1.33/1.58 tff(6899,plain,
% 1.33/1.58 (~r(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6898, 112, 6892, 6884, 6847])).
% 1.33/1.58 tff(6900,plain,
% 1.33/1.58 (s(s(s(z))) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[4200, 6899, 3413, 6887, 6885])).
% 1.33/1.58 tff(6901,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6900])).
% 1.33/1.58 tff(6902,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(symmetry,[status(thm)],[6901])).
% 1.33/1.58 tff(6903,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6890, 6902])).
% 1.33/1.58 tff(6904,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6484, 6903])).
% 1.33/1.58 tff(6905,plain,((~r(s(s(s(z))), s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), z)) | (elem!1 = z) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6906,plain,
% 1.33/1.58 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6905, 2252, 3, 344, 179, 157, 6255, 6484, 2, 12])).
% 1.33/1.58 tff(6907,plain,
% 1.33/1.58 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[135, 68, 132, 6906])).
% 1.33/1.58 tff(6908,plain,
% 1.33/1.58 (~b(s(s(elem!1)), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6853, 6907, 3434, 2252])).
% 1.33/1.58 tff(6909,plain,
% 1.33/1.58 (r(s(s(elem!1)), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[901, 6908])).
% 1.33/1.58 tff(6910,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2841, 363, 179])).
% 1.33/1.58 tff(6911,plain,
% 1.33/1.58 (b(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[454, 6910, 129])).
% 1.33/1.58 tff(6912,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[4200, 384, 370, 2083, 362, 6911])).
% 1.33/1.58 tff(6913,plain,((~r(elem!1, z)) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), z)) | (s(z) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6914,plain,
% 1.33/1.58 (~r(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6913, 362, 177, 91, 179])).
% 1.33/1.58 tff(6915,plain,
% 1.33/1.58 (b(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[403, 6914, 157])).
% 1.33/1.58 tff(6916,plain,
% 1.33/1.58 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3407, 6915, 344, 1240])).
% 1.33/1.58 tff(6917,plain,
% 1.33/1.58 (r(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[360, 6916, 353])).
% 1.33/1.58 tff(6918,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[4065, 6917, 887])).
% 1.33/1.58 tff(6919,plain,
% 1.33/1.58 (~r(s(s(s(z))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[5988, 6917, 2252, 2, 2083])).
% 1.33/1.58 tff(6920,plain,
% 1.33/1.58 (r(elem!1, s(s(s(z))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2951, 6919, 2083, 6916, 6918, 362])).
% 1.33/1.58 tff(6921,plain,
% 1.33/1.58 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[613, 6915, 1180, 1240])).
% 1.33/1.58 tff(6922,plain,
% 1.33/1.58 (r(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[558, 6921, 3])).
% 1.33/1.58 tff(6923,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6924,plain,
% 1.33/1.58 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6925,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6924])).
% 1.33/1.58 tff(6926,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[6925, 6923])).
% 1.33/1.58 tff(6927,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(6928,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 1.33/1.58 tff(6929,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6928, 112, 6922, 6917, 6920, 827])).
% 1.33/1.58 tff(6930,plain,((s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (elem!1 = z) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6931,plain,
% 1.33/1.58 (s(s(s(z))) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6930, 2252, 6554, 2, 6909, 3, 344, 6861, 6859, 157, 73, 179])).
% 1.33/1.58 tff(6932,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6931])).
% 1.33/1.58 tff(6933,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(symmetry,[status(thm)],[6932])).
% 1.33/1.58 tff(6934,plain,
% 1.33/1.58 (~b(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2437, 6931, 12])).
% 1.33/1.58 tff(6935,plain,
% 1.33/1.58 (r(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[403, 6934, 157])).
% 1.33/1.58 tff(6936,plain,
% 1.33/1.58 (~r(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1259, 6935, 179])).
% 1.33/1.58 tff(6937,plain,
% 1.33/1.58 (b(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1277, 6936, 83])).
% 1.33/1.58 tff(6938,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2841, 6935, 179])).
% 1.33/1.58 tff(6939,plain,
% 1.33/1.58 (b(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[454, 6938, 91])).
% 1.33/1.58 tff(6940,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6742, 6939, 6861, 6859, 3, 6846, 344, 409, 6935, 6937])).
% 1.33/1.58 tff(6941,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6940, 6933])).
% 1.33/1.58 tff(6942,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6484, 6941])).
% 1.33/1.58 tff(6943,plain,((~b(s(z), s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), z)) | (elem!1 = z) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6944,plain,
% 1.33/1.58 (~b(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6943, 6484, 3, 344, 179, 157, 12, 2, 6255])).
% 1.33/1.58 tff(6945,plain,
% 1.33/1.58 (r(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[653, 6944])).
% 1.33/1.58 tff(6946,plain,
% 1.33/1.58 (~r(z, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6325, 6945, 6846])).
% 1.33/1.58 tff(6947,plain,
% 1.33/1.58 (b(z, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[752, 6946])).
% 1.33/1.58 tff(6948,plain,
% 1.33/1.58 (~r(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6913, 362, 177, 149, 179])).
% 1.33/1.58 tff(6949,plain,
% 1.33/1.58 (b(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[403, 6948, 157])).
% 1.33/1.58 tff(6950,plain,
% 1.33/1.58 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[613, 6949, 1180, 1240])).
% 1.33/1.58 tff(6951,plain,
% 1.33/1.58 (r(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[558, 6950, 3])).
% 1.33/1.58 tff(6952,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6953,plain,
% 1.33/1.58 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6954,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6953])).
% 1.33/1.58 tff(6955,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[6954, 6952])).
% 1.33/1.58 tff(6956,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(6957,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 1.33/1.58 tff(6958,plain,
% 1.33/1.58 (~r(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6957, 112, 6951, 179, 656])).
% 1.33/1.58 tff(6959,plain,
% 1.33/1.58 (b(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1277, 6958, 88])).
% 1.33/1.58 tff(6960,plain,
% 1.33/1.58 (~b(elem!1, s(s(s(z))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3008, 224, 6959, 2083, 3001])).
% 1.33/1.58 tff(6961,plain,
% 1.33/1.58 (r(elem!1, s(s(s(z))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[388, 6960, 4197])).
% 1.33/1.58 tff(6962,plain,
% 1.33/1.58 (~b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3407, 6949, 344, 1240])).
% 1.33/1.58 tff(6963,plain,
% 1.33/1.58 (r(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[360, 6962, 353])).
% 1.33/1.58 tff(6964,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, 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)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6965,plain,
% 1.33/1.58 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(6966,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6965])).
% 1.33/1.58 tff(6967,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[6966, 6964])).
% 1.33/1.58 tff(6968,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(6969,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 1.33/1.58 tff(6970,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6969, 112, 6963, 6961, 827])).
% 1.33/1.58 tff(6971,plain,((s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(s(s(z))))) | (elem!1 = s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (elem!1 = z) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6972,plain,
% 1.33/1.58 (s(s(s(z))) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6971, 6554, 83, 179, 6945, 3, 344, 6861, 6947, 157, 73])).
% 1.33/1.58 tff(6973,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[6972])).
% 1.33/1.58 tff(6974,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(symmetry,[status(thm)],[6973])).
% 1.33/1.58 tff(6975,plain,
% 1.33/1.58 (~b(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2437, 6972, 12])).
% 1.33/1.58 tff(6976,plain,
% 1.33/1.58 (r(elem!1, z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[403, 6975, 157])).
% 1.33/1.58 tff(6977,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6510, 6947, 3, 157, 344, 6945, 6861])).
% 1.33/1.58 tff(6978,plain,
% 1.33/1.58 (b(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[454, 6977, 91])).
% 1.33/1.58 tff(6979,plain,
% 1.33/1.58 (~r(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1259, 6976, 179])).
% 1.33/1.58 tff(6980,plain,
% 1.33/1.58 (b(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1277, 6979, 83])).
% 1.33/1.58 tff(6981,plain,
% 1.33/1.58 (b(s(s(elem!1)), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6742, 6980, 6861, 6947, 3, 6846, 344, 409, 6978, 6976])).
% 1.33/1.58 tff(6982,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[6981, 6974])).
% 1.33/1.58 tff(6983,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6484, 6982])).
% 1.33/1.58 tff(6984,plain,(b(s(s(elem!1)), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), z)) | (elem!1 = z) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(6985,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6984, 3, 6842, 6834, 11, 12, 2, 6254])).
% 1.33/1.58 tff(6986,plain,
% 1.33/1.58 (~b(s(s(elem!1)), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[3206, 152, 2083, 3001])).
% 1.33/1.58 tff(6987,plain,
% 1.33/1.58 (r(s(s(elem!1)), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[901, 6986])).
% 1.33/1.58 tff(6988,plain,
% 1.33/1.58 (~b(z, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6404, 3001, 6255, 2083])).
% 1.33/1.58 tff(6989,plain,
% 1.33/1.58 (r(z, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[5459, 6988])).
% 1.33/1.58 tff(6990,plain,
% 1.33/1.58 (~r(z, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[5570, 112, 6989, 6987])).
% 1.33/1.58 tff(6991,plain,
% 1.33/1.58 (b(z, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[752, 6990])).
% 1.33/1.58 tff(6992,plain,
% 1.33/1.58 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[613, 405, 6991, 1240])).
% 1.33/1.58 tff(6993,plain,
% 1.33/1.58 (r(elem!1, s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[558, 6992, 3])).
% 1.33/1.58 tff(6994,plain,
% 1.33/1.58 (~r(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1001, 6993, 6987])).
% 1.33/1.58 tff(6995,plain,
% 1.33/1.58 (b(elem!1, s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1277, 6994, 88])).
% 1.33/1.58 tff(6996,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[4065, 6863, 6987])).
% 1.33/1.58 tff(6997,plain,
% 1.33/1.58 (b(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[454, 6996, 149])).
% 1.33/1.58 tff(6998,plain,
% 1.33/1.58 (~b(s(elem!1), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6548, 6997, 3, 1240, 6989, 344, 166, 6862, 6995])).
% 1.33/1.58 tff(6999,plain,
% 1.33/1.58 (r(s(elem!1), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[939, 6998, 303])).
% 1.33/1.58 tff(7000,plain,
% 1.33/1.58 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6557, 6999, 6863])).
% 1.33/1.58 tff(7001,plain,
% 1.33/1.58 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1521, 7000, 319])).
% 1.33/1.58 tff(7002,plain,
% 1.33/1.58 (~b(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[4154, 7001, 1240, 6991])).
% 1.33/1.58 tff(7003,plain,
% 1.33/1.58 (r(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[498, 7002])).
% 1.33/1.58 tff(7004,plain,
% 1.33/1.58 (~r(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[473, 112, 6999, 179, 7003])).
% 1.33/1.58 tff(7005,plain,
% 1.33/1.58 (b(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[670, 7004, 415])).
% 1.33/1.58 tff(7006,plain,
% 1.33/1.58 (~r(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[5576, 6987, 319, 6989])).
% 1.33/1.58 tff(7007,plain,
% 1.33/1.58 (b(s(elem!1), s(z))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1476, 7006, 166])).
% 1.33/1.58 tff(7008,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7009,plain,
% 1.33/1.58 (((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7010,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7009])).
% 1.33/1.58 tff(7011,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7010, 7008])).
% 1.33/1.58 tff(7012,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7013,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7012, 7011])).
% 1.33/1.58 tff(7014,plain,
% 1.33/1.58 (~b(s(s(s(z))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7013, 224, 7007, 7005, 3001])).
% 1.33/1.58 tff(7015,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), 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), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7016,plain,
% 1.33/1.58 (((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7017,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7016])).
% 1.33/1.59 tff(7018,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7017, 7015])).
% 1.33/1.59 tff(7019,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7020,plain,
% 1.33/1.59 ((~![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(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7019, 7018])).
% 1.33/1.59 tff(7021,plain,
% 1.33/1.59 (~r(s(s(s(z))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7020, 112, 6999, 7003, 177])).
% 1.33/1.59 tff(7022,plain,
% 1.33/1.59 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[816, 68, 7021])).
% 1.33/1.59 tff(7023,plain,
% 1.33/1.59 (s(s(s(z))) = s(elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7022, 7014])).
% 1.33/1.59 tff(7024,plain,
% 1.33/1.59 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7023])).
% 1.33/1.59 tff(7025,plain,
% 1.33/1.59 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.33/1.59 inference(symmetry,[status(thm)],[7024])).
% 1.33/1.59 tff(7026,plain,
% 1.33/1.59 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7025])).
% 1.33/1.59 tff(7027,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7028,plain,
% 1.33/1.59 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7029,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7028])).
% 1.33/1.59 tff(7030,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7029, 7027])).
% 1.33/1.59 tff(7031,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7032,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7031, 7030])).
% 1.33/1.59 tff(7033,plain,
% 1.33/1.59 (~b(z, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7032, 224, 7001, 6991, 152, 6255])).
% 1.33/1.59 tff(7034,plain,
% 1.33/1.59 (~b(z, s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7033, 7026])).
% 1.33/1.59 tff(7035,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6255, 7034])).
% 1.33/1.59 tff(7036,plain,((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7037,plain,
% 1.33/1.59 (~b(elem!1, z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7036, 6985, 6254, 73, 6834, 6844, 3, 6842, 160, 83])).
% 1.33/1.59 tff(7038,plain,
% 1.33/1.59 (r(elem!1, z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[403, 7037, 11])).
% 1.33/1.59 tff(7039,plain,
% 1.33/1.59 (s(s(s(z))) = elem!1),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6913, 7038, 73, 91, 6834])).
% 1.33/1.59 tff(7040,plain,
% 1.33/1.59 (s(s(s(s(z)))) = s(elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7039])).
% 1.33/1.59 tff(7041,plain,
% 1.33/1.59 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7040])).
% 1.33/1.59 tff(7042,plain,
% 1.33/1.59 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.33/1.59 inference(symmetry,[status(thm)],[7041])).
% 1.33/1.59 tff(7043,plain,
% 1.33/1.59 (~b(s(s(elem!1)), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3206, 6985, 6836, 6838])).
% 1.33/1.59 tff(7044,plain,
% 1.33/1.59 (r(s(s(elem!1)), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[901, 7043])).
% 1.33/1.59 tff(7045,plain,
% 1.33/1.59 (~r(z, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[5570, 112, 6840, 7044])).
% 1.33/1.59 tff(7046,plain,
% 1.33/1.59 (b(z, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[752, 7045])).
% 1.33/1.59 tff(7047,plain,
% 1.33/1.59 (~r(elem!1, s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1259, 7038, 6834])).
% 1.33/1.59 tff(7048,plain,
% 1.33/1.59 (b(elem!1, s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1277, 7047, 83])).
% 1.33/1.59 tff(7049,plain,
% 1.33/1.59 (~r(s(z), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2841, 7038, 6834])).
% 1.33/1.59 tff(7050,plain,
% 1.33/1.59 (b(s(z), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[454, 7049, 91])).
% 1.33/1.59 tff(7051,plain,
% 1.33/1.59 (b(s(s(elem!1)), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6742, 7050, 6844, 7046, 3, 6840, 6842, 160, 7038, 7048])).
% 1.33/1.59 tff(7052,plain,
% 1.33/1.59 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[743, 7051, 7046, 6842])).
% 1.33/1.59 tff(7053,plain,
% 1.33/1.59 (r(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[558, 7052, 3])).
% 1.33/1.59 tff(7054,plain,
% 1.33/1.59 (~r(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[4279, 7053, 6844, 319, 7046, 7038])).
% 1.33/1.59 tff(7055,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[939, 7054, 303])).
% 1.33/1.59 tff(7056,plain,
% 1.33/1.59 (b(s(s(s(s(z)))), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7055, 7042])).
% 1.33/1.59 tff(7057,plain,
% 1.33/1.59 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7039])).
% 1.33/1.59 tff(7058,plain,
% 1.33/1.59 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7057])).
% 1.33/1.59 tff(7059,plain,
% 1.33/1.59 (~r(s(elem!1), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[5576, 7044, 319, 6840])).
% 1.33/1.59 tff(7060,plain,
% 1.33/1.59 (b(s(elem!1), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1476, 7059, 160])).
% 1.33/1.59 tff(7061,plain,
% 1.33/1.59 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[4136, 7039, 7060])).
% 1.33/1.59 tff(7062,plain,
% 1.33/1.59 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1579, 7061, 6836, 6838])).
% 1.33/1.59 tff(7063,plain,
% 1.33/1.59 (~b(s(s(s(s(z)))), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7062, 7058])).
% 1.33/1.59 tff(7064,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7063, 7056])).
% 1.33/1.59 tff(7065,plain,((elem!1 = s(s(elem!1))) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7066,plain,
% 1.33/1.59 (b(s(s(s(z))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7065, 4, 2, 3])).
% 1.33/1.59 tff(7067,plain,
% 1.33/1.59 (r(z, elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[289, 4, 4538])).
% 1.33/1.59 tff(7068,plain,
% 1.33/1.59 (z = elem!1),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7065, 12, 2, 3])).
% 1.33/1.59 tff(7069,plain,
% 1.33/1.59 (s(z) = s(elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7070,plain,
% 1.33/1.59 (s(s(z)) = s(s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7069])).
% 1.33/1.59 tff(7071,plain,
% 1.33/1.59 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7070])).
% 1.33/1.59 tff(7072,plain,
% 1.33/1.59 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7071])).
% 1.33/1.59 tff(7073,plain,
% 1.33/1.59 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7074,plain,
% 1.33/1.59 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7073])).
% 1.33/1.59 tff(7075,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[1614, 7074])).
% 1.33/1.59 tff(7076,plain,
% 1.33/1.59 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3878, 7068])).
% 1.33/1.59 tff(7077,plain,
% 1.33/1.59 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7078,plain,
% 1.33/1.59 (r(s(s(s(z))), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[73, 7077])).
% 1.33/1.59 tff(7079,plain,
% 1.33/1.59 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[4692, 3340, 7068, 7078])).
% 1.33/1.59 tff(7080,plain,
% 1.33/1.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3905, 7079, 7076])).
% 1.33/1.59 tff(7081,plain,
% 1.33/1.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.33/1.59 inference(symmetry,[status(thm)],[7071])).
% 1.33/1.59 tff(7082,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7081])).
% 1.33/1.59 tff(7083,plain,
% 1.33/1.59 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.33/1.59 inference(symmetry,[status(thm)],[7082])).
% 1.33/1.59 tff(7084,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7078, 7083])).
% 1.33/1.59 tff(7085,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1716, 7068])).
% 1.33/1.59 tff(7086,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1735, 7068])).
% 1.33/1.59 tff(7087,plain,
% 1.33/1.59 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7070])).
% 1.33/1.59 tff(7088,plain,
% 1.33/1.59 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7087, 7072])).
% 1.33/1.59 tff(7089,plain,
% 1.33/1.59 (~r(s(z), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[187, 73, 178])).
% 1.33/1.59 tff(7090,plain,
% 1.33/1.59 (b(s(z), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[194, 7089])).
% 1.33/1.59 tff(7091,plain,
% 1.33/1.59 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.33/1.59 inference(symmetry,[status(thm)],[3942])).
% 1.33/1.59 tff(7092,plain,
% 1.33/1.59 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7091])).
% 1.33/1.59 tff(7093,plain,
% 1.33/1.59 (~b(s(s(elem!1)), z)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[354, 7092])).
% 1.33/1.59 tff(7094,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1240, 7093])).
% 1.33/1.59 tff(7095,plain,((~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7096,plain,
% 1.33/1.59 (~b(s(s(elem!1)), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7095, 354, 7068])).
% 1.33/1.59 tff(7097,plain,
% 1.33/1.59 (r(s(s(elem!1)), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[593, 7096])).
% 1.33/1.59 tff(7098,plain,
% 1.33/1.59 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7081])).
% 1.33/1.59 tff(7099,plain,
% 1.33/1.59 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.33/1.59 inference(symmetry,[status(thm)],[7098])).
% 1.33/1.59 tff(7100,plain,
% 1.33/1.59 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7101,plain,
% 1.33/1.59 (b(elem!1, s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[6255, 7100])).
% 1.33/1.59 tff(7102,plain,
% 1.33/1.59 (b(elem!1, s(s(s(elem!1))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7101, 7099])).
% 1.33/1.59 tff(7103,plain,
% 1.33/1.59 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7071, 7069])).
% 1.33/1.59 tff(7104,plain,
% 1.33/1.59 (s(elem!1) = s(z)),
% 1.33/1.59 inference(symmetry,[status(thm)],[7069])).
% 1.33/1.59 tff(7105,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7081, 7104])).
% 1.33/1.59 tff(7106,plain,
% 1.33/1.59 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7105])).
% 1.33/1.59 tff(7107,plain,
% 1.33/1.59 (~r(z, s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6329, 73, 6255, 2, 102])).
% 1.33/1.59 tff(7108,plain,
% 1.33/1.59 (b(z, s(z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[5459, 7107])).
% 1.33/1.59 tff(7109,plain,
% 1.33/1.59 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[243, 7090, 178, 7108, 73])).
% 1.33/1.59 tff(7110,plain,
% 1.33/1.59 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[249, 7109])).
% 1.33/1.59 tff(7111,plain,
% 1.33/1.59 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7110, 7087])).
% 1.33/1.59 tff(7112,plain,
% 1.33/1.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7111, 7072])).
% 1.33/1.59 tff(7113,plain,
% 1.33/1.59 (elem!1 = z),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[338, 7068])).
% 1.33/1.59 tff(7114,plain,
% 1.33/1.59 (r(s(s(elem!1)), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[333, 7113, 102])).
% 1.33/1.59 tff(7115,plain,
% 1.33/1.59 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[4689, 112, 7114, 7084])).
% 1.33/1.59 tff(7116,plain,
% 1.33/1.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[3905, 7115, 7076])).
% 1.33/1.59 tff(7117,plain,
% 1.33/1.59 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1772, 7116, 7114, 7086, 7085, 7084, 7112])).
% 1.33/1.59 tff(7118,plain,
% 1.33/1.59 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1777, 7117, 7075])).
% 1.33/1.59 tff(7119,plain,
% 1.33/1.59 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7069])).
% 1.33/1.59 tff(7120,plain,
% 1.33/1.59 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7121,plain,
% 1.33/1.59 (b(s(z), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7090, 7120])).
% 1.33/1.59 tff(7122,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7121, 7119])).
% 1.33/1.59 tff(7123,plain,
% 1.33/1.59 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7069])).
% 1.33/1.59 tff(7124,plain,
% 1.33/1.59 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.33/1.59 tff(7125,plain,
% 1.33/1.59 (b(elem!1, s(z))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7108, 7124])).
% 1.33/1.59 tff(7126,plain,
% 1.33/1.59 (b(elem!1, s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7125, 7123])).
% 1.33/1.59 tff(7127,plain,
% 1.33/1.59 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1845, 224, 7126, 7122, 7118])).
% 1.33/1.59 tff(7128,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1853, 7068])).
% 1.33/1.59 tff(7129,plain,
% 1.33/1.59 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1857, 68, 7128, 7127])).
% 1.33/1.59 tff(7130,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7131,plain,
% 1.33/1.59 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7132,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7131])).
% 1.33/1.59 tff(7133,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7132, 7130])).
% 1.33/1.59 tff(7134,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7135,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7134, 7133])).
% 1.33/1.59 tff(7136,plain,
% 1.33/1.59 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7135, 224, 7116, 7102, 7112])).
% 1.33/1.59 tff(7137,plain,
% 1.33/1.59 (r(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[558, 7136, 3])).
% 1.33/1.59 tff(7138,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.33/1.59 tff(7139,plain,
% 1.33/1.59 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.33/1.59 inference(symmetry,[status(thm)],[7138])).
% 1.33/1.59 tff(7140,assumption,(~(s(s(s(s(s(s(s(z))))))) = elem!1)), introduced(assumption)).
% 1.33/1.59 tff(7141,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7140, 7139])).
% 1.33/1.59 tff(7142,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7143,plain,
% 1.33/1.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7142, 7075])).
% 1.33/1.59 tff(7144,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.33/1.59 tff(7145,assumption,(r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.33/1.59 tff(7146,plain,
% 1.33/1.59 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1995, 112, 7145])).
% 1.33/1.59 tff(7147,plain,
% 1.33/1.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7146, 7144])).
% 1.33/1.59 tff(7148,plain,
% 1.33/1.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1751, 68, 1748, 7147])).
% 1.33/1.59 tff(7149,plain,
% 1.33/1.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2002, 224, 1698, 1737, 7148])).
% 1.33/1.59 tff(7150,plain,
% 1.33/1.59 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1763, 68, 1760, 7149])).
% 1.33/1.59 tff(7151,plain,
% 1.33/1.59 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2010, 112, 545, 7150])).
% 1.33/1.59 tff(7152,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.33/1.59 tff(7153,plain,
% 1.33/1.59 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.33/1.59 inference(commutativity,[status(thm)],[])).
% 1.33/1.59 tff(7154,plain,
% 1.33/1.59 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.33/1.59 inference(symmetry,[status(thm)],[7153])).
% 1.33/1.59 tff(7155,plain,
% 1.33/1.59 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7154])).
% 1.33/1.59 tff(7156,plain,
% 1.33/1.59 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[1748, 7155])).
% 1.33/1.59 tff(7157,plain,
% 1.33/1.59 (((~![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))), s(elem!1))) | (~r(s(s(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(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7158,plain,
% 1.33/1.59 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7159,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7158])).
% 1.33/1.59 tff(7160,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7159, 7157])).
% 1.33/1.59 tff(7161,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7162,plain,
% 1.33/1.59 ((~![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))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 1.33/1.59 tff(7163,plain,
% 1.33/1.59 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7162, 112, 7145])).
% 1.33/1.59 tff(7164,plain,
% 1.33/1.59 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7163, 7144])).
% 1.33/1.59 tff(7165,plain,
% 1.33/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7166,plain,
% 1.43/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7167,plain,
% 1.43/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7166, 7165])).
% 1.43/1.60 tff(7168,plain,
% 1.43/1.60 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7167, 68, 7164])).
% 1.43/1.60 tff(7169,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7168, 7156])).
% 1.43/1.60 tff(7170,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.60 tff(7171,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7172,plain,
% 1.43/1.60 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7173,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7172])).
% 1.43/1.60 tff(7174,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7173, 7171])).
% 1.43/1.60 tff(7175,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7176,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7175, 7174])).
% 1.43/1.60 tff(7177,plain,
% 1.43/1.60 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7176, 224, 7170, 7148, 7169])).
% 1.43/1.60 tff(7178,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2014, 68, 7177, 7152, 7151])).
% 1.43/1.60 tff(7179,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7180,plain,
% 1.43/1.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7179, 7143, 7137, 7102, 7085, 7116, 7112, 7086, 7129])).
% 1.43/1.60 tff(7181,plain,
% 1.43/1.60 (~r(s(s(s(z))), s(z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7180, 7106])).
% 1.43/1.60 tff(7182,plain,
% 1.43/1.60 (b(s(s(s(z))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[925, 7181])).
% 1.43/1.60 tff(7183,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7182, 7103])).
% 1.43/1.60 tff(7184,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.60 tff(7185,plain,
% 1.43/1.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2002, 224, 1698, 1737, 7184])).
% 1.43/1.60 tff(7186,plain,
% 1.43/1.60 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1763, 68, 1760, 7185])).
% 1.43/1.60 tff(7187,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7188,plain,
% 1.43/1.60 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7189,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7188])).
% 1.43/1.60 tff(7190,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7189, 7187])).
% 1.43/1.60 tff(7191,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7192,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7191, 7190])).
% 1.43/1.60 tff(7193,plain,
% 1.43/1.60 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7192, 224, 501, 4651, 7170, 7184])).
% 1.43/1.60 tff(7194,plain,
% 1.43/1.60 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2014, 68, 7193, 7152])).
% 1.43/1.60 tff(7195,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2010, 112, 545, 7194, 7186])).
% 1.43/1.60 tff(7196,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7197,plain,
% 1.43/1.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7196, 7137, 7085, 7143, 7116, 7112, 7126, 7183, 7102])).
% 1.43/1.60 tff(7198,plain,
% 1.43/1.60 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1751, 68, 7086, 7197])).
% 1.43/1.60 tff(7199,plain,
% 1.43/1.60 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7081])).
% 1.43/1.60 tff(7200,plain,
% 1.43/1.60 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[7199])).
% 1.43/1.60 tff(7201,plain,
% 1.43/1.60 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7069])).
% 1.43/1.60 tff(7202,plain,
% 1.43/1.60 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[178, 7201])).
% 1.43/1.60 tff(7203,plain,
% 1.43/1.60 (r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7202, 7200])).
% 1.43/1.60 tff(7204,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1971, 112, 7203, 7129, 7198])).
% 1.43/1.60 tff(7205,plain,(b(s(s(s(z))), z) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7206,plain,
% 1.43/1.60 (~b(z, s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7205, 7097, 178, 12, 3, 2])).
% 1.43/1.60 tff(7207,plain,
% 1.43/1.60 (r(z, s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[100, 7206])).
% 1.43/1.60 tff(7208,plain,
% 1.43/1.60 (~r(z, s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[5470, 7207, 178])).
% 1.43/1.60 tff(7209,plain,
% 1.43/1.60 (b(z, s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[5459, 7208])).
% 1.43/1.60 tff(7210,plain,
% 1.43/1.60 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[243, 7209, 178, 7090, 73])).
% 1.43/1.60 tff(7211,plain,
% 1.43/1.60 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[249, 7210])).
% 1.43/1.60 tff(7212,plain,
% 1.43/1.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7211, 7088])).
% 1.43/1.60 tff(7213,plain,
% 1.43/1.60 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1772, 7212, 3340, 7086, 7085, 7084, 7080])).
% 1.43/1.60 tff(7214,plain,
% 1.43/1.60 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1777, 7213, 7075])).
% 1.43/1.60 tff(7215,plain,
% 1.43/1.60 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7124, 7123])).
% 1.43/1.60 tff(7216,plain,
% 1.43/1.60 (b(elem!1, s(elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7209, 7215])).
% 1.43/1.60 tff(7217,plain,
% 1.43/1.60 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1845, 224, 7216, 7122, 7214])).
% 1.43/1.60 tff(7218,plain,
% 1.43/1.60 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1857, 68, 7128, 7217])).
% 1.43/1.60 tff(7219,plain,
% 1.43/1.60 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7068])).
% 1.43/1.60 tff(7220,plain,
% 1.43/1.60 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.43/1.60 inference(symmetry,[status(thm)],[7219])).
% 1.43/1.60 tff(7221,plain,
% 1.43/1.60 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7124, 7123, 7220])).
% 1.43/1.60 tff(7222,plain,
% 1.43/1.60 (b(z, s(elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7209, 7221])).
% 1.43/1.60 tff(7223,plain,
% 1.43/1.60 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7068])).
% 1.43/1.60 tff(7224,plain,
% 1.43/1.60 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[7223])).
% 1.43/1.60 tff(7225,plain,
% 1.43/1.60 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7224])).
% 1.43/1.60 tff(7226,plain,
% 1.43/1.60 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7227,plain,
% 1.43/1.60 (~r(elem!1, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7226, 5125])).
% 1.43/1.60 tff(7228,plain,
% 1.43/1.60 (~r(z, elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7227, 7225])).
% 1.43/1.60 tff(7229,plain,
% 1.43/1.60 (~r(z, s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2332, 7209, 73, 7097, 3, 83, 7206, 7228])).
% 1.43/1.60 tff(7230,plain,
% 1.43/1.60 (b(z, s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[752, 7229])).
% 1.43/1.60 tff(7231,plain,
% 1.43/1.60 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7069])).
% 1.43/1.60 tff(7232,plain,
% 1.43/1.60 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7068])).
% 1.43/1.60 tff(7233,plain,
% 1.43/1.60 (r(elem!1, s(s(s(z))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7207, 7232])).
% 1.43/1.60 tff(7234,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1388, 1384])).
% 1.43/1.60 tff(7235,plain,
% 1.43/1.60 (s(s(s(s(elem!1)))) = elem!1),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1380, 7234])).
% 1.43/1.60 tff(7236,plain,
% 1.43/1.60 (elem!1 = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[7235])).
% 1.43/1.60 tff(7237,plain,
% 1.43/1.60 (elem!1 = s(s(elem!1))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7236, 1384])).
% 1.43/1.60 tff(7238,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3, 7237])).
% 1.43/1.60 tff(7239,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7240,plain,
% 1.43/1.60 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7239, 3])).
% 1.43/1.60 tff(7241,plain,
% 1.43/1.60 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7070])).
% 1.43/1.60 tff(7242,plain,
% 1.43/1.60 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7068])).
% 1.43/1.60 tff(7243,plain,
% 1.43/1.60 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7242, 7241])).
% 1.43/1.60 tff(7244,plain,
% 1.43/1.60 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1637])).
% 1.43/1.60 tff(7245,plain,
% 1.43/1.60 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1619])).
% 1.43/1.60 tff(7246,plain,
% 1.43/1.60 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[335])).
% 1.43/1.60 tff(7247,plain,
% 1.43/1.60 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7246, 7245, 7244])).
% 1.43/1.60 tff(7248,plain,
% 1.43/1.60 (r(z, s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3750, 7247])).
% 1.43/1.60 tff(7249,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[749, 7248])).
% 1.43/1.60 tff(7250,plain,((~r(z, s(s(z)))) | r(z, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7251,plain,
% 1.43/1.60 (~r(z, s(s(z)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7250, 7229, 7068])).
% 1.43/1.60 tff(7252,plain,
% 1.43/1.60 (b(z, s(s(z)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1088, 7251])).
% 1.43/1.60 tff(7253,plain,
% 1.43/1.60 (b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7252, 7243])).
% 1.43/1.60 tff(7254,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1710])).
% 1.43/1.60 tff(7255,plain,
% 1.43/1.60 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3878, 335])).
% 1.43/1.60 tff(7256,plain,
% 1.43/1.60 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[4692, 1181, 335, 690])).
% 1.43/1.60 tff(7257,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3905, 7256, 7255])).
% 1.43/1.60 tff(7258,plain,
% 1.43/1.60 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1617])).
% 1.43/1.60 tff(7259,plain,
% 1.43/1.60 (r(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[656, 7258])).
% 1.43/1.60 tff(7260,plain,
% 1.43/1.60 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1878, 7259, 1488, 501, 1737, 7257, 1181, 690, 335, 1020])).
% 1.43/1.60 tff(7261,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1884, 7260])).
% 1.43/1.60 tff(7262,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7261, 1699])).
% 1.43/1.60 tff(7263,plain,
% 1.43/1.60 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2029, 1020, 1737, 1181, 335, 7257])).
% 1.43/1.60 tff(7264,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1294, 7263, 1733])).
% 1.43/1.60 tff(7265,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7266,plain,
% 1.43/1.60 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7267,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7266])).
% 1.43/1.60 tff(7268,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7267, 7265])).
% 1.43/1.60 tff(7269,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7270,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7269, 7268])).
% 1.43/1.60 tff(7271,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7270, 224, 682, 7264, 7262, 1737])).
% 1.43/1.60 tff(7272,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1401, 68, 7271, 2287])).
% 1.43/1.60 tff(7273,plain,
% 1.43/1.60 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7272, 7254])).
% 1.43/1.60 tff(7274,plain,
% 1.43/1.60 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1687, 1617])).
% 1.43/1.60 tff(7275,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.43/1.60 inference(symmetry,[status(thm)],[7274])).
% 1.43/1.60 tff(7276,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2054, 224, 501, 1488, 7264])).
% 1.43/1.60 tff(7277,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1345, 7276, 1832])).
% 1.43/1.60 tff(7278,plain,
% 1.43/1.60 (r(s(s(s(s(z)))), s(z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7277, 7275])).
% 1.43/1.60 tff(7279,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3154, 112, 656, 3317, 3136])).
% 1.43/1.60 tff(7280,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7281,plain,
% 1.43/1.60 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7280, 656, 7278])).
% 1.43/1.60 tff(7282,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7281, 7273])).
% 1.43/1.60 tff(7283,plain,((~r(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7284,plain,
% 1.43/1.60 (~r(s(z), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7283, 7253, 7240, 7068, 7212, 7122, 7216, 3340, 7078, 7233])).
% 1.43/1.60 tff(7285,plain,
% 1.43/1.60 (b(s(z), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[653, 7284])).
% 1.43/1.60 tff(7286,plain,
% 1.43/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7285, 7231])).
% 1.43/1.60 tff(7287,plain,
% 1.43/1.60 (~b(s(s(elem!1)), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[4124, 7286, 7230, 7222])).
% 1.43/1.60 tff(7288,plain,
% 1.43/1.60 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[530, 7287, 526])).
% 1.43/1.60 tff(7289,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7290,plain,
% 1.43/1.60 (((~r(s(s(elem!1)), s(elem!1))) | (~r(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(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7291,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(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(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(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7290])).
% 1.43/1.60 tff(7292,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(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(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(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7291, 7289])).
% 1.43/1.61 tff(7293,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(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(z))))))), s(s(elem!1)))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7294,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 1.43/1.61 tff(7295,plain,
% 1.43/1.61 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7294, 112, 7288, 7218])).
% 1.43/1.61 tff(7296,plain,
% 1.43/1.61 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7068])).
% 1.43/1.61 tff(7297,plain,
% 1.43/1.61 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7296])).
% 1.43/1.61 tff(7298,plain,
% 1.43/1.61 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1334, 7297])).
% 1.43/1.61 tff(7299,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2029, 7233, 7212, 3340, 7068, 7080])).
% 1.43/1.61 tff(7300,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1294, 7299, 7298])).
% 1.43/1.61 tff(7301,plain,
% 1.43/1.61 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1682, 7113])).
% 1.43/1.61 tff(7302,plain,
% 1.43/1.61 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1831, 7301])).
% 1.43/1.61 tff(7303,plain,
% 1.43/1.61 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1834, 7068])).
% 1.43/1.61 tff(7304,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.61 tff(7305,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.43/1.61 tff(7306,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7307,plain,
% 1.43/1.61 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7308,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7307])).
% 1.43/1.61 tff(7309,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7308, 7306])).
% 1.43/1.61 tff(7310,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(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(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7311,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7310, 7309])).
% 1.43/1.61 tff(7312,plain,
% 1.43/1.61 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7311, 224, 682, 3919, 7305, 7304])).
% 1.43/1.61 tff(7313,plain,
% 1.43/1.61 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1838, 68, 2041, 7312])).
% 1.43/1.61 tff(7314,plain,
% 1.43/1.61 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2054, 224, 501, 1488, 3919])).
% 1.43/1.61 tff(7315,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1345, 7314, 1286])).
% 1.43/1.61 tff(7316,plain,
% 1.43/1.61 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7317,plain,
% 1.43/1.61 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7318,plain,
% 1.43/1.61 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7317])).
% 1.43/1.61 tff(7319,plain,
% 1.43/1.61 (((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7318, 7316])).
% 1.43/1.61 tff(7320,plain,
% 1.43/1.61 ((~![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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7321,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7320, 7319])).
% 1.43/1.61 tff(7322,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7321, 112, 7315, 7145, 7313])).
% 1.43/1.61 tff(7323,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(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))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7324,plain,
% 1.43/1.61 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7323, 7218, 7303, 7302, 7216, 7122, 7253, 7214, 7300])).
% 1.43/1.61 tff(7325,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1763, 68, 7085, 7324, 7295])).
% 1.43/1.61 tff(7326,plain,(b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7327,plain,
% 1.43/1.61 (b(s(s(elem!1)), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7326, 12, 178, 3, 2])).
% 1.43/1.61 tff(7328,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1620])).
% 1.43/1.61 tff(7329,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1619])).
% 1.43/1.61 tff(7330,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7329, 7328])).
% 1.43/1.61 tff(7331,plain,
% 1.43/1.61 (~r(s(z), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[187, 177, 178])).
% 1.43/1.61 tff(7332,plain,
% 1.43/1.61 (b(s(z), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[194, 7331])).
% 1.43/1.61 tff(7333,plain,
% 1.43/1.61 (b(s(s(elem!1)), z)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[390, 7091])).
% 1.43/1.61 tff(7334,plain,
% 1.43/1.61 (~b(z, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4051, 2252, 7332, 7333])).
% 1.43/1.61 tff(7335,plain,
% 1.43/1.61 (r(z, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[752, 7334])).
% 1.43/1.61 tff(7336,plain,
% 1.43/1.61 (~b(s(s(s(z))), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6857, 4569, 308, 177, 293, 2252])).
% 1.43/1.61 tff(7337,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[925, 7336, 5772])).
% 1.43/1.61 tff(7338,plain,((~r(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7339,plain,
% 1.43/1.61 (~r(z, s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7338, 7335, 177, 308, 2252])).
% 1.43/1.61 tff(7340,plain,
% 1.43/1.61 (b(z, s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[5459, 7339])).
% 1.43/1.61 tff(7341,plain,
% 1.43/1.61 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[243, 7340, 178, 7332, 177])).
% 1.43/1.61 tff(7342,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[249, 7341])).
% 1.43/1.61 tff(7343,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7342, 7330])).
% 1.43/1.61 tff(7344,plain,
% 1.43/1.61 (b(s(z), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7332, 1927])).
% 1.43/1.61 tff(7345,plain,
% 1.43/1.61 (~b(elem!1, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3685, 2252, 7344, 390])).
% 1.43/1.61 tff(7346,plain,
% 1.43/1.61 (r(elem!1, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[558, 7345, 3])).
% 1.43/1.61 tff(7347,plain,
% 1.43/1.61 (b(s(elem!1), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7344, 1926])).
% 1.43/1.61 tff(7348,plain,
% 1.43/1.61 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1634, 1633])).
% 1.43/1.61 tff(7349,plain,
% 1.43/1.61 (b(elem!1, s(elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7340, 7348])).
% 1.43/1.61 tff(7350,plain,
% 1.43/1.61 (~b(s(s(elem!1)), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1249, 7340, 7332, 7333])).
% 1.43/1.61 tff(7351,plain,
% 1.43/1.61 (r(s(s(elem!1)), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[901, 7350])).
% 1.43/1.61 tff(7352,plain,
% 1.43/1.61 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7351, 1929])).
% 1.43/1.61 tff(7353,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.61 tff(7354,plain,
% 1.43/1.61 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3896, 1785, 545])).
% 1.43/1.61 tff(7355,plain,
% 1.43/1.61 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3903, 68, 7354])).
% 1.43/1.61 tff(7356,plain,
% 1.43/1.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7355, 4553])).
% 1.43/1.61 tff(7357,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3915, 7356, 545, 1737, 335, 1020])).
% 1.43/1.61 tff(7358,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1294, 7357, 1733])).
% 1.43/1.61 tff(7359,plain,
% 1.43/1.61 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2054, 224, 501, 1488, 7358])).
% 1.43/1.61 tff(7360,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1345, 7359, 1832])).
% 1.43/1.61 tff(7361,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3939, 112, 544, 7360])).
% 1.43/1.61 tff(7362,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1401, 68, 1694, 7361])).
% 1.43/1.61 tff(7363,plain,
% 1.43/1.61 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3949, 224, 7358, 390, 7356])).
% 1.43/1.61 tff(7364,plain,
% 1.43/1.61 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7363, 7362])).
% 1.43/1.61 tff(7365,plain,
% 1.43/1.61 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7364, 3933])).
% 1.43/1.61 tff(7366,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1884, 7365])).
% 1.43/1.61 tff(7367,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7366, 1786])).
% 1.43/1.61 tff(7368,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4855, 112, 7360, 7367, 7353])).
% 1.43/1.61 tff(7369,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7370,plain,
% 1.43/1.61 (~r(elem!1, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7369, 7352, 4719, 390, 7349, 7347, 7346, 7343, 335])).
% 1.43/1.61 tff(7371,plain,
% 1.43/1.61 (b(elem!1, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[388, 7370, 4561])).
% 1.43/1.61 tff(7372,plain,
% 1.43/1.61 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7371, 4559])).
% 1.43/1.61 tff(7373,plain,
% 1.43/1.61 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1383])).
% 1.43/1.61 tff(7374,plain,
% 1.43/1.61 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7240, 7373])).
% 1.43/1.61 tff(7375,plain,
% 1.43/1.61 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[243, 77, 178, 7332, 177])).
% 1.43/1.61 tff(7376,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[249, 7375])).
% 1.43/1.61 tff(7377,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7376, 7330])).
% 1.43/1.61 tff(7378,plain,
% 1.43/1.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1621])).
% 1.43/1.61 tff(7379,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7378])).
% 1.43/1.61 tff(7380,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1621])).
% 1.43/1.61 tff(7381,plain,
% 1.43/1.61 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7380])).
% 1.43/1.61 tff(7382,plain,
% 1.43/1.61 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7383,plain,
% 1.43/1.61 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7384,plain,
% 1.43/1.61 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7383])).
% 1.43/1.61 tff(7385,plain,
% 1.43/1.61 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7384, 7382])).
% 1.43/1.61 tff(7386,plain,
% 1.43/1.61 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7387,plain,
% 1.43/1.61 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7386, 7385])).
% 1.43/1.61 tff(7388,plain,
% 1.43/1.61 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7387, 112, 1798, 1739])).
% 1.43/1.61 tff(7389,plain,
% 1.43/1.61 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7388, 7381])).
% 1.43/1.61 tff(7390,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[5426, 7389])).
% 1.43/1.61 tff(7391,plain,
% 1.43/1.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7390, 7379])).
% 1.43/1.61 tff(7392,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1786])).
% 1.43/1.61 tff(7393,plain,
% 1.43/1.61 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7392])).
% 1.43/1.61 tff(7394,plain,
% 1.43/1.61 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7395,plain,
% 1.43/1.62 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7396,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7395])).
% 1.43/1.62 tff(7397,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7396, 7394])).
% 1.43/1.62 tff(7398,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7399,plain,
% 1.43/1.62 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7398, 7397])).
% 1.43/1.62 tff(7400,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7399, 112, 1798, 1739])).
% 1.43/1.62 tff(7401,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7400, 7393])).
% 1.43/1.62 tff(7402,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1884, 7401])).
% 1.43/1.62 tff(7403,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7402, 1699])).
% 1.43/1.62 tff(7404,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7405,plain,
% 1.43/1.62 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7406,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7405])).
% 1.43/1.62 tff(7407,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7406, 7404])).
% 1.43/1.62 tff(7408,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7409,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7408, 7407])).
% 1.43/1.62 tff(7410,plain,
% 1.43/1.62 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7409, 224, 7403, 1737])).
% 1.43/1.62 tff(7411,plain,
% 1.43/1.62 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7410, 7391])).
% 1.43/1.62 tff(7412,plain,
% 1.43/1.62 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1422, 68, 1386, 7411])).
% 1.43/1.62 tff(7413,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7414,plain,
% 1.43/1.62 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7415,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7414])).
% 1.43/1.62 tff(7416,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7415, 7413])).
% 1.43/1.62 tff(7417,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7418,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7417, 7416])).
% 1.43/1.62 tff(7419,plain,
% 1.43/1.62 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7418, 224, 7403, 7170])).
% 1.43/1.62 tff(7420,plain,
% 1.43/1.62 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7419, 7391])).
% 1.43/1.62 tff(7421,plain,
% 1.43/1.62 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1439, 7420, 1782])).
% 1.43/1.62 tff(7422,plain,
% 1.43/1.62 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7423,plain,
% 1.43/1.62 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7424,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7423])).
% 1.43/1.62 tff(7425,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7424, 7422])).
% 1.43/1.62 tff(7426,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7427,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 1.43/1.62 tff(7428,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7427, 112, 545, 7421, 7412])).
% 1.43/1.62 tff(7429,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7430,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7429, 7377, 1386, 545, 7170, 335, 1656])).
% 1.43/1.62 tff(7431,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1294, 7430, 1733])).
% 1.43/1.62 tff(7432,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7433,plain,
% 1.43/1.62 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7434,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7433])).
% 1.43/1.62 tff(7435,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7434, 7432])).
% 1.43/1.62 tff(7436,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7437,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7436, 7435])).
% 1.43/1.62 tff(7438,plain,
% 1.43/1.62 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7437, 224, 7431, 390, 7170, 7377])).
% 1.43/1.62 tff(7439,plain,
% 1.43/1.62 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1422, 68, 1386, 7438])).
% 1.43/1.62 tff(7440,plain,
% 1.43/1.62 (b(elem!1, s(elem!1))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[77, 7348])).
% 1.43/1.62 tff(7441,plain,
% 1.43/1.62 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2054, 224, 7440, 7347, 7431])).
% 1.43/1.62 tff(7442,plain,
% 1.43/1.62 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1345, 7441, 1832])).
% 1.43/1.62 tff(7443,plain,
% 1.43/1.62 (~b(s(s(elem!1)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1249, 77, 7332, 7333])).
% 1.43/1.62 tff(7444,plain,
% 1.43/1.62 (r(s(s(elem!1)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[901, 7443])).
% 1.43/1.62 tff(7445,plain,
% 1.43/1.62 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7444, 1929])).
% 1.43/1.62 tff(7446,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3929, 112, 7445, 7442, 7439])).
% 1.43/1.62 tff(7447,plain,((~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7448,plain,
% 1.43/1.62 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7447, 7340, 390, 7374, 7346, 335, 178, 177])).
% 1.43/1.62 tff(7449,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7448, 7372])).
% 1.43/1.62 tff(7450,plain,((~b(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7451,plain,
% 1.43/1.62 (~b(s(z), s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7450, 7068, 7327, 178, 73, 132, 3])).
% 1.43/1.62 tff(7452,plain,
% 1.43/1.62 (r(s(z), s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[653, 7451])).
% 1.43/1.62 tff(7453,plain,
% 1.43/1.62 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[835, 7452, 178])).
% 1.43/1.62 tff(7454,plain,
% 1.43/1.62 (b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[147, 7453, 2])).
% 1.43/1.62 tff(7455,plain,
% 1.43/1.62 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7454, 7072])).
% 1.43/1.62 tff(7456,plain,
% 1.43/1.62 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7100, 7099])).
% 1.43/1.62 tff(7457,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7458,plain,
% 1.43/1.62 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7459,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7458])).
% 1.43/1.62 tff(7460,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7459, 7457])).
% 1.43/1.63 tff(7461,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7462,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7461, 7460])).
% 1.43/1.63 tff(7463,plain,
% 1.43/1.63 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7462, 224, 682, 390, 7305])).
% 1.43/1.63 tff(7464,plain,
% 1.43/1.63 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1763, 68, 1760, 7463])).
% 1.43/1.63 tff(7465,plain,
% 1.43/1.63 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1845, 224, 501, 1488, 7305])).
% 1.43/1.63 tff(7466,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(7467,plain,
% 1.43/1.63 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1857, 68, 7466, 7465])).
% 1.43/1.63 tff(7468,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7294, 112, 544, 7467, 7464])).
% 1.43/1.63 tff(7469,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7470,plain,
% 1.43/1.63 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7469, 682, 1717, 1854, 544, 390, 501, 1488])).
% 1.43/1.63 tff(7471,plain,
% 1.43/1.63 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1777, 7470, 1615])).
% 1.43/1.63 tff(7472,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7473,plain,
% 1.43/1.63 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7474,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7473])).
% 1.43/1.63 tff(7475,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7474, 7472])).
% 1.43/1.63 tff(7476,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7477,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7476, 7475])).
% 1.43/1.63 tff(7478,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7477, 224, 682, 3919, 390])).
% 1.43/1.63 tff(7479,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1401, 68, 7478, 2287])).
% 1.43/1.63 tff(7480,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3939, 112, 544, 7315, 7479])).
% 1.43/1.63 tff(7481,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7482,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7481, 682, 2287, 1832, 544, 390, 501, 1488])).
% 1.43/1.63 tff(7483,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1294, 7482, 1733])).
% 1.43/1.63 tff(7484,plain,
% 1.43/1.63 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7485,plain,
% 1.43/1.63 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7486,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7485])).
% 1.43/1.63 tff(7487,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(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(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7486, 7484])).
% 1.43/1.63 tff(7488,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7489,plain,
% 1.43/1.63 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7488, 7487])).
% 1.43/1.63 tff(7490,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7489, 112, 7483, 7471])).
% 1.43/1.63 tff(7491,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[2047, 68, 2044, 7490])).
% 1.43/1.63 tff(7492,plain,
% 1.43/1.63 (((~![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(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(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(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(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7493,plain,
% 1.43/1.63 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(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(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7494,plain,
% 1.43/1.63 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7493])).
% 1.43/1.63 tff(7495,plain,
% 1.43/1.63 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7494, 7492])).
% 1.43/1.63 tff(7496,plain,
% 1.43/1.63 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7497,plain,
% 1.43/1.63 ((~![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(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(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7496, 7495])).
% 1.43/1.63 tff(7498,plain,
% 1.43/1.63 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7497, 112, 7483, 7471])).
% 1.43/1.63 tff(7499,plain,
% 1.43/1.63 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 7498])).
% 1.43/1.63 tff(7500,plain,
% 1.43/1.63 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1736, 7155])).
% 1.43/1.63 tff(7501,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7502,plain,
% 1.43/1.63 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7503,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7502])).
% 1.43/1.63 tff(7504,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7503, 7501])).
% 1.43/1.63 tff(7505,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7506,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7505, 7504])).
% 1.43/1.63 tff(7507,plain,
% 1.43/1.63 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7506, 112, 7471, 1739])).
% 1.43/1.63 tff(7508,plain,
% 1.43/1.63 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7167, 68, 7507])).
% 1.43/1.63 tff(7509,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7508, 7500])).
% 1.43/1.63 tff(7510,plain,
% 1.43/1.63 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7387, 112, 7483, 1739])).
% 1.43/1.63 tff(7511,plain,
% 1.43/1.63 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7510, 7381])).
% 1.43/1.63 tff(7512,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[5426, 7511])).
% 1.43/1.63 tff(7513,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7512, 7379])).
% 1.43/1.63 tff(7514,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7515,plain,
% 1.43/1.63 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7516,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7515])).
% 1.43/1.63 tff(7517,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7516, 7514])).
% 1.43/1.63 tff(7518,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7519,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7518, 7517])).
% 1.43/1.63 tff(7520,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7519, 224, 7513, 7509, 7499, 7491])).
% 1.43/1.63 tff(7521,plain,((~b(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7522,plain,
% 1.43/1.63 (~b(elem!1, s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7521, 7445, 1656, 7240, 335, 390, 7440, 7347])).
% 1.43/1.63 tff(7523,plain,
% 1.43/1.63 (r(elem!1, s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[558, 7522, 3])).
% 1.43/1.63 tff(7524,plain,
% 1.43/1.63 (~r(elem!1, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7369, 7523, 4719, 390, 7440, 7347, 7445, 1737, 335])).
% 1.43/1.63 tff(7525,plain,
% 1.43/1.63 (b(elem!1, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[388, 7524, 4561])).
% 1.43/1.63 tff(7526,plain,
% 1.43/1.63 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7525, 4559])).
% 1.43/1.63 tff(7527,plain,
% 1.43/1.63 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7447, 7523, 390, 7374, 77, 335, 178, 177])).
% 1.43/1.63 tff(7528,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7527, 7526])).
% 1.43/1.63 tff(7529,plain,((~b(z, s(z))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7530,plain,
% 1.43/1.63 (~b(z, s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7529, 7068, 7327, 7455, 178, 73, 3])).
% 1.43/1.63 tff(7531,plain,
% 1.43/1.63 (r(z, s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[5459, 7530])).
% 1.43/1.63 tff(7532,plain,
% 1.43/1.63 (~r(z, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[5470, 7531, 178])).
% 1.43/1.63 tff(7533,plain,
% 1.43/1.63 (b(z, s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[100, 7532])).
% 1.43/1.63 tff(7534,plain,
% 1.43/1.63 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7533, 7456])).
% 1.43/1.63 tff(7535,plain,
% 1.43/1.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7081])).
% 1.43/1.63 tff(7536,plain,
% 1.43/1.63 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[7535])).
% 1.43/1.63 tff(7537,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7081])).
% 1.43/1.63 tff(7538,plain,
% 1.43/1.63 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7537])).
% 1.43/1.63 tff(7539,plain,
% 1.43/1.63 (~r(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4608, 7531, 73])).
% 1.43/1.63 tff(7540,plain,
% 1.43/1.63 (b(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[925, 7539])).
% 1.43/1.63 tff(7541,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7540, 7103])).
% 1.43/1.63 tff(7542,plain,
% 1.43/1.63 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[335])).
% 1.43/1.63 tff(7543,plain,
% 1.43/1.63 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[7542])).
% 1.43/1.63 tff(7544,plain,
% 1.43/1.63 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(z, s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7543])).
% 1.43/1.63 tff(7545,plain,
% 1.43/1.63 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7418, 224, 7403, 7170, 7391])).
% 1.43/1.63 tff(7546,plain,
% 1.43/1.63 (~b(z, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 1.43/1.63 tff(7547,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4592, 4575, 1668, 4569])).
% 1.43/1.63 tff(7548,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1345, 7547, 1832])).
% 1.43/1.63 tff(7549,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3163, 4760])).
% 1.43/1.63 tff(7550,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | b(s(s(s(s(z)))), s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7551,plain,
% 1.43/1.63 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7550, 7548, 335])).
% 1.43/1.63 tff(7552,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1687])).
% 1.43/1.63 tff(7553,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[7552])).
% 1.43/1.63 tff(7554,plain,
% 1.43/1.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7390, 7553])).
% 1.43/1.63 tff(7555,plain,
% 1.43/1.63 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4576, 4580])).
% 1.43/1.63 tff(7556,plain,
% 1.43/1.63 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[7555])).
% 1.43/1.63 tff(7557,plain,
% 1.43/1.63 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1682, 7])).
% 1.43/1.63 tff(7558,plain,
% 1.43/1.63 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[4576, 4580])).
% 1.43/1.63 tff(7559,plain,
% 1.43/1.63 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7558])).
% 1.43/1.63 tff(7560,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.63 tff(7561,plain,
% 1.43/1.63 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7560, 7559])).
% 1.43/1.63 tff(7562,plain,
% 1.43/1.63 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1869, 7561, 7557])).
% 1.43/1.64 tff(7563,plain,
% 1.43/1.64 (b(s(z), s(s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7562, 7556])).
% 1.43/1.64 tff(7564,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.64 tff(7565,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7566,plain,
% 1.43/1.64 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7567,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7566])).
% 1.43/1.64 tff(7568,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7567, 7565])).
% 1.43/1.64 tff(7569,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7570,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7569, 7568])).
% 1.43/1.64 tff(7571,plain,
% 1.43/1.64 (~b(s(z), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7570, 224, 560, 7564, 1570])).
% 1.43/1.64 tff(7572,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7571, 7563])).
% 1.43/1.64 tff(7573,plain,((~b(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7574,plain,
% 1.43/1.64 (r(s(z), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7573, 7554, 1668, 560, 7551])).
% 1.43/1.64 tff(7575,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.64 tff(7576,plain,
% 1.43/1.64 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[4580])).
% 1.43/1.64 tff(7577,plain,
% 1.43/1.64 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[7576])).
% 1.43/1.64 tff(7578,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.64 tff(7579,plain,
% 1.43/1.64 (r(z, s(s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7578, 7577])).
% 1.43/1.64 tff(7580,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7581,plain,
% 1.43/1.64 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7582,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7581])).
% 1.43/1.64 tff(7583,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7582, 7580])).
% 1.43/1.64 tff(7584,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7585,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7584, 7583])).
% 1.43/1.64 tff(7586,plain,
% 1.43/1.64 ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7585, 112, 4569])).
% 1.43/1.64 tff(7587,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7586, 7579, 7575])).
% 1.43/1.64 tff(7588,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7589,plain,
% 1.43/1.64 (~r(z, s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7588, 7574, 1668, 4569])).
% 1.43/1.64 tff(7590,plain,
% 1.43/1.64 (b(z, s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4412, 7589])).
% 1.43/1.64 tff(7591,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7590, 7546])).
% 1.43/1.64 tff(7592,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7593,plain,
% 1.43/1.64 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7592, 7068, 7531, 7540, 7534, 7084])).
% 1.43/1.64 tff(7594,plain,
% 1.43/1.64 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1294, 7593, 7298])).
% 1.43/1.64 tff(7595,plain,
% 1.43/1.64 (~r(z, s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[6325, 7531, 7452])).
% 1.43/1.64 tff(7596,plain,
% 1.43/1.64 (~r(z, s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7250, 7595, 7068])).
% 1.43/1.64 tff(7597,plain,
% 1.43/1.64 (b(z, s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1088, 7596])).
% 1.43/1.64 tff(7598,plain,
% 1.43/1.64 (b(elem!1, s(s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7597, 7243])).
% 1.43/1.64 tff(7599,plain,
% 1.43/1.64 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7477, 224, 7598, 7594, 7327])).
% 1.43/1.64 tff(7600,plain,
% 1.43/1.64 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1401, 68, 7599, 7240])).
% 1.43/1.64 tff(7601,plain,
% 1.43/1.64 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7069])).
% 1.43/1.64 tff(7602,plain,
% 1.43/1.64 (r(s(elem!1), s(s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7452, 7601])).
% 1.43/1.64 tff(7603,plain,
% 1.43/1.64 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1900, 112, 7602, 7600])).
% 1.43/1.64 tff(7604,plain,
% 1.43/1.64 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1869, 7603, 7301])).
% 1.43/1.64 tff(7605,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7606,plain,
% 1.43/1.64 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7607,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7606])).
% 1.43/1.64 tff(7608,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7607, 7605])).
% 1.43/1.64 tff(7609,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7610,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7609, 7608])).
% 1.43/1.64 tff(7611,plain,
% 1.43/1.64 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7610, 112, 7602, 7600])).
% 1.43/1.64 tff(7612,plain,
% 1.43/1.64 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1345, 7611, 7302])).
% 1.43/1.64 tff(7613,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7614,plain,
% 1.43/1.64 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7615,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7614])).
% 1.43/1.64 tff(7616,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7615, 7613])).
% 1.43/1.64 tff(7617,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7618,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7617, 7616])).
% 1.43/1.64 tff(7619,plain,
% 1.43/1.64 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7618, 224, 7612, 7604, 7541])).
% 1.43/1.64 tff(7620,plain,
% 1.43/1.64 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7619, 7538])).
% 1.43/1.64 tff(7621,plain,
% 1.43/1.64 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[5426, 7620])).
% 1.43/1.64 tff(7622,plain,
% 1.43/1.64 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7621, 7536])).
% 1.43/1.64 tff(7623,plain,
% 1.43/1.64 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7437, 224, 7594, 7327, 7534, 7455])).
% 1.43/1.64 tff(7624,plain,
% 1.43/1.64 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1422, 68, 7374, 7623])).
% 1.43/1.64 tff(7625,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7626,plain,
% 1.43/1.64 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7627,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7626])).
% 1.43/1.64 tff(7628,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7627, 7625])).
% 1.43/1.64 tff(7629,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7630,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7629, 7628])).
% 1.43/1.64 tff(7631,plain,
% 1.43/1.64 (~b(s(s(elem!1)), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7630, 224, 7122, 7327, 7534, 7455])).
% 1.43/1.64 tff(7632,plain,
% 1.43/1.64 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[530, 7631, 526])).
% 1.43/1.64 tff(7633,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7634,plain,
% 1.43/1.64 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7635,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7634])).
% 1.43/1.64 tff(7636,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7635, 7633])).
% 1.43/1.64 tff(7637,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7638,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7637, 7636])).
% 1.43/1.65 tff(7639,plain,
% 1.43/1.65 ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7638, 112, 7632, 7624])).
% 1.43/1.65 tff(7640,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7639, 7622])).
% 1.43/1.65 tff(7641,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3905, 7640, 7076])).
% 1.43/1.65 tff(7642,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7135, 224, 7598, 7641, 7534, 7455])).
% 1.43/1.65 tff(7643,plain,(b(s(s(s(z))), z) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(7644,plain,
% 1.43/1.65 (b(s(s(s(z))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7643, 176, 3, 2])).
% 1.43/1.65 tff(7645,plain,
% 1.43/1.65 (~r(z, s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3500, 3340, 7067])).
% 1.43/1.65 tff(7646,plain,
% 1.43/1.65 (b(z, s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[752, 7645])).
% 1.43/1.65 tff(7647,plain,
% 1.43/1.65 (~r(s(s(elem!1)), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2346, 3340, 7067])).
% 1.43/1.65 tff(7648,plain,
% 1.43/1.65 (b(s(s(elem!1)), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[593, 7647])).
% 1.43/1.65 tff(7649,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7650,plain,
% 1.43/1.65 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7651,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7650])).
% 1.43/1.65 tff(7652,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7651, 7649])).
% 1.43/1.65 tff(7653,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7654,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 1.43/1.65 tff(7655,plain,
% 1.43/1.65 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7654, 224, 7648, 7646, 7644])).
% 1.43/1.65 tff(7656,plain,
% 1.43/1.65 (r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[135, 68, 132, 7655])).
% 1.43/1.65 tff(7657,plain,
% 1.43/1.65 (~r(z, s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3500, 3340, 688])).
% 1.43/1.65 tff(7658,plain,
% 1.43/1.65 (b(z, s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[752, 7657])).
% 1.43/1.65 tff(7659,plain,
% 1.43/1.65 (~r(s(s(elem!1)), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2346, 3340, 688])).
% 1.43/1.65 tff(7660,plain,
% 1.43/1.65 (b(s(s(elem!1)), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[593, 7659])).
% 1.43/1.65 tff(7661,plain,
% 1.43/1.65 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7654, 224, 7660, 7658, 7644])).
% 1.43/1.65 tff(7662,plain,
% 1.43/1.65 (r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[135, 68, 132, 7661])).
% 1.43/1.65 tff(7663,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7664,plain,
% 1.43/1.65 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7665,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7664])).
% 1.43/1.65 tff(7666,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7665, 7663])).
% 1.43/1.65 tff(7667,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7668,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7667, 7666])).
% 1.43/1.65 tff(7669,plain,
% 1.43/1.65 (~r(s(s(s(z))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7668, 112, 545, 7662])).
% 1.43/1.65 tff(7670,plain,
% 1.43/1.65 (~r(s(elem!1), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4126, 3340, 688, 319])).
% 1.43/1.65 tff(7671,plain,
% 1.43/1.65 (b(s(elem!1), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[939, 7670, 303])).
% 1.43/1.65 tff(7672,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.43/1.65 tff(7673,plain,
% 1.43/1.65 (~r(z, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2420, 1020, 688])).
% 1.43/1.65 tff(7674,plain,
% 1.43/1.65 (b(z, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[100, 7673])).
% 1.43/1.65 tff(7675,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7676,plain,
% 1.43/1.65 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7677,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7676])).
% 1.43/1.65 tff(7678,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7677, 7675])).
% 1.43/1.65 tff(7679,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7680,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7679, 7678])).
% 1.43/1.65 tff(7681,plain,
% 1.43/1.65 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7680, 224, 5604, 7674, 7672])).
% 1.43/1.65 tff(7682,plain,
% 1.43/1.65 (r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[147, 7681, 2])).
% 1.43/1.65 tff(7683,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6969, 112, 1181, 1020, 7682])).
% 1.43/1.65 tff(7684,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(7685,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7684, 3340, 7644, 2, 688])).
% 1.43/1.65 tff(7686,plain,
% 1.43/1.65 (r(elem!1, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[515, 517, 327])).
% 1.43/1.65 tff(7687,plain,
% 1.43/1.65 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[541, 517, 3, 354])).
% 1.43/1.65 tff(7688,plain,
% 1.43/1.65 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7654, 224, 1240, 1180, 7672])).
% 1.43/1.65 tff(7689,plain,
% 1.43/1.65 (r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[135, 68, 681, 7688])).
% 1.43/1.65 tff(7690,plain,
% 1.43/1.65 (~r(s(z), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1205, 77, 1180, 1181])).
% 1.43/1.65 tff(7691,plain,
% 1.43/1.65 (b(s(z), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[454, 7690, 129])).
% 1.43/1.65 tff(7692,plain,
% 1.43/1.65 (~(elem!1 = s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2477, 7691, 170])).
% 1.43/1.65 tff(7693,plain,
% 1.43/1.65 (~(s(s(s(z))) = elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2487, 7692])).
% 1.43/1.65 tff(7694,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7695,plain,
% 1.43/1.65 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7696,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(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(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7695])).
% 1.43/1.65 tff(7697,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(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(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7696, 7694])).
% 1.43/1.65 tff(7698,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7699,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7698, 7697])).
% 1.43/1.65 tff(7700,plain,
% 1.43/1.65 (~r(s(s(s(z))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7699, 112, 543, 545, 7689])).
% 1.43/1.65 tff(7701,plain,
% 1.43/1.65 (b(s(s(s(z))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[374, 7700, 7693])).
% 1.43/1.65 tff(7702,plain,
% 1.43/1.65 (~b(s(s(s(z))), s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[706, 224, 77, 7691, 7701, 7672])).
% 1.43/1.65 tff(7703,plain,
% 1.43/1.65 (r(s(s(s(z))), s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[925, 7702])).
% 1.43/1.65 tff(7704,plain,
% 1.43/1.65 (b(elem!1, s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[388, 7692, 2440])).
% 1.43/1.65 tff(7705,plain,
% 1.43/1.65 (~(s(elem!1) = s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[784, 7704, 517])).
% 1.43/1.65 tff(7706,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7707,plain,
% 1.43/1.65 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7708,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7707])).
% 1.43/1.65 tff(7709,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7708, 7706])).
% 1.43/1.65 tff(7710,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7711,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7710, 7709])).
% 1.43/1.65 tff(7712,plain,
% 1.43/1.65 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7711, 224, 1488, 7704, 7701])).
% 1.43/1.65 tff(7713,plain,
% 1.43/1.65 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1534, 7712, 7705])).
% 1.43/1.65 tff(7714,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7715,plain,
% 1.43/1.65 (((~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))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(7716,plain,
% 1.43/1.65 (((~![X0: $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)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[7715])).
% 1.43/1.65 tff(7717,plain,
% 1.43/1.65 (((~![X0: $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))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[7716, 7714])).
% 1.43/1.65 tff(7718,plain,
% 1.43/1.65 ((~![X0: $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))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(7719,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[7718, 7717])).
% 1.43/1.65 tff(7720,plain,
% 1.43/1.65 (~r(s(z), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7719, 112, 176, 7713])).
% 1.43/1.65 tff(7721,plain,
% 1.43/1.65 (b(s(z), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[670, 7720, 666])).
% 1.43/1.65 tff(7722,plain,
% 1.43/1.65 ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6004, 224, 1488, 1391, 7691])).
% 1.43/1.65 tff(7723,plain,
% 1.43/1.65 (~b(s(z), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[7722, 7721])).
% 1.43/1.66 tff(7724,plain,
% 1.43/1.66 (r(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[653, 7723])).
% 1.43/1.66 tff(7725,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5271, 112, 7724, 7703, 7689])).
% 1.43/1.66 tff(7726,plain,((~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | b(elem!1, s(elem!1)) | r(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | (s(z) = elem!1) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7727,plain,
% 1.43/1.66 (~b(z, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7726, 7687, 7671, 561, 7672, 7686, 545, 7660, 7658, 517, 2440, 170, 129, 3340])).
% 1.43/1.66 tff(7728,plain,
% 1.43/1.66 (r(z, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5459, 7727])).
% 1.43/1.66 tff(7729,plain,
% 1.43/1.66 (~r(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5470, 7728, 176])).
% 1.43/1.66 tff(7730,plain,
% 1.43/1.66 (b(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[100, 7729])).
% 1.43/1.66 tff(7731,plain,
% 1.43/1.66 (~r(s(z), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5480, 4569, 688])).
% 1.43/1.66 tff(7732,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.43/1.66 tff(7733,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.43/1.66 tff(7734,plain,
% 1.43/1.66 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[84])).
% 1.43/1.66 tff(7735,plain,
% 1.43/1.66 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[80])).
% 1.43/1.66 tff(7736,plain,
% 1.43/1.66 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7735])).
% 1.43/1.66 tff(7737,plain,
% 1.43/1.66 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7736])).
% 1.43/1.66 tff(7738,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.66 tff(7739,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7738])).
% 1.43/1.66 tff(7740,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.66 tff(7741,plain,
% 1.43/1.66 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7740])).
% 1.43/1.66 tff(7742,plain,
% 1.43/1.66 (s(z) = elem!1),
% 1.43/1.66 inference(symmetry,[status(thm)],[78])).
% 1.43/1.66 tff(7743,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737, 7742])).
% 1.43/1.66 tff(7744,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7743])).
% 1.43/1.66 tff(7745,plain,
% 1.43/1.66 (s(z) = elem!1),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2654, 78])).
% 1.43/1.66 tff(7746,plain,
% 1.43/1.66 (s(z) = s(s(s(s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[86, 2768])).
% 1.43/1.66 tff(7747,plain,
% 1.43/1.66 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7746])).
% 1.43/1.66 tff(7748,plain,
% 1.43/1.66 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7747])).
% 1.43/1.66 tff(7749,plain,
% 1.43/1.66 (s(s(s(elem!1))) = z),
% 1.43/1.66 inference(transitivity,[status(thm)],[1153, 7748, 27])).
% 1.43/1.66 tff(7750,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1362, 7749])).
% 1.43/1.66 tff(7751,plain,((~(s(z) = elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7752,plain,
% 1.43/1.66 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7751, 7745])).
% 1.43/1.66 tff(7753,plain,
% 1.43/1.66 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7754,plain,
% 1.43/1.66 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7753])).
% 1.43/1.66 tff(7755,plain,
% 1.43/1.66 (r(elem!1, s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[176, 7754])).
% 1.43/1.66 tff(7756,plain,
% 1.43/1.66 (~r(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2420, 7755, 688])).
% 1.43/1.66 tff(7757,plain,
% 1.43/1.66 (b(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[100, 7756])).
% 1.43/1.66 tff(7758,plain,
% 1.43/1.66 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7759,plain,
% 1.43/1.66 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[7758])).
% 1.43/1.66 tff(7760,plain,
% 1.43/1.66 (s(s(z)) = s(elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[79])).
% 1.43/1.66 tff(7761,plain,
% 1.43/1.66 (b(s(s(z)), elem!1) <=> b(s(elem!1), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7760, 78])).
% 1.43/1.66 tff(7762,plain,
% 1.43/1.66 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.43/1.66 inference(transitivity,[status(thm)],[7761, 7759])).
% 1.43/1.66 tff(7763,plain,
% 1.43/1.66 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1306, 7752])).
% 1.43/1.66 tff(7764,plain,
% 1.43/1.66 (~(s(elem!1) = elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[302, 7763])).
% 1.43/1.66 tff(7765,plain,
% 1.43/1.66 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[318, 7763])).
% 1.43/1.66 tff(7766,plain,
% 1.43/1.66 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7767,plain,
% 1.43/1.66 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[7766])).
% 1.43/1.66 tff(7768,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737, 7760])).
% 1.43/1.66 tff(7769,plain,
% 1.43/1.66 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7768])).
% 1.43/1.66 tff(7770,plain,
% 1.43/1.66 (s(s(z)) = s(elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[86])).
% 1.43/1.66 tff(7771,plain,
% 1.43/1.66 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7770])).
% 1.43/1.66 tff(7772,plain,
% 1.43/1.66 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7771, 1143])).
% 1.43/1.66 tff(7773,plain,
% 1.43/1.66 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7772])).
% 1.43/1.66 tff(7774,plain,
% 1.43/1.66 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1827, 7773])).
% 1.43/1.66 tff(7775,plain,
% 1.43/1.66 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.66 inference(symmetry,[status(thm)],[80])).
% 1.43/1.66 tff(7776,plain,
% 1.43/1.66 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7775])).
% 1.43/1.66 tff(7777,plain,
% 1.43/1.66 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7776])).
% 1.43/1.66 tff(7778,assumption,(s(s(z)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.66 tff(7779,plain,
% 1.43/1.66 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7778])).
% 1.43/1.66 tff(7780,plain,
% 1.43/1.66 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7779])).
% 1.43/1.66 tff(7781,plain,
% 1.43/1.66 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7780])).
% 1.43/1.66 tff(7782,plain,
% 1.43/1.66 (s(z) = s(s(s(s(z))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[50, 7781, 989, 7777])).
% 1.43/1.66 tff(7783,plain,
% 1.43/1.66 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7782])).
% 1.43/1.66 tff(7784,plain,
% 1.43/1.66 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7783])).
% 1.43/1.66 tff(7785,plain,
% 1.43/1.66 (s(s(s(z))) = z),
% 1.43/1.66 inference(transitivity,[status(thm)],[1679, 7784, 27])).
% 1.43/1.66 tff(7786,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[58, 7785])).
% 1.43/1.66 tff(7787,plain,((~(s(s(z)) = s(s(s(s(elem!1)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7788,plain,
% 1.43/1.66 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7787, 87])).
% 1.43/1.66 tff(7789,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7788, 7774])).
% 1.43/1.66 tff(7790,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7791,plain,
% 1.43/1.66 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7790, 7745])).
% 1.43/1.66 tff(7792,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737, 7760])).
% 1.43/1.66 tff(7793,plain,
% 1.43/1.66 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7792])).
% 1.43/1.66 tff(7794,plain,
% 1.43/1.66 (r(elem!1, s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[178, 7754])).
% 1.43/1.66 tff(7795,plain,
% 1.43/1.66 (~r(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2420, 7794, 688])).
% 1.43/1.66 tff(7796,plain,
% 1.43/1.66 (b(z, s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[100, 7795])).
% 1.43/1.66 tff(7797,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[80])).
% 1.43/1.66 tff(7798,plain,
% 1.43/1.66 (r(s(s(s(z))), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[887, 7797])).
% 1.43/1.66 tff(7799,plain,
% 1.43/1.66 (~r(s(s(s(z))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4606, 112, 4569, 7798])).
% 1.43/1.66 tff(7800,plain,
% 1.43/1.66 (b(s(s(s(z))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[72, 7799])).
% 1.43/1.66 tff(7801,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.66 tff(7802,plain,
% 1.43/1.66 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7801])).
% 1.43/1.66 tff(7803,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737, 7742])).
% 1.43/1.66 tff(7804,plain,
% 1.43/1.66 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7803])).
% 1.43/1.66 tff(7805,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1798, 7804])).
% 1.43/1.66 tff(7806,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7807,plain,
% 1.43/1.66 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7808,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7807])).
% 1.43/1.66 tff(7809,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7808, 7806])).
% 1.43/1.66 tff(7810,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(7811,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7810, 7809])).
% 1.43/1.66 tff(7812,plain,
% 1.43/1.66 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7811, 112, 4569])).
% 1.43/1.66 tff(7813,plain,
% 1.43/1.66 (~r(s(s(s(s(s(z))))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7812, 7805])).
% 1.43/1.66 tff(7814,plain,
% 1.43/1.66 (~r(s(s(s(s(elem!1)))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7813, 7802])).
% 1.43/1.66 tff(7815,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.66 tff(7816,plain,
% 1.43/1.66 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7815])).
% 1.43/1.66 tff(7817,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.66 tff(7818,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7817])).
% 1.43/1.66 tff(7819,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[2025, 7818])).
% 1.43/1.66 tff(7820,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7821,plain,
% 1.43/1.66 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7822,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7821])).
% 1.43/1.66 tff(7823,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7822, 7820])).
% 1.43/1.66 tff(7824,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(7825,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7824, 7823])).
% 1.43/1.66 tff(7826,plain,
% 1.43/1.66 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7825, 224, 6255, 7672])).
% 1.43/1.66 tff(7827,plain,
% 1.43/1.66 (~b(s(s(s(s(s(z))))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7826, 7819])).
% 1.43/1.66 tff(7828,plain,
% 1.43/1.66 (~b(s(s(s(s(elem!1)))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7827, 7816])).
% 1.43/1.66 tff(7829,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1338, 7828, 7814])).
% 1.43/1.66 tff(7830,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(elem!1 = s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7831,plain,
% 1.43/1.66 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7830, 7800, 7796, 78, 4569, 7794])).
% 1.43/1.66 tff(7832,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1294, 7831, 7752])).
% 1.43/1.66 tff(7833,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7832, 7744])).
% 1.43/1.66 tff(7834,plain,
% 1.43/1.66 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7742])).
% 1.43/1.66 tff(7835,plain,
% 1.43/1.66 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7834])).
% 1.43/1.66 tff(7836,plain,
% 1.43/1.66 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7837,plain,
% 1.43/1.66 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7836])).
% 1.43/1.66 tff(7838,plain,
% 1.43/1.66 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[80])).
% 1.43/1.66 tff(7839,plain,
% 1.43/1.66 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7838])).
% 1.43/1.66 tff(7840,plain,
% 1.43/1.66 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7839, 7837])).
% 1.43/1.66 tff(7841,plain,
% 1.43/1.66 (r(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[178, 7840])).
% 1.43/1.66 tff(7842,plain,
% 1.43/1.66 (r(s(z), s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[178, 7839])).
% 1.43/1.66 tff(7843,plain,
% 1.43/1.66 (~r(z, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[6325, 7842, 4569])).
% 1.43/1.66 tff(7844,plain,
% 1.43/1.66 (b(z, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[752, 7843])).
% 1.43/1.66 tff(7845,plain,
% 1.43/1.66 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7846,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[7845])).
% 1.43/1.66 tff(7847,plain,
% 1.43/1.66 (r(s(s(elem!1)), elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[887, 7846])).
% 1.43/1.66 tff(7848,plain,
% 1.43/1.66 (~r(s(s(elem!1)), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2346, 7847, 688])).
% 1.43/1.66 tff(7849,plain,
% 1.43/1.66 (b(s(s(elem!1)), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[593, 7848])).
% 1.43/1.66 tff(7850,plain,
% 1.43/1.66 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7742])).
% 1.43/1.66 tff(7851,plain,
% 1.43/1.66 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7850])).
% 1.43/1.66 tff(7852,plain,
% 1.43/1.66 (r(s(s(z)), elem!1) <=> r(s(elem!1), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7760, 78])).
% 1.43/1.66 tff(7853,plain,
% 1.43/1.66 (r(s(elem!1), s(z)) <=> r(s(s(z)), elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[7852])).
% 1.43/1.66 tff(7854,plain,
% 1.43/1.66 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7855,plain,
% 1.43/1.66 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.43/1.66 inference(transitivity,[status(thm)],[7854, 7853])).
% 1.43/1.66 tff(7856,plain,
% 1.43/1.66 (r(s(s(z)), elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[408, 7855])).
% 1.43/1.66 tff(7857,plain,
% 1.43/1.66 (r(s(s(z)), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7856, 7851])).
% 1.43/1.66 tff(7858,plain,
% 1.43/1.66 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.66 tff(7859,plain,
% 1.43/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1521, 4276, 7765])).
% 1.43/1.66 tff(7860,plain,
% 1.43/1.66 (~b(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4154, 7859, 1240, 1180])).
% 1.43/1.66 tff(7861,plain,
% 1.43/1.66 (r(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[498, 7860])).
% 1.43/1.66 tff(7862,plain,
% 1.43/1.66 (r(s(s(z)), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7861, 7858])).
% 1.43/1.66 tff(7863,plain,
% 1.43/1.66 (~r(s(s(z)), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[6165, 112, 4569, 7862])).
% 1.43/1.66 tff(7864,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7863, 7857])).
% 1.43/1.66 tff(7865,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (~r(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7866,plain,
% 1.43/1.66 (~r(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7865, 7849, 4569, 78, 7844, 7841])).
% 1.43/1.66 tff(7867,plain,
% 1.43/1.66 (b(s(elem!1), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[939, 7866, 7764])).
% 1.43/1.66 tff(7868,plain,
% 1.43/1.66 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7770])).
% 1.43/1.66 tff(7869,plain,
% 1.43/1.66 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.43/1.66 inference(symmetry,[status(thm)],[7868])).
% 1.43/1.66 tff(7870,plain,
% 1.43/1.66 (b(s(s(z)), elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1488, 7869])).
% 1.43/1.66 tff(7871,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5829, 7870])).
% 1.43/1.66 tff(7872,plain,((~(s(z) = elem!1)) | b(s(s(z)), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7873,plain,
% 1.43/1.66 (b(s(s(z)), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7872, 7867, 7745])).
% 1.43/1.66 tff(7874,plain,
% 1.43/1.66 (b(s(s(z)), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7873, 7835])).
% 1.43/1.66 tff(7875,plain,
% 1.43/1.66 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.66 tff(7876,plain,
% 1.43/1.66 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.66 tff(7877,plain,
% 1.43/1.66 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7876, 7875])).
% 1.43/1.66 tff(7878,plain,
% 1.43/1.66 (~(elem!1 = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[326, 7764])).
% 1.43/1.66 tff(7879,plain,
% 1.43/1.66 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[79, 80])).
% 1.43/1.66 tff(7880,plain,
% 1.43/1.66 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7879])).
% 1.43/1.66 tff(7881,plain,
% 1.43/1.66 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.66 tff(7882,plain,
% 1.43/1.66 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7881, 7880])).
% 1.43/1.66 tff(7883,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.43/1.66 tff(7884,plain,
% 1.43/1.66 (((~![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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7885,plain,
% 1.43/1.66 (((~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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(7886,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7885])).
% 1.43/1.66 tff(7887,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7886, 7884])).
% 1.43/1.66 tff(7888,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(7889,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7888, 7887])).
% 1.43/1.66 tff(7890,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7889, 112, 543, 1020, 7883])).
% 1.43/1.66 tff(7891,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(7892,plain,
% 1.43/1.66 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[7891, 543, 1020])).
% 1.43/1.66 tff(7893,plain,
% 1.43/1.66 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1534, 7892, 7733])).
% 1.43/1.66 tff(7894,plain,
% 1.43/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7893, 7882])).
% 1.43/1.66 tff(7895,plain,
% 1.43/1.66 (~(s(s(elem!1)) = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[525, 7765])).
% 1.43/1.66 tff(7896,plain,
% 1.43/1.66 (~r(s(s(elem!1)), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[553, 543, 545])).
% 1.43/1.66 tff(7897,plain,
% 1.43/1.66 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[530, 7896, 7895])).
% 1.43/1.66 tff(7898,plain,
% 1.43/1.66 (~b(z, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4868, 1390, 1391, 543, 4538, 1181, 1488])).
% 1.43/1.66 tff(7899,plain,
% 1.43/1.66 (r(z, s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[752, 7898])).
% 1.43/1.66 tff(7900,plain,
% 1.43/1.66 (~r(z, elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3500, 7899, 1181])).
% 1.43/1.66 tff(7901,plain,
% 1.43/1.66 (z = elem!1),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[289, 7900, 4538])).
% 1.43/1.66 tff(7902,plain,
% 1.43/1.66 (elem!1 = z),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[338, 7901])).
% 1.43/1.66 tff(7903,plain,
% 1.43/1.66 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1682, 7902])).
% 1.43/1.66 tff(7904,plain,
% 1.43/1.66 (s(z) = s(elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7901])).
% 1.43/1.66 tff(7905,plain,
% 1.43/1.66 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7904])).
% 1.43/1.66 tff(7906,plain,
% 1.43/1.66 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7905])).
% 1.43/1.66 tff(7907,plain,
% 1.43/1.66 (r(elem!1, s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[543, 7906])).
% 1.43/1.66 tff(7908,plain,
% 1.43/1.66 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7901])).
% 1.43/1.66 tff(7909,plain,
% 1.43/1.66 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7908])).
% 1.43/1.66 tff(7910,plain,
% 1.43/1.66 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1334, 7909])).
% 1.43/1.66 tff(7911,plain,
% 1.43/1.66 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7901])).
% 1.43/1.66 tff(7912,plain,
% 1.43/1.66 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7911])).
% 1.43/1.66 tff(7913,plain,
% 1.43/1.66 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.43/1.66 inference(transitivity,[status(thm)],[7906, 7912])).
% 1.43/1.66 tff(7914,plain,
% 1.43/1.66 (r(z, s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[543, 7913])).
% 1.43/1.66 tff(7915,plain,
% 1.43/1.66 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4596, 7914, 1390, 1391, 1181, 7901])).
% 1.43/1.66 tff(7916,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1294, 7915, 7910])).
% 1.43/1.66 tff(7917,plain,
% 1.43/1.66 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1831, 7903])).
% 1.43/1.66 tff(7918,plain,
% 1.43/1.66 (s(s(z)) = s(s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7904])).
% 1.43/1.66 tff(7919,plain,
% 1.43/1.66 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7918])).
% 1.43/1.66 tff(7920,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7919])).
% 1.43/1.66 tff(7921,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7920])).
% 1.43/1.66 tff(7922,plain,
% 1.43/1.66 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7921])).
% 1.43/1.66 tff(7923,plain,
% 1.43/1.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[4702, 7901, 1181, 1391, 543, 1390])).
% 1.43/1.66 tff(7924,plain,
% 1.43/1.66 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[7923, 7922])).
% 1.43/1.66 tff(7925,plain,
% 1.43/1.66 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1884, 7924])).
% 1.43/1.66 tff(7926,plain,
% 1.43/1.66 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7919, 7904])).
% 1.43/1.66 tff(7927,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.43/1.66 inference(symmetry,[status(thm)],[7926])).
% 1.43/1.66 tff(7928,plain,
% 1.43/1.66 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[7927])).
% 1.43/1.67 tff(7929,plain,
% 1.43/1.67 (r(z, s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1020, 4751])).
% 1.43/1.67 tff(7930,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4621, 7929, 4567])).
% 1.43/1.67 tff(7931,plain,
% 1.43/1.67 (b(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[925, 7930])).
% 1.43/1.67 tff(7932,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7931, 4555])).
% 1.43/1.67 tff(7933,plain,
% 1.43/1.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4671, 1020, 1181, 335, 1391, 543])).
% 1.43/1.67 tff(7934,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7933, 7932])).
% 1.43/1.67 tff(7935,plain,((~r(elem!1, s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(7936,plain,
% 1.43/1.67 (~r(elem!1, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7935, 7901, 1181, 1391, 543])).
% 1.43/1.67 tff(7937,plain,
% 1.43/1.67 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7901])).
% 1.43/1.67 tff(7938,plain,
% 1.43/1.67 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[7937, 283])).
% 1.43/1.67 tff(7939,plain,
% 1.43/1.67 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7938])).
% 1.43/1.67 tff(7940,plain,
% 1.43/1.67 (~(elem!1 = s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[58, 7939])).
% 1.43/1.67 tff(7941,plain,
% 1.43/1.67 (b(elem!1, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[388, 7940, 7936])).
% 1.43/1.67 tff(7942,plain,
% 1.43/1.67 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.67 inference(symmetry,[status(thm)],[7919])).
% 1.43/1.67 tff(7943,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7942])).
% 1.43/1.67 tff(7944,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[7943])).
% 1.43/1.67 tff(7945,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7925, 7944])).
% 1.43/1.67 tff(7946,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.67 tff(7947,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3903, 68, 3899])).
% 1.43/1.67 tff(7948,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7947, 4553])).
% 1.43/1.67 tff(7949,plain,
% 1.43/1.67 (~r(s(s(s(z))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4692, 7948, 1181, 335])).
% 1.43/1.67 tff(7950,plain,
% 1.43/1.67 (b(s(s(s(z))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[374, 7949, 4549])).
% 1.43/1.67 tff(7951,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7950, 4544])).
% 1.43/1.67 tff(7952,plain,
% 1.43/1.67 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4814, 224, 1488, 7951, 4724])).
% 1.43/1.67 tff(7953,plain,
% 1.43/1.67 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7952, 1953])).
% 1.43/1.67 tff(7954,plain,
% 1.43/1.67 (r(s(elem!1), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1534, 7953, 4542])).
% 1.43/1.67 tff(7955,plain,
% 1.43/1.67 (r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7954, 1948])).
% 1.43/1.67 tff(7956,plain,
% 1.43/1.67 ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4855, 112, 7946])).
% 1.43/1.67 tff(7957,plain,
% 1.43/1.67 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7956, 7955])).
% 1.43/1.67 tff(7958,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1345, 7957, 1832])).
% 1.43/1.67 tff(7959,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4777, 7958])).
% 1.43/1.67 tff(7960,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1401, 68, 7959, 1694])).
% 1.43/1.67 tff(7961,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(7962,plain,
% 1.43/1.67 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(7963,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7962])).
% 1.43/1.67 tff(7964,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[7963, 7961])).
% 1.43/1.67 tff(7965,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(7966,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7965, 7964])).
% 1.43/1.67 tff(7967,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7966, 112, 7960, 7948, 7946])).
% 1.43/1.67 tff(7968,plain,(b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(7969,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7968, 7945, 1488, 7916, 1391, 7901, 1181, 7941])).
% 1.43/1.67 tff(7970,plain,
% 1.43/1.67 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1981, 224, 1391, 1390, 7969])).
% 1.43/1.67 tff(7971,plain,
% 1.43/1.67 (~b(s(s(s(z))), s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7970, 7928])).
% 1.43/1.67 tff(7972,plain,
% 1.43/1.67 (r(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[925, 7971])).
% 1.43/1.67 tff(7973,plain,
% 1.43/1.67 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4829, 7972, 7901, 7925])).
% 1.43/1.67 tff(7974,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1345, 7973, 7917])).
% 1.43/1.67 tff(7975,plain,
% 1.43/1.67 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4817, 7974, 1488, 7901, 1391, 7914, 7916, 7907])).
% 1.43/1.67 tff(7976,plain,
% 1.43/1.67 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1869, 7975, 7903])).
% 1.43/1.67 tff(7977,plain,
% 1.43/1.67 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[7908, 1779])).
% 1.43/1.67 tff(7978,plain,
% 1.43/1.67 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7977])).
% 1.43/1.67 tff(7979,plain,
% 1.43/1.67 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1334, 7978])).
% 1.43/1.67 tff(7980,plain,
% 1.43/1.67 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1693, 7901])).
% 1.43/1.67 tff(7981,plain,
% 1.43/1.67 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4776, 224, 1488, 7916, 1391])).
% 1.43/1.67 tff(7982,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7981, 7974])).
% 1.43/1.67 tff(7983,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1401, 68, 7982, 7980])).
% 1.43/1.67 tff(7984,plain,
% 1.43/1.67 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7901])).
% 1.43/1.67 tff(7985,plain,
% 1.43/1.67 (r(elem!1, s(s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7899, 7984])).
% 1.43/1.67 tff(7986,plain,
% 1.43/1.67 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1908, 112, 7985, 7983])).
% 1.43/1.67 tff(7987,plain,
% 1.43/1.67 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1439, 7986, 7979])).
% 1.43/1.67 tff(7988,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1864, 224, 1488, 7916, 7987, 7976])).
% 1.43/1.67 tff(7989,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(7990,plain,
% 1.43/1.67 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7989, 7897, 1488, 1181, 543, 4538])).
% 1.43/1.67 tff(7991,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7990, 7894])).
% 1.43/1.67 tff(7992,plain,((~r(elem!1, s(elem!1))) | (~(elem!1 = s(z))) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | b(z, elem!1) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(7993,plain,
% 1.43/1.67 (~r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7992, 7867, 78, 7847, 4538, 7733, 7841, 7794])).
% 1.43/1.67 tff(7994,plain,
% 1.43/1.67 (b(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[515, 7993, 7878])).
% 1.43/1.67 tff(7995,plain,
% 1.43/1.67 (b(s(z), s(s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[7994, 7877])).
% 1.43/1.67 tff(7996,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(7997,plain,
% 1.43/1.67 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(7998,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7997])).
% 1.43/1.67 tff(7999,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[7998, 7996])).
% 1.43/1.67 tff(8000,plain,
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% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8001,plain,
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% 1.43/1.67 inference(modus_ponens,[status(thm)],[8000, 7999])).
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% 1.43/1.67 inference(unit_resolution,[status(thm)],[8001, 224, 7995, 7874, 7833])).
% 1.43/1.67 tff(8003,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8002, 7793])).
% 1.43/1.67 tff(8004,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1345, 8003, 7791])).
% 1.43/1.67 tff(8005,plain,
% 1.43/1.67 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8004, 7769])).
% 1.43/1.67 tff(8006,plain,
% 1.43/1.67 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.67 tff(8007,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8006])).
% 1.43/1.67 tff(8008,plain,
% 1.43/1.67 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7817])).
% 1.43/1.67 tff(8009,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.43/1.67 inference(symmetry,[status(thm)],[7815])).
% 1.43/1.67 tff(8010,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.43/1.67 tff(8011,plain,
% 1.43/1.67 (b(elem!1, z) <=> b(s(z), z)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.67 tff(8012,plain,
% 1.43/1.67 (b(s(z), z) <=> b(elem!1, z)),
% 1.43/1.67 inference(symmetry,[status(thm)],[8011])).
% 1.43/1.67 tff(8013,plain,
% 1.43/1.67 (b(elem!1, z)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1, 8012])).
% 1.43/1.67 tff(8014,plain,
% 1.43/1.67 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.67 tff(8015,plain,
% 1.43/1.67 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8014])).
% 1.43/1.67 tff(8016,plain,
% 1.43/1.67 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[80])).
% 1.43/1.67 tff(8017,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8016])).
% 1.43/1.67 tff(8018,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8019,plain,
% 1.43/1.67 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8020,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8019])).
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% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8020, 8018])).
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% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8023,plain,
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% 1.43/1.67 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 1.43/1.67 tff(8024,plain,
% 1.43/1.67 (~r(s(s(s(s(s(z))))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8023, 112, 3750, 8010])).
% 1.43/1.67 tff(8025,plain,
% 1.43/1.67 (~r(s(s(s(s(elem!1)))), z)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8024, 7802])).
% 1.43/1.67 tff(8026,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1338, 8025])).
% 1.43/1.67 tff(8027,plain,
% 1.43/1.67 (b(s(s(s(s(s(z))))), z)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8026, 8009])).
% 1.43/1.67 tff(8028,plain,
% 1.43/1.67 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.67 tff(8029,plain,
% 1.43/1.67 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8028])).
% 1.43/1.67 tff(8030,plain,
% 1.43/1.67 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[7737])).
% 1.43/1.67 tff(8031,plain,
% 1.43/1.67 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8030])).
% 1.43/1.67 tff(8032,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8033,plain,
% 1.43/1.67 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8034,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8033])).
% 1.43/1.67 tff(8035,plain,
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% 1.43/1.67 inference(transitivity,[status(thm)],[8034, 8032])).
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% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
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% 1.43/1.67 inference(modus_ponens,[status(thm)],[8036, 8035])).
% 1.43/1.67 tff(8038,plain,
% 1.43/1.67 (~r(z, s(s(s(s(s(z))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8037, 112, 3750, 8010])).
% 1.43/1.67 tff(8039,plain,
% 1.43/1.67 (~r(z, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8038, 8031])).
% 1.43/1.68 tff(8040,plain,
% 1.43/1.68 (b(z, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4412, 8039])).
% 1.43/1.68 tff(8041,plain,
% 1.43/1.68 (b(z, s(s(s(s(s(z))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8040, 8029])).
% 1.43/1.68 tff(8042,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8043,plain,
% 1.43/1.68 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8044,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8043])).
% 1.43/1.68 tff(8045,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8044, 8042])).
% 1.43/1.68 tff(8046,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8047,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8046, 8045])).
% 1.43/1.68 tff(8048,plain,
% 1.43/1.68 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8047, 224, 7672])).
% 1.43/1.68 tff(8049,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8048, 8041, 8027])).
% 1.43/1.68 tff(8050,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8049, 7741])).
% 1.43/1.68 tff(8051,plain,
% 1.43/1.68 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[5426, 8050])).
% 1.43/1.68 tff(8052,plain,
% 1.43/1.68 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8051, 8017])).
% 1.43/1.68 tff(8053,plain,
% 1.43/1.68 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1407, 7752])).
% 1.43/1.68 tff(8054,plain,
% 1.43/1.68 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[7742, 7737])).
% 1.43/1.68 tff(8055,plain,
% 1.43/1.68 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8054])).
% 1.43/1.68 tff(8056,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8057,plain,
% 1.43/1.68 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8058,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8057])).
% 1.43/1.68 tff(8059,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8058, 8056])).
% 1.43/1.68 tff(8060,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8061,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8060, 8059])).
% 1.43/1.68 tff(8062,plain,
% 1.43/1.68 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8061, 224, 1])).
% 1.43/1.68 tff(8063,plain,
% 1.43/1.68 (~b(s(z), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8062, 8041, 8027])).
% 1.43/1.68 tff(8064,plain,
% 1.43/1.68 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8063, 8055])).
% 1.43/1.68 tff(8065,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1439, 8064, 8053])).
% 1.43/1.68 tff(8066,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.68 tff(8067,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.68 tff(8068,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8069,plain,
% 1.43/1.68 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8070,plain,
% 1.43/1.68 (((~![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(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8069])).
% 1.43/1.68 tff(8071,plain,
% 1.43/1.68 (((~![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(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8070, 8068])).
% 1.43/1.68 tff(8072,plain,
% 1.43/1.68 ((~![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(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8073,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8072, 8071])).
% 1.43/1.68 tff(8074,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8073, 112, 1181, 8067, 8066])).
% 1.43/1.68 tff(8075,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8076,plain,
% 1.43/1.68 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8075, 8065, 1181])).
% 1.43/1.68 tff(8077,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8076, 8052])).
% 1.43/1.68 tff(8078,plain,((~r(z, s(s(z)))) | (~(elem!1 = s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8079,plain,
% 1.43/1.68 (~r(z, s(s(z)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8078, 8010, 1181, 7672, 1, 78])).
% 1.43/1.68 tff(8080,plain,
% 1.43/1.68 (b(z, s(s(z)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1088, 8079])).
% 1.43/1.68 tff(8081,plain,
% 1.43/1.68 (b(z, s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8080, 8015])).
% 1.43/1.68 tff(8082,plain,
% 1.43/1.68 (~b(s(elem!1), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[509, 8081, 8013, 501])).
% 1.43/1.68 tff(8083,plain,
% 1.43/1.68 (r(s(elem!1), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[498, 8082])).
% 1.43/1.68 tff(8084,plain,
% 1.43/1.68 (r(s(s(z)), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8083, 7858])).
% 1.43/1.68 tff(8085,plain,
% 1.43/1.68 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.43/1.68 inference(symmetry,[status(thm)],[7801])).
% 1.43/1.68 tff(8086,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.43/1.68 tff(8087,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 1.43/1.68 tff(8088,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8089,plain,
% 1.43/1.68 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8090,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8089])).
% 1.43/1.68 tff(8091,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8090, 8088])).
% 1.43/1.68 tff(8092,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8093,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8092, 8091])).
% 1.43/1.68 tff(8094,plain,
% 1.43/1.68 (~r(s(s(s(s(s(z))))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8093, 112, 268, 8010])).
% 1.43/1.68 tff(8095,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8094, 8087])).
% 1.43/1.68 tff(8096,plain,((~r(s(s(s(s(elem!1)))), z)) | (~(elem!1 = s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8097,plain,
% 1.43/1.68 (~r(s(s(s(s(elem!1)))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8096, 8084, 78, 8010])).
% 1.43/1.68 tff(8098,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1338, 8097])).
% 1.43/1.68 tff(8099,plain,
% 1.43/1.68 (b(s(s(s(s(s(z))))), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8098, 8009])).
% 1.43/1.68 tff(8100,plain,
% 1.43/1.68 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8101,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8100])).
% 1.43/1.68 tff(8102,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8101, 7820])).
% 1.43/1.68 tff(8103,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8104,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 1.43/1.68 tff(8105,plain,
% 1.43/1.68 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8104, 224, 6255, 7672])).
% 1.43/1.68 tff(8106,plain,
% 1.43/1.68 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8105, 8099])).
% 1.43/1.68 tff(8107,plain,
% 1.43/1.68 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8106, 8008])).
% 1.43/1.68 tff(8108,plain,
% 1.43/1.68 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1884, 8107])).
% 1.43/1.68 tff(8109,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8108, 8007])).
% 1.43/1.68 tff(8110,plain,
% 1.43/1.68 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[7742, 7737])).
% 1.43/1.68 tff(8111,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8110])).
% 1.43/1.68 tff(8112,plain,
% 1.43/1.68 (b(s(z), s(s(z)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[501, 7877])).
% 1.43/1.68 tff(8113,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8114,plain,
% 1.43/1.68 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8115,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8114])).
% 1.43/1.68 tff(8116,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8115, 8113])).
% 1.43/1.68 tff(8117,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8118,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8117, 8116])).
% 1.43/1.68 tff(8119,plain,
% 1.43/1.68 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8118, 224, 1, 8080, 8112])).
% 1.43/1.68 tff(8120,plain,
% 1.43/1.68 (~b(s(z), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8119, 8099])).
% 1.43/1.68 tff(8121,plain,
% 1.43/1.68 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8120, 8055])).
% 1.43/1.68 tff(8122,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1439, 8121, 8053])).
% 1.43/1.68 tff(8123,plain,
% 1.43/1.68 (r(s(z), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8122, 8111])).
% 1.43/1.68 tff(8124,plain,
% 1.43/1.68 (((~![X0: $i, 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))))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8125,plain,
% 1.43/1.69 (((~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))))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8126,plain,
% 1.43/1.69 (((~![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(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)))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8125])).
% 1.43/1.69 tff(8127,plain,
% 1.43/1.69 (((~![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(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))))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8126, 8124])).
% 1.43/1.69 tff(8128,plain,
% 1.43/1.69 ((~![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(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))))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8129,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8128, 8127])).
% 1.43/1.69 tff(8130,plain,
% 1.43/1.69 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8129, 112, 178])).
% 1.43/1.69 tff(8131,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8130, 8123, 8109])).
% 1.43/1.69 tff(8132,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8133,plain,
% 1.43/1.69 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8132, 7994, 78, 7796, 7800, 1, 178, 7847])).
% 1.43/1.69 tff(8134,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8133, 8005])).
% 1.43/1.69 tff(8135,plain,((~r(s(s(elem!1)), s(z))) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | b(z, elem!1) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8136,plain,
% 1.43/1.69 (~r(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8135, 78, 1, 176, 4538, 7733, 4569, 688])).
% 1.43/1.69 tff(8137,plain,
% 1.43/1.69 (b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[901, 8136])).
% 1.43/1.69 tff(8138,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8137, 7767])).
% 1.43/1.69 tff(8139,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.43/1.69 tff(8140,plain,
% 1.43/1.69 (r(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[925, 8139])).
% 1.43/1.69 tff(8141,plain,
% 1.43/1.69 (b(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[454, 129, 2931])).
% 1.43/1.69 tff(8142,plain,
% 1.43/1.69 (~(elem!1 = s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2477, 8141, 170])).
% 1.43/1.69 tff(8143,plain,
% 1.43/1.69 (r(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[388, 8142, 7732])).
% 1.43/1.69 tff(8144,plain,
% 1.43/1.69 (~r(elem!1, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1028, 8143, 176])).
% 1.43/1.69 tff(8145,plain,
% 1.43/1.69 (b(elem!1, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1277, 8144, 2655])).
% 1.43/1.69 tff(8146,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5674, 224, 8141, 8145, 390])).
% 1.43/1.69 tff(8147,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[901, 8146])).
% 1.43/1.69 tff(8148,plain,
% 1.43/1.69 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5342, 112, 8147, 3188])).
% 1.43/1.69 tff(8149,plain,
% 1.43/1.69 (~r(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5688, 112, 4569, 8147])).
% 1.43/1.69 tff(8150,plain,
% 1.43/1.69 (b(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[593, 8149])).
% 1.43/1.69 tff(8151,plain,
% 1.43/1.69 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[284])).
% 1.43/1.69 tff(8152,plain,
% 1.43/1.69 (~(s(s(s(z))) = elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8142, 8151])).
% 1.43/1.69 tff(8153,plain,
% 1.43/1.69 (r(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[374, 8152, 5799])).
% 1.43/1.69 tff(8154,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8155,plain,
% 1.43/1.69 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8156,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8155])).
% 1.43/1.69 tff(8157,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8156, 8154])).
% 1.43/1.69 tff(8158,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8159,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8158, 8157])).
% 1.43/1.69 tff(8160,plain,
% 1.43/1.69 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8159, 112, 8147, 8153, 3188])).
% 1.43/1.69 tff(8161,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[7680, 224, 8150, 4623, 4610])).
% 1.43/1.69 tff(8162,plain,
% 1.43/1.69 (s(s(elem!1)) = s(s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[147, 8161, 8160])).
% 1.43/1.69 tff(8163,plain,
% 1.43/1.69 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8162, 305])).
% 1.43/1.69 tff(8164,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[681, 8163])).
% 1.43/1.69 tff(8165,plain,((s(z) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | b(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)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8166,plain,
% 1.43/1.69 (b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8165, 129, 4569, 390, 3188, 7732, 170, 2931])).
% 1.43/1.69 tff(8167,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8168,plain,
% 1.43/1.69 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8169,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8168])).
% 1.43/1.69 tff(8170,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8169, 8167])).
% 1.43/1.69 tff(8171,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8172,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8171, 8170])).
% 1.43/1.69 tff(8173,plain,
% 1.43/1.69 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8172, 224, 390, 8166, 4623])).
% 1.43/1.69 tff(8174,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8173, 8150])).
% 1.43/1.69 tff(8175,plain,
% 1.43/1.69 (s(s(elem!1)) = s(s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[147, 8174, 8148])).
% 1.43/1.69 tff(8176,plain,
% 1.43/1.69 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8175, 305])).
% 1.43/1.69 tff(8177,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[681, 8176])).
% 1.43/1.69 tff(8178,plain,((s(z) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8179,plain,
% 1.43/1.69 (s(z) = elem!1),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8178, 8140, 390, 4569, 7732, 170, 2931])).
% 1.43/1.69 tff(8180,plain,
% 1.43/1.69 (s(s(z)) = s(elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8179])).
% 1.43/1.69 tff(8181,plain,
% 1.43/1.69 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8180])).
% 1.43/1.69 tff(8182,plain,
% 1.43/1.69 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8181])).
% 1.43/1.69 tff(8183,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[8182])).
% 1.43/1.69 tff(8184,plain,
% 1.43/1.69 (b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[390, 8183])).
% 1.43/1.69 tff(8185,plain,
% 1.43/1.69 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8179])).
% 1.43/1.69 tff(8186,plain,
% 1.43/1.69 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8185])).
% 1.43/1.69 tff(8187,plain,
% 1.43/1.69 (~b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8139, 8186])).
% 1.43/1.69 tff(8188,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8187, 8184])).
% 1.43/1.69 tff(8189,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8190,plain,
% 1.43/1.69 (b(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8189, 170, 4569, 7732, 390, 7731])).
% 1.43/1.69 tff(8191,plain,
% 1.43/1.69 (b(s(z), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[454, 129, 7731])).
% 1.43/1.69 tff(8192,plain,
% 1.43/1.69 (~(elem!1 = s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2477, 8191, 170])).
% 1.43/1.69 tff(8193,plain,
% 1.43/1.69 (r(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[388, 8192, 7732])).
% 1.43/1.69 tff(8194,plain,
% 1.43/1.69 (~r(elem!1, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1028, 8193, 176])).
% 1.43/1.69 tff(8195,plain,
% 1.43/1.69 (b(elem!1, s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1277, 8194, 2655])).
% 1.43/1.69 tff(8196,plain,
% 1.43/1.69 (~b(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5502, 224, 8191, 8195, 8190])).
% 1.43/1.69 tff(8197,plain,
% 1.43/1.69 (~(s(s(s(z))) = elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2487, 8192])).
% 1.43/1.69 tff(8198,plain,
% 1.43/1.69 (r(s(s(s(z))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[374, 8197, 8196])).
% 1.43/1.69 tff(8199,plain,
% 1.43/1.69 (~r(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2431, 8198, 688])).
% 1.43/1.69 tff(8200,plain,
% 1.43/1.69 (b(s(s(s(z))), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[72, 8199])).
% 1.43/1.69 tff(8201,plain,
% 1.43/1.69 (~r(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2420, 8193, 688])).
% 1.43/1.69 tff(8202,plain,
% 1.43/1.69 (b(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[100, 8201])).
% 1.43/1.69 tff(8203,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5674, 224, 8191, 8195, 390])).
% 1.43/1.69 tff(8204,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[901, 8203])).
% 1.43/1.69 tff(8205,plain,
% 1.43/1.69 (~r(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5688, 112, 4569, 8204])).
% 1.43/1.69 tff(8206,plain,
% 1.43/1.69 (b(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[593, 8205])).
% 1.43/1.69 tff(8207,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[7680, 224, 8206, 8202, 8200])).
% 1.43/1.69 tff(8208,plain,
% 1.43/1.69 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[310, 681])).
% 1.43/1.69 tff(8209,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[147, 8208, 8207])).
% 1.43/1.69 tff(8210,plain,
% 1.43/1.69 (~r(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[835, 8209, 176])).
% 1.43/1.69 tff(8211,plain,
% 1.43/1.69 (b(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[653, 8210])).
% 1.43/1.69 tff(8212,plain,
% 1.43/1.69 (~r(z, s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5570, 112, 4569, 8204])).
% 1.43/1.69 tff(8213,plain,
% 1.43/1.69 (b(z, s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[752, 8212])).
% 1.43/1.69 tff(8214,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8215,plain,
% 1.43/1.69 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8216,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8215])).
% 1.43/1.69 tff(8217,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8216, 8214])).
% 1.43/1.69 tff(8218,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8219,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8218, 8217])).
% 1.43/1.69 tff(8220,plain,
% 1.43/1.69 ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8219, 224, 8191, 8213, 390])).
% 1.43/1.69 tff(8221,plain,
% 1.43/1.69 (~b(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8220, 8211])).
% 1.43/1.69 tff(8222,plain,
% 1.43/1.69 (r(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[194, 8221])).
% 1.43/1.69 tff(8223,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8224,plain,
% 1.43/1.69 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8225,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8224])).
% 1.43/1.69 tff(8226,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8225, 8223])).
% 1.43/1.69 tff(8227,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8228,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8227, 8226])).
% 1.43/1.69 tff(8229,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8228, 112, 8222, 8204, 176, 8209])).
% 1.43/1.69 tff(8230,plain,((s(z) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8231,plain,
% 1.43/1.69 (s(z) = elem!1),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8230, 170, 688, 4569, 7732, 390])).
% 1.43/1.69 tff(8232,plain,
% 1.43/1.69 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8231])).
% 1.43/1.69 tff(8233,plain,
% 1.43/1.69 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8232])).
% 1.43/1.69 tff(8234,plain,
% 1.43/1.69 (s(s(z)) = s(elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8231])).
% 1.43/1.69 tff(8235,plain,
% 1.43/1.69 (s(s(s(z))) = s(s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8234])).
% 1.43/1.69 tff(8236,plain,
% 1.43/1.69 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8235])).
% 1.43/1.69 tff(8237,plain,
% 1.43/1.69 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8236, 8233])).
% 1.43/1.69 tff(8238,plain,
% 1.43/1.69 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8231])).
% 1.43/1.69 tff(8239,plain,
% 1.43/1.69 (r(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[176, 8238])).
% 1.43/1.69 tff(8240,plain,
% 1.43/1.69 (r(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8239, 8237])).
% 1.43/1.69 tff(8241,plain,
% 1.43/1.69 (~r(z, s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6325, 8240, 4569])).
% 1.43/1.69 tff(8242,plain,
% 1.43/1.69 (b(z, s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[752, 8241])).
% 1.43/1.69 tff(8243,plain,
% 1.43/1.69 (~b(s(elem!1), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[7872, 8231, 5829])).
% 1.43/1.69 tff(8244,plain,
% 1.43/1.69 (r(s(elem!1), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[939, 8243, 324])).
% 1.43/1.69 tff(8245,plain,
% 1.43/1.69 (~r(s(elem!1), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[722, 112, 8244, 688])).
% 1.43/1.69 tff(8246,plain,
% 1.43/1.69 (b(s(elem!1), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[498, 8245])).
% 1.43/1.69 tff(8247,plain,
% 1.43/1.69 (r(elem!1, s(s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8239, 8236])).
% 1.43/1.69 tff(8248,plain,
% 1.43/1.69 (~r(s(elem!1), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4010, 8247, 8244])).
% 1.43/1.69 tff(8249,plain,
% 1.43/1.69 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1521, 8248, 523])).
% 1.43/1.69 tff(8250,plain,
% 1.43/1.69 (~b(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4154, 8249, 8246, 8242])).
% 1.43/1.69 tff(8251,plain,
% 1.43/1.69 (r(s(s(elem!1)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[593, 8250])).
% 1.43/1.69 tff(8252,plain,
% 1.43/1.69 ((s(z) = z) <=> (elem!1 = z)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8231])).
% 1.43/1.69 tff(8253,plain,
% 1.43/1.69 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8252])).
% 1.43/1.69 tff(8254,plain,
% 1.43/1.69 (~(elem!1 = z)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[190, 8253])).
% 1.43/1.69 tff(8255,plain,
% 1.43/1.69 (~r(z, s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2499, 8244, 688])).
% 1.43/1.69 tff(8256,plain,
% 1.43/1.69 (b(z, s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[625, 8255])).
% 1.43/1.69 tff(8257,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4124, 8249, 8242, 8256])).
% 1.43/1.69 tff(8258,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[530, 8257, 1923])).
% 1.43/1.69 tff(8259,plain,
% 1.43/1.69 (~r(elem!1, s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[553, 8258, 8247])).
% 1.43/1.69 tff(8260,plain,
% 1.43/1.69 (b(elem!1, s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[515, 8259, 2618])).
% 1.43/1.69 tff(8261,plain,
% 1.43/1.69 (~b(elem!1, z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[509, 8260, 8246, 8256])).
% 1.43/1.69 tff(8262,plain,
% 1.43/1.69 (r(elem!1, z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[403, 8261, 8254])).
% 1.43/1.70 tff(8263,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(8264,plain,
% 1.43/1.70 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(8265,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[8264])).
% 1.43/1.70 tff(8266,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.43/1.70 inference(transitivity,[status(thm)],[8265, 8263])).
% 1.43/1.70 tff(8267,plain,
% 1.43/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.43/1.70 inference(quant_inst,[status(thm)],[])).
% 1.43/1.70 tff(8268,plain,
% 1.43/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8267, 8266])).
% 1.43/1.70 tff(8269,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8268, 112, 8247, 8258, 8262, 8251])).
% 1.43/1.70 tff(8270,plain,(b(s(z), s(s(s(z)))) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | b(s(s(z)), elem!1) | b(elem!1, s(s(s(z)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(8271,plain,
% 1.43/1.70 (b(s(s(z)), elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8270, 8138, 4569, 688, 170, 7765, 7732, 7764])).
% 1.43/1.70 tff(8272,plain,
% 1.43/1.70 (b(s(elem!1), elem!1)),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8271, 7762])).
% 1.43/1.70 tff(8273,plain,
% 1.43/1.70 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.70 tff(8274,plain,
% 1.43/1.70 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[78])).
% 1.43/1.70 tff(8275,plain,
% 1.43/1.70 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.43/1.70 inference(transitivity,[status(thm)],[8274, 8273])).
% 1.43/1.70 tff(8276,plain,
% 1.43/1.70 (r(s(z), s(s(z)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[543, 8275])).
% 1.43/1.70 tff(8277,plain,
% 1.43/1.70 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[79])).
% 1.43/1.70 tff(8278,plain,
% 1.43/1.70 (~r(s(s(elem!1)), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[553, 543, 7841])).
% 1.43/1.70 tff(8279,plain,
% 1.43/1.70 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[530, 8278, 7895])).
% 1.43/1.70 tff(8280,plain,
% 1.43/1.70 (~r(s(elem!1), s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[7891, 543, 7794])).
% 1.43/1.70 tff(8281,plain,
% 1.43/1.70 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1534, 8280, 7733])).
% 1.43/1.70 tff(8282,plain,
% 1.43/1.70 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8281, 7882])).
% 1.43/1.70 tff(8283,plain,
% 1.43/1.70 (~b(z, s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4124, 8282, 7844, 8279])).
% 1.53/1.70 tff(8284,plain,
% 1.53/1.70 (r(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[625, 8283])).
% 1.53/1.70 tff(8285,plain,
% 1.53/1.70 (r(z, s(s(z)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8284, 8277])).
% 1.53/1.70 tff(8286,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8287,plain,
% 1.53/1.70 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8288,plain,
% 1.53/1.70 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8287])).
% 1.53/1.70 tff(8289,plain,
% 1.53/1.70 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8288, 8286])).
% 1.53/1.70 tff(8290,plain,
% 1.53/1.70 ((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8291,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8290, 8289])).
% 1.53/1.70 tff(8292,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8291, 112, 4569, 178, 8285, 8276])).
% 1.53/1.70 tff(8293,plain,((~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8294,plain,
% 1.53/1.70 (~r(elem!1, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8293, 78, 176, 4569, 7733])).
% 1.53/1.70 tff(8295,plain,
% 1.53/1.70 (b(elem!1, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[515, 8294, 7878])).
% 1.53/1.70 tff(8296,plain,
% 1.53/1.70 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1496, 501, 390, 1488])).
% 1.53/1.70 tff(8297,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[530, 8296, 7895])).
% 1.53/1.70 tff(8298,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[7775, 7760])).
% 1.53/1.70 tff(8299,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.53/1.70 inference(symmetry,[status(thm)],[8298])).
% 1.53/1.70 tff(8300,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[544, 8299])).
% 1.53/1.70 tff(8301,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.53/1.70 tff(8302,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8301, 8300])).
% 1.53/1.70 tff(8303,plain,(r(s(s(s(z))), s(s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8304,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8303, 8297, 78])).
% 1.53/1.70 tff(8305,plain,
% 1.53/1.70 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.53/1.70 inference(symmetry,[status(thm)],[7858])).
% 1.53/1.70 tff(8306,plain,
% 1.53/1.70 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8305])).
% 1.53/1.70 tff(8307,plain,
% 1.53/1.70 (~r(s(s(z)), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[3531, 8304, 177])).
% 1.53/1.70 tff(8308,plain,
% 1.53/1.70 (~r(s(elem!1), z)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8307, 8306])).
% 1.53/1.70 tff(8309,plain,
% 1.53/1.70 (b(s(elem!1), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[498, 8308])).
% 1.53/1.70 tff(8310,plain,
% 1.53/1.70 (~b(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[509, 8309, 405, 501])).
% 1.53/1.70 tff(8311,plain,
% 1.53/1.70 (r(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[625, 8310])).
% 1.53/1.70 tff(8312,plain,
% 1.53/1.70 (r(z, s(s(z)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8311, 8277])).
% 1.53/1.70 tff(8313,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8314,plain,
% 1.53/1.70 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8315,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8314])).
% 1.53/1.70 tff(8316,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8315, 8313])).
% 1.53/1.70 tff(8317,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8318,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8317, 8316])).
% 1.53/1.70 tff(8319,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8318, 112, 177, 8312, 8304])).
% 1.53/1.70 tff(8320,plain,((~b(elem!1, s(elem!1))) | (~r(s(s(s(z))), z)) | (~(elem!1 = s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8321,plain,
% 1.53/1.70 (~r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8320, 8295, 78, 8013, 8138, 8272])).
% 1.53/1.70 tff(8322,plain,
% 1.53/1.70 (b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[72, 8321])).
% 1.53/1.70 tff(8323,plain,
% 1.53/1.70 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[7830, 8322, 7757, 78, 4569, 7755])).
% 1.53/1.70 tff(8324,plain,
% 1.53/1.70 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1294, 8323, 7752])).
% 1.53/1.70 tff(8325,plain,
% 1.53/1.70 (b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8324, 7744])).
% 1.53/1.70 tff(8326,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[80])).
% 1.53/1.70 tff(8327,plain,
% 1.53/1.70 (b(s(s(s(z))), s(z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8137, 8326])).
% 1.53/1.70 tff(8328,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8329,plain,
% 1.53/1.70 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8330,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8329])).
% 1.53/1.70 tff(8331,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8330, 8328])).
% 1.53/1.70 tff(8332,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8333,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 1.53/1.70 tff(8334,plain,
% 1.53/1.70 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8333, 224, 1, 8322, 8327])).
% 1.53/1.70 tff(8335,plain,
% 1.53/1.70 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8334, 8325])).
% 1.53/1.70 tff(8336,plain,
% 1.53/1.70 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8335, 7741])).
% 1.53/1.70 tff(8337,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5426, 8336])).
% 1.53/1.70 tff(8338,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8337, 7739])).
% 1.53/1.70 tff(8339,plain,
% 1.53/1.70 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1496, 8295, 8138, 8272])).
% 1.53/1.70 tff(8340,plain,
% 1.53/1.70 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[530, 8339, 7895])).
% 1.53/1.70 tff(8341,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8303, 8340, 78])).
% 1.53/1.70 tff(8342,plain,
% 1.53/1.70 (b(s(s(z)), s(z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8271, 7835])).
% 1.53/1.70 tff(8343,plain,
% 1.53/1.70 (b(s(z), s(s(z)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8295, 7877])).
% 1.53/1.70 tff(8344,plain,
% 1.53/1.70 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8001, 224, 8343, 8342])).
% 1.53/1.70 tff(8345,plain,
% 1.53/1.70 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8344, 8325])).
% 1.53/1.70 tff(8346,plain,
% 1.53/1.70 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8345, 7793])).
% 1.53/1.70 tff(8347,plain,
% 1.53/1.70 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1345, 8346, 7791])).
% 1.53/1.70 tff(8348,plain,
% 1.53/1.70 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1289, 7769])).
% 1.53/1.70 tff(8349,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.53/1.70 tff(8350,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8349, 8348])).
% 1.53/1.70 tff(8351,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | r(s(s(s(s(s(z))))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8352,plain,
% 1.53/1.70 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8351, 8347, 78])).
% 1.53/1.70 tff(8353,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8354,plain,
% 1.53/1.70 (((~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(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8355,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8354])).
% 1.53/1.70 tff(8356,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8355, 8353])).
% 1.53/1.70 tff(8357,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8358,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8357, 8356])).
% 1.53/1.70 tff(8359,plain,
% 1.53/1.70 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8358, 112, 8352, 8341])).
% 1.53/1.70 tff(8360,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8359, 8338])).
% 1.53/1.70 tff(8361,plain,((~(elem!1 = s(z))) | (~b(s(z), z)) | (~r(z, s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(z, elem!1)) | b(s(z), s(s(s(z)))) | b(elem!1, s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8362,plain,
% 1.53/1.70 (~(elem!1 = s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8361, 1, 4569, 7733, 688, 170, 7732, 4538])).
% 1.53/1.70 tff(8363,plain,
% 1.53/1.70 (~(s(z) = elem!1)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8362, 7734])).
% 1.53/1.70 tff(8364,plain,
% 1.53/1.70 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8230, 8363, 688, 4569, 7732, 170])).
% 1.53/1.70 tff(8365,plain,
% 1.53/1.70 (b(s(z), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[454, 8363, 7731])).
% 1.53/1.70 tff(8366,plain,
% 1.53/1.70 (~(elem!1 = s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2477, 8365, 170])).
% 1.53/1.70 tff(8367,plain,
% 1.53/1.70 (~(s(s(s(z))) = elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2487, 8366])).
% 1.53/1.70 tff(8368,plain,
% 1.53/1.70 (~r(elem!1, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5490, 4569, 688])).
% 1.53/1.70 tff(8369,plain,
% 1.53/1.70 (b(elem!1, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1277, 8362, 8368])).
% 1.53/1.70 tff(8370,plain,
% 1.53/1.70 (~r(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5504, 8365, 8369, 8367, 688, 4569])).
% 1.53/1.70 tff(8371,plain,
% 1.53/1.70 (b(s(s(s(z))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[72, 8370])).
% 1.53/1.70 tff(8372,plain,
% 1.53/1.70 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[131, 8363])).
% 1.53/1.70 tff(8373,plain,
% 1.53/1.70 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[310, 8372])).
% 1.53/1.70 tff(8374,plain,
% 1.53/1.70 (r(elem!1, s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[388, 8366, 7732])).
% 1.53/1.70 tff(8375,plain,
% 1.53/1.70 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[7684, 8374, 8373, 8371, 688])).
% 1.53/1.70 tff(8376,plain,
% 1.53/1.70 (s(s(elem!1)) = elem!1),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[360, 8375, 8364])).
% 1.53/1.70 tff(8377,plain,
% 1.53/1.70 (elem!1 = s(s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[352, 8376])).
% 1.53/1.70 tff(8378,plain,
% 1.53/1.70 ((elem!1 = z) <=> (s(s(elem!1)) = z)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.70 tff(8379,plain,
% 1.53/1.70 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.53/1.70 inference(symmetry,[status(thm)],[8378])).
% 1.53/1.70 tff(8380,plain,
% 1.53/1.70 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8379])).
% 1.53/1.70 tff(8381,plain,
% 1.53/1.70 (~(elem!1 = z)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[566, 8380])).
% 1.53/1.70 tff(8382,plain,
% 1.53/1.70 (~(s(elem!1) = s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[159, 8381])).
% 1.53/1.70 tff(8383,plain,
% 1.53/1.70 (~(s(z) = s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[414, 8382])).
% 1.53/1.70 tff(8384,plain,
% 1.53/1.70 (s(elem!1) = s(s(s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.70 tff(8385,plain,
% 1.53/1.70 (s(s(s(elem!1))) = s(elem!1)),
% 1.53/1.70 inference(symmetry,[status(thm)],[8384])).
% 1.53/1.70 tff(8386,plain,
% 1.53/1.70 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8385])).
% 1.53/1.70 tff(8387,plain,
% 1.53/1.70 ((~r(s(z), s(s(s(elem!1))))) <=> (~r(s(z), s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8386])).
% 1.53/1.70 tff(8388,plain,
% 1.53/1.70 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8385])).
% 1.53/1.70 tff(8389,plain,
% 1.53/1.70 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[8388])).
% 1.53/1.70 tff(8390,plain,
% 1.53/1.70 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8385])).
% 1.53/1.70 tff(8391,plain,
% 1.53/1.70 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8390])).
% 1.53/1.70 tff(8392,plain,
% 1.53/1.70 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8385])).
% 1.53/1.70 tff(8393,plain,
% 1.53/1.70 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.53/1.70 inference(symmetry,[status(thm)],[8392])).
% 1.53/1.70 tff(8394,plain,
% 1.53/1.70 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.70 tff(8395,plain,
% 1.53/1.70 (b(s(s(elem!1)), s(z))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8369, 8394])).
% 1.53/1.70 tff(8396,plain,
% 1.53/1.70 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.70 tff(8397,plain,
% 1.53/1.70 (b(s(z), s(s(elem!1)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8365, 8396])).
% 1.53/1.70 tff(8398,plain,
% 1.53/1.70 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[520])).
% 1.53/1.70 tff(8399,plain,
% 1.53/1.70 (s(elem!1) = s(s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[525, 521])).
% 1.53/1.70 tff(8400,plain,
% 1.53/1.70 (elem!1 = s(s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[318, 8399])).
% 1.53/1.70 tff(8401,plain,
% 1.53/1.70 (s(s(elem!1)) = elem!1),
% 1.53/1.70 inference(symmetry,[status(thm)],[8400])).
% 1.53/1.70 tff(8402,plain,
% 1.53/1.70 (s(elem!1) = s(s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[521])).
% 1.53/1.70 tff(8403,plain,
% 1.53/1.70 (s(elem!1) = elem!1),
% 1.53/1.70 inference(transitivity,[status(thm)],[8402, 8401])).
% 1.53/1.70 tff(8404,plain,
% 1.53/1.70 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8403])).
% 1.53/1.70 tff(8405,plain,
% 1.53/1.70 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[8404])).
% 1.53/1.70 tff(8406,plain,
% 1.53/1.70 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2588])).
% 1.53/1.71 tff(8407,plain,
% 1.53/1.71 (s(s(s(s(elem!1)))) = elem!1),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1306, 8400])).
% 1.53/1.71 tff(8408,plain,
% 1.53/1.71 (~(elem!1 = s(s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2783, 8400, 8407])).
% 1.53/1.71 tff(8409,plain,
% 1.53/1.71 (~(s(s(z)) = elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8408, 8406])).
% 1.53/1.71 tff(8410,plain,
% 1.53/1.71 (elem!1 = s(elem!1)),
% 1.53/1.71 inference(transitivity,[status(thm)],[8400, 521])).
% 1.53/1.71 tff(8411,plain,
% 1.53/1.71 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8410])).
% 1.53/1.71 tff(8412,plain,
% 1.53/1.71 (r(s(elem!1), s(s(s(z))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1020, 8411])).
% 1.53/1.71 tff(8413,plain,
% 1.53/1.71 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8410])).
% 1.53/1.71 tff(8414,plain,
% 1.53/1.71 (b(s(elem!1), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2896, 8413])).
% 1.53/1.71 tff(8415,plain,
% 1.53/1.71 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), elem!1)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8403])).
% 1.53/1.71 tff(8416,plain,
% 1.53/1.71 ((~r(s(s(z)), s(elem!1))) <=> (~r(s(s(z)), elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8415])).
% 1.53/1.71 tff(8417,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8418,plain,
% 1.53/1.71 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8419,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8418])).
% 1.53/1.71 tff(8420,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8419, 8417])).
% 1.53/1.71 tff(8421,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8422,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8421, 8420])).
% 1.53/1.71 tff(8423,plain,
% 1.53/1.71 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8422, 224, 6255, 7672, 1118])).
% 1.53/1.71 tff(8424,plain,
% 1.53/1.71 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[249, 8423])).
% 1.53/1.71 tff(8425,plain,
% 1.53/1.71 (((~![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(elem!1))) | (~r(s(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(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8426,plain,
% 1.53/1.71 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8427,plain,
% 1.53/1.71 (((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), 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(elem!1))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8426])).
% 1.53/1.71 tff(8428,plain,
% 1.53/1.71 (((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), 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(elem!1))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8427, 8425])).
% 1.53/1.71 tff(8429,plain,
% 1.53/1.71 ((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8430,plain,
% 1.53/1.71 ((~![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(elem!1))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8429, 8428])).
% 1.53/1.71 tff(8431,plain,
% 1.53/1.71 (~r(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8430, 112, 8424, 7883])).
% 1.53/1.71 tff(8432,plain,
% 1.53/1.71 (~r(s(s(z)), elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8431, 8416])).
% 1.53/1.71 tff(8433,plain,
% 1.53/1.71 (b(s(s(z)), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1135, 8432, 8409])).
% 1.53/1.71 tff(8434,plain,
% 1.53/1.71 (b(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8433, 8405])).
% 1.53/1.71 tff(8435,plain,
% 1.53/1.71 (~r(s(s(z)), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[202, 112, 8424, 178])).
% 1.53/1.71 tff(8436,plain,
% 1.53/1.71 (b(s(s(z)), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[213, 68, 210, 8435])).
% 1.53/1.71 tff(8437,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8438,plain,
% 1.53/1.71 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8439,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8438])).
% 1.53/1.71 tff(8440,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8439, 8437])).
% 1.53/1.71 tff(8441,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8442,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8441, 8440])).
% 1.53/1.71 tff(8443,plain,
% 1.53/1.71 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8442, 224, 1, 1347, 1118])).
% 1.53/1.71 tff(8444,plain,
% 1.53/1.71 (~b(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8443, 8436])).
% 1.53/1.71 tff(8445,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8444, 8434])).
% 1.53/1.71 tff(8446,plain,((~b(s(s(z)), z)) | (~(s(s(elem!1)) = s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8447,plain,
% 1.53/1.71 (~b(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8446, 521, 1, 8414, 8412, 178, 7674, 7672])).
% 1.53/1.71 tff(8448,plain,
% 1.53/1.71 (r(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[281, 8447])).
% 1.53/1.71 tff(8449,plain,
% 1.53/1.71 (r(z, elem!1) <=> r(z, s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8410])).
% 1.53/1.71 tff(8450,plain,
% 1.53/1.71 (r(z, s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[688, 8449])).
% 1.53/1.71 tff(8451,plain,
% 1.53/1.71 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8415])).
% 1.53/1.71 tff(8452,plain,
% 1.53/1.71 (r(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1047, 8451])).
% 1.53/1.71 tff(8453,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8454,plain,
% 1.53/1.71 (((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8455,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8454])).
% 1.53/1.71 tff(8456,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8455, 8453])).
% 1.53/1.71 tff(8457,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8458,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8457, 8456])).
% 1.53/1.71 tff(8459,plain,
% 1.53/1.71 (~r(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8458, 112, 4569, 568, 268])).
% 1.53/1.71 tff(8460,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8459, 8452])).
% 1.53/1.71 tff(8461,plain,((~r(s(s(z)), elem!1)) | (~(s(s(elem!1)) = s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8462,plain,
% 1.53/1.71 (~r(s(s(z)), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8461, 521, 4569, 8450, 8448])).
% 1.53/1.71 tff(8463,plain,
% 1.53/1.71 (b(s(s(z)), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1135, 8462, 8409])).
% 1.53/1.71 tff(8464,plain,
% 1.53/1.71 (b(s(s(z)), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8463, 8405])).
% 1.53/1.71 tff(8465,plain,
% 1.53/1.71 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8410])).
% 1.53/1.71 tff(8466,plain,
% 1.53/1.71 (b(s(z), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[684, 8465])).
% 1.53/1.71 tff(8467,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8468,plain,
% 1.53/1.71 (((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8469,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8468])).
% 1.53/1.71 tff(8470,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8469, 8467])).
% 1.53/1.71 tff(8471,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8472,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8471, 8470])).
% 1.53/1.71 tff(8473,plain,
% 1.53/1.71 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8472, 224, 8414, 8466])).
% 1.53/1.71 tff(8474,plain,
% 1.53/1.71 (~b(s(s(z)), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8473, 8464])).
% 1.53/1.71 tff(8475,plain,
% 1.53/1.71 (r(s(s(z)), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[213, 68, 210, 8474])).
% 1.53/1.71 tff(8476,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[6165, 112, 4569, 8448, 8475])).
% 1.53/1.71 tff(8477,plain,((~(s(s(elem!1)) = s(elem!1))) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8478,plain,
% 1.53/1.71 (~(s(s(elem!1)) = s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8477, 1, 4569, 176, 8371, 688, 8374, 8369, 8365])).
% 1.53/1.71 tff(8479,plain,
% 1.53/1.71 (~(s(elem!1) = s(s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8478, 8398])).
% 1.53/1.71 tff(8480,plain,
% 1.53/1.71 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.71 tff(8481,plain,
% 1.53/1.71 (r(z, s(s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[688, 8480])).
% 1.53/1.71 tff(8482,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.71 tff(8483,plain,
% 1.53/1.71 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(symmetry,[status(thm)],[8482])).
% 1.53/1.71 tff(8484,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[467, 8483])).
% 1.53/1.71 tff(8485,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.71 tff(8486,plain,
% 1.53/1.71 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8485])).
% 1.53/1.71 tff(8487,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.71 tff(8488,plain,
% 1.53/1.71 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8487])).
% 1.53/1.71 tff(8489,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.71 tff(8490,plain,
% 1.53/1.71 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8489])).
% 1.53/1.71 tff(8491,plain,
% 1.53/1.71 ((elem!1 = z) <=> (s(s(elem!1)) = z)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1296])).
% 1.53/1.71 tff(8492,plain,
% 1.53/1.71 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.53/1.71 inference(symmetry,[status(thm)],[8491])).
% 1.53/1.71 tff(8493,plain,
% 1.53/1.71 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8492])).
% 1.53/1.71 tff(8494,plain,
% 1.53/1.71 (~(elem!1 = z)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[566, 8493])).
% 1.53/1.71 tff(8495,plain,
% 1.53/1.71 (~(s(elem!1) = s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[159, 8494])).
% 1.53/1.71 tff(8496,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.71 tff(8497,plain,
% 1.53/1.71 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8496])).
% 1.53/1.71 tff(8498,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8499,plain,
% 1.53/1.71 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8500,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8499])).
% 1.53/1.71 tff(8501,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8500, 8498])).
% 1.53/1.72 tff(8502,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8503,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 1.53/1.72 tff(8504,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8503, 224, 2252, 1241, 1698])).
% 1.53/1.72 tff(8505,plain,
% 1.53/1.72 (~b(s(elem!1), s(z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8504, 8497])).
% 1.53/1.72 tff(8506,plain,
% 1.53/1.72 (r(s(elem!1), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1476, 8505, 8495])).
% 1.53/1.72 tff(8507,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8506, 8490])).
% 1.53/1.72 tff(8508,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8509,plain,
% 1.53/1.72 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8510,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8509])).
% 1.53/1.72 tff(8511,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8510, 8508])).
% 1.53/1.72 tff(8512,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8513,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8512, 8511])).
% 1.53/1.72 tff(8514,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8513, 112, 4569, 8484, 8507])).
% 1.53/1.72 tff(8515,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8516,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8515, 467, 1296, 2252, 1241, 4569])).
% 1.53/1.72 tff(8517,plain,
% 1.53/1.72 (~b(s(elem!1), s(s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8516, 8488])).
% 1.53/1.72 tff(8518,plain,
% 1.53/1.72 (r(s(elem!1), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1521, 8517, 523])).
% 1.53/1.72 tff(8519,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8518, 8486])).
% 1.53/1.72 tff(8520,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8521,plain,
% 1.53/1.72 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8522,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8521])).
% 1.53/1.72 tff(8523,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8522, 8520])).
% 1.53/1.72 tff(8524,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8525,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8524, 8523])).
% 1.53/1.72 tff(8526,plain,
% 1.53/1.72 (~r(s(s(s(elem!1))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8525, 112, 4569, 293, 8519])).
% 1.53/1.72 tff(8527,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8526, 8484])).
% 1.53/1.72 tff(8528,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8529,plain,
% 1.53/1.72 (~r(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8528, 8377, 4569, 8481, 8479, 8397, 8395])).
% 1.53/1.72 tff(8530,plain,
% 1.53/1.72 (b(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[498, 8529])).
% 1.53/1.72 tff(8531,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), z)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8530, 8393])).
% 1.53/1.72 tff(8532,plain,
% 1.53/1.72 (~r(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2420, 8374, 688])).
% 1.53/1.72 tff(8533,plain,
% 1.53/1.72 (b(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[100, 8532])).
% 1.53/1.72 tff(8534,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8535,plain,
% 1.53/1.72 (((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8536,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8535])).
% 1.53/1.72 tff(8537,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8536, 8534])).
% 1.53/1.72 tff(8538,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8539,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8538, 8537])).
% 1.53/1.72 tff(8540,plain,
% 1.53/1.72 ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8539, 224, 8533, 8371])).
% 1.53/1.72 tff(8541,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8540, 8531])).
% 1.53/1.72 tff(8542,plain,
% 1.53/1.72 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8541, 8391])).
% 1.53/1.72 tff(8543,plain,
% 1.53/1.72 (r(s(elem!1), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1534, 8542, 7733])).
% 1.53/1.72 tff(8544,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8543, 8389])).
% 1.53/1.72 tff(8545,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8546,plain,
% 1.53/1.72 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8547,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8546])).
% 1.53/1.72 tff(8548,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8547, 8545])).
% 1.53/1.72 tff(8549,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8550,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8549, 8548])).
% 1.53/1.72 tff(8551,plain,
% 1.53/1.72 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8550, 112, 176])).
% 1.53/1.72 tff(8552,plain,
% 1.53/1.72 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8551, 8544])).
% 1.53/1.72 tff(8553,plain,
% 1.53/1.72 (~r(s(z), s(elem!1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8552, 8387])).
% 1.53/1.72 tff(8554,plain,
% 1.53/1.72 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8385])).
% 1.53/1.72 tff(8555,plain,
% 1.53/1.72 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(elem!1)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8554])).
% 1.53/1.72 tff(8556,plain,
% 1.53/1.72 (s(s(elem!1)) = elem!1),
% 1.53/1.72 inference(symmetry,[status(thm)],[8377])).
% 1.53/1.72 tff(8557,plain,
% 1.53/1.72 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8556])).
% 1.53/1.72 tff(8558,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8557])).
% 1.53/1.72 tff(8559,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8377, 8385])).
% 1.53/1.72 tff(8560,plain,
% 1.53/1.72 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8559])).
% 1.53/1.72 tff(8561,plain,
% 1.53/1.72 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.72 tff(8562,plain,
% 1.53/1.72 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8561, 8560])).
% 1.53/1.72 tff(8563,plain,
% 1.53/1.72 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8377])).
% 1.53/1.72 tff(8564,plain,
% 1.53/1.72 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8563])).
% 1.53/1.72 tff(8565,plain,
% 1.53/1.72 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8564])).
% 1.53/1.72 tff(8566,plain,
% 1.53/1.72 (~(elem!1 = s(elem!1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8478, 8565])).
% 1.53/1.72 tff(8567,plain,
% 1.53/1.72 (~r(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7891, 8543, 8374])).
% 1.53/1.72 tff(8568,plain,
% 1.53/1.72 (b(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[515, 8567, 8566])).
% 1.53/1.72 tff(8569,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8568, 8562])).
% 1.53/1.72 tff(8570,plain,
% 1.53/1.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8569, 8558])).
% 1.53/1.72 tff(8571,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8572,plain,
% 1.53/1.72 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8573,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8572])).
% 1.53/1.72 tff(8574,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8573, 8571])).
% 1.53/1.72 tff(8575,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8576,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8575, 8574])).
% 1.53/1.72 tff(8577,plain,
% 1.53/1.72 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8576, 224, 1, 8397, 8531])).
% 1.53/1.72 tff(8578,plain,
% 1.53/1.72 (~b(s(z), s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8577, 8570])).
% 1.53/1.72 tff(8579,plain,
% 1.53/1.72 (~b(s(z), s(elem!1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8578, 8555])).
% 1.53/1.72 tff(8580,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[670, 8579, 8553, 8383])).
% 1.53/1.72 tff(8581,plain,((~b(s(z), z)) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8582,plain,
% 1.53/1.72 (~b(s(z), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8581, 7733, 4569, 688, 7732, 170, 4538])).
% 1.53/1.72 tff(8583,plain,
% 1.53/1.72 (r(s(z), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[194, 8582])).
% 1.53/1.72 tff(8584,plain,
% 1.53/1.72 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8230, 149, 688, 4569, 7732, 170])).
% 1.53/1.72 tff(8585,plain,
% 1.53/1.72 (b(s(z), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[454, 149, 7731])).
% 1.53/1.72 tff(8586,plain,
% 1.53/1.72 (~(elem!1 = s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2477, 8585, 170])).
% 1.53/1.72 tff(8587,plain,
% 1.53/1.72 (r(elem!1, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[388, 8586, 7732])).
% 1.53/1.72 tff(8588,plain,
% 1.53/1.72 (b(elem!1, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1277, 88, 8368])).
% 1.53/1.72 tff(8589,plain,
% 1.53/1.72 (~(s(s(s(z))) = elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2487, 8586])).
% 1.53/1.72 tff(8590,plain,
% 1.53/1.72 (~r(s(s(s(z))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5504, 8589, 8588, 8585, 688, 4569])).
% 1.53/1.72 tff(8591,plain,
% 1.53/1.72 (b(s(s(s(z))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[72, 8590])).
% 1.53/1.72 tff(8592,plain,
% 1.53/1.72 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7684, 8591, 311, 8587, 688])).
% 1.53/1.72 tff(8593,plain,
% 1.53/1.72 (s(s(elem!1)) = elem!1),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[360, 8592, 8584])).
% 1.53/1.72 tff(8594,plain,
% 1.53/1.72 (elem!1 = s(s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[352, 8593])).
% 1.53/1.73 tff(8595,plain,
% 1.53/1.73 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8594])).
% 1.53/1.73 tff(8596,plain,
% 1.53/1.73 (r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8587, 8595])).
% 1.53/1.73 tff(8597,plain,
% 1.53/1.73 (~r(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2420, 8587, 688])).
% 1.53/1.73 tff(8598,plain,
% 1.53/1.73 (b(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[100, 8597])).
% 1.53/1.73 tff(8599,plain,
% 1.53/1.73 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8594])).
% 1.53/1.73 tff(8600,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8588, 8599])).
% 1.53/1.73 tff(8601,plain,
% 1.53/1.73 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8594])).
% 1.53/1.73 tff(8602,plain,
% 1.53/1.73 (b(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8585, 8601])).
% 1.53/1.73 tff(8603,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8604,plain,
% 1.53/1.73 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8605,plain,
% 1.53/1.73 (((~![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(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8604])).
% 1.53/1.73 tff(8606,plain,
% 1.53/1.73 (((~![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(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8605, 8603])).
% 1.53/1.73 tff(8607,plain,
% 1.53/1.73 ((~![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(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(8608,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8607, 8606])).
% 1.53/1.73 tff(8609,plain,
% 1.53/1.73 (~r(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8608, 112, 179, 8424, 178])).
% 1.53/1.73 tff(8610,plain,
% 1.53/1.73 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1300])).
% 1.53/1.73 tff(8611,plain,
% 1.53/1.73 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8610])).
% 1.53/1.73 tff(8612,plain,
% 1.53/1.73 (~(elem!1 = s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2783, 1296, 2831])).
% 1.53/1.73 tff(8613,plain,
% 1.53/1.73 (~(s(s(z)) = elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8612, 8406])).
% 1.53/1.73 tff(8614,plain,
% 1.53/1.73 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1300])).
% 1.53/1.73 tff(8615,plain,
% 1.53/1.73 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8614])).
% 1.53/1.73 tff(8616,plain,
% 1.53/1.73 (((~![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(z))))) | (~r(s(s(z)), s(s(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8617,plain,
% 1.53/1.73 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8618,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(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(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8617])).
% 1.53/1.73 tff(8619,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(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(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8618, 8616])).
% 1.53/1.73 tff(8620,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(8621,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8620, 8619])).
% 1.53/1.73 tff(8622,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8621, 112, 8424, 827, 267])).
% 1.53/1.73 tff(8623,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(8624,plain,
% 1.53/1.73 (~r(s(s(z)), s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8623, 1118, 6255, 7672, 827])).
% 1.53/1.73 tff(8625,plain,
% 1.53/1.73 (~r(s(s(z)), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8624, 8615])).
% 1.53/1.73 tff(8626,plain,
% 1.53/1.73 (b(s(s(z)), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1135, 8625, 8613])).
% 1.53/1.73 tff(8627,plain,
% 1.53/1.73 (b(s(s(z)), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8626, 8611])).
% 1.53/1.73 tff(8628,plain,
% 1.53/1.73 (~b(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 1241, 8627])).
% 1.53/1.73 tff(8629,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[213, 68, 210, 8628, 8609])).
% 1.53/1.73 tff(8630,plain,((~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(8631,plain,
% 1.53/1.73 (~b(s(s(z)), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8630, 8602, 176, 179, 8600, 8594, 8598, 8591, 8596])).
% 1.53/1.73 tff(8632,plain,
% 1.53/1.73 (r(s(s(z)), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[281, 8631])).
% 1.53/1.73 tff(8633,plain,
% 1.53/1.73 (~r(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3470, 112, 179, 8632])).
% 1.53/1.73 tff(8634,plain,
% 1.53/1.73 (s(s(elem!1)) = elem!1),
% 1.53/1.73 inference(symmetry,[status(thm)],[8594])).
% 1.53/1.73 tff(8635,plain,
% 1.53/1.73 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8634])).
% 1.53/1.73 tff(8636,plain,
% 1.53/1.73 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8635])).
% 1.53/1.73 tff(8637,plain,
% 1.53/1.73 (s(s(s(s(elem!1)))) = elem!1),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1306, 8594])).
% 1.53/1.73 tff(8638,plain,
% 1.53/1.73 (~(elem!1 = s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2783, 8594, 8637])).
% 1.53/1.73 tff(8639,plain,
% 1.53/1.73 (~(s(s(z)) = elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8638, 8406])).
% 1.53/1.73 tff(8640,plain,
% 1.53/1.73 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8594])).
% 1.53/1.73 tff(8641,plain,
% 1.53/1.73 (r(z, s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[688, 8640])).
% 1.53/1.73 tff(8642,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.73 tff(8643,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8642])).
% 1.53/1.73 tff(8644,plain,
% 1.53/1.73 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.73 tff(8645,plain,
% 1.53/1.73 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8644])).
% 1.53/1.73 tff(8646,plain,
% 1.53/1.73 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1296])).
% 1.53/1.73 tff(8647,plain,
% 1.53/1.73 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.53/1.73 inference(symmetry,[status(thm)],[8646])).
% 1.53/1.73 tff(8648,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.53/1.73 inference(transitivity,[status(thm)],[8487, 8647])).
% 1.53/1.73 tff(8649,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.73 tff(8650,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8649, 519])).
% 1.53/1.73 tff(8651,plain,
% 1.53/1.73 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8650])).
% 1.53/1.73 tff(8652,plain,
% 1.53/1.73 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8651])).
% 1.53/1.73 tff(8653,plain,
% 1.53/1.73 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2505, 8652])).
% 1.53/1.73 tff(8654,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.53/1.73 tff(8655,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(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(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8656,plain,
% 1.53/1.73 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8657,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8656])).
% 1.53/1.73 tff(8658,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8657, 8655])).
% 1.53/1.73 tff(8659,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(8660,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8659, 8658])).
% 1.53/1.73 tff(8661,plain,
% 1.53/1.73 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8660, 112, 827])).
% 1.53/1.73 tff(8662,plain,
% 1.53/1.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8661, 8654])).
% 1.53/1.73 tff(8663,plain,
% 1.53/1.73 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3903, 68, 8662])).
% 1.53/1.73 tff(8664,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8663, 8653])).
% 1.53/1.73 tff(8665,plain,
% 1.53/1.73 (b(s(elem!1), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8664, 8648])).
% 1.53/1.73 tff(8666,plain,
% 1.53/1.73 (~(s(z) = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[414, 8495])).
% 1.53/1.73 tff(8667,plain,
% 1.53/1.73 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.73 tff(8668,plain,
% 1.53/1.73 ((~r(s(z), s(s(s(elem!1))))) <=> (~r(s(z), s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8667])).
% 1.53/1.73 tff(8669,plain,
% 1.53/1.73 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8550, 112, 178])).
% 1.53/1.73 tff(8670,plain,
% 1.53/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8669, 8654])).
% 1.53/1.73 tff(8671,plain,
% 1.53/1.73 (~r(s(z), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8670, 8668])).
% 1.53/1.73 tff(8672,plain,
% 1.53/1.73 (b(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[670, 8671, 8666])).
% 1.53/1.73 tff(8673,plain,
% 1.53/1.73 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1296])).
% 1.53/1.73 tff(8674,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8673])).
% 1.53/1.73 tff(8675,plain,
% 1.53/1.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[6055, 1298])).
% 1.53/1.73 tff(8676,plain,
% 1.53/1.73 (elem!1 = s(s(s(s(elem!1))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[2831])).
% 1.53/1.73 tff(8677,plain,
% 1.53/1.73 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1300, 8676])).
% 1.53/1.73 tff(8678,plain,
% 1.53/1.73 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8677])).
% 1.53/1.73 tff(8679,plain,
% 1.53/1.73 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8678, 8675])).
% 1.53/1.73 tff(8680,plain,
% 1.53/1.73 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8679])).
% 1.53/1.73 tff(8681,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(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(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8682,plain,
% 1.53/1.73 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8683,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8682])).
% 1.53/1.73 tff(8684,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8683, 8681])).
% 1.53/1.73 tff(8685,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(8686,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8685, 8684])).
% 1.53/1.73 tff(8687,plain,
% 1.53/1.73 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8686, 112, 827])).
% 1.53/1.73 tff(8688,plain,
% 1.53/1.73 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8687, 8654])).
% 1.53/1.73 tff(8689,plain,
% 1.53/1.73 (~r(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8688, 8680])).
% 1.53/1.73 tff(8690,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[530, 8689, 2505])).
% 1.53/1.73 tff(8691,plain,
% 1.53/1.73 (b(elem!1, s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8690, 8674])).
% 1.53/1.73 tff(8692,plain,
% 1.53/1.73 (~b(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4221, 8691, 684, 8672])).
% 1.53/1.73 tff(8693,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8692, 8665])).
% 1.53/1.73 tff(8694,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(8695,plain,
% 1.53/1.73 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8694, 2505, 684, 1296, 827, 178])).
% 1.53/1.73 tff(8696,plain,
% 1.53/1.73 (~r(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8695, 8645])).
% 1.53/1.73 tff(8697,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1534, 8696, 7733])).
% 1.53/1.73 tff(8698,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8697, 8643])).
% 1.53/1.73 tff(8699,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1298])).
% 1.53/1.73 tff(8700,plain,
% 1.53/1.73 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(symmetry,[status(thm)],[8699])).
% 1.53/1.73 tff(8701,plain,
% 1.53/1.73 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1296])).
% 1.53/1.73 tff(8702,plain,
% 1.53/1.73 (b(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[684, 8701])).
% 1.53/1.73 tff(8703,plain,
% 1.53/1.73 (~(s(elem!1) = s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2505, 8398])).
% 1.53/1.73 tff(8704,plain,
% 1.53/1.73 (~r(s(elem!1), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8528, 8703, 4569, 1296, 293, 8702, 1241])).
% 1.53/1.73 tff(8705,plain,
% 1.53/1.73 (b(s(elem!1), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[498, 8704])).
% 1.53/1.73 tff(8706,plain,
% 1.53/1.73 (b(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8705, 8700])).
% 1.53/1.73 tff(8707,plain,
% 1.53/1.73 (((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(8708,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8707])).
% 1.53/1.73 tff(8709,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8708, 8534])).
% 1.53/1.73 tff(8710,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(8711,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8710, 8709])).
% 1.53/1.73 tff(8712,plain,
% 1.53/1.73 ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8711, 224, 6255, 7672])).
% 1.53/1.73 tff(8713,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8712, 8706, 8698])).
% 1.53/1.73 tff(8714,plain,((s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(elem!1 = s(s(elem!1)))) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(8715,plain,
% 1.53/1.73 (s(s(elem!1)) = s(elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8714, 8598, 8591, 8594, 7733, 4569, 8641, 8600, 8585, 8596, 176])).
% 1.53/1.73 tff(8716,plain,
% 1.53/1.73 (s(elem!1) = s(s(elem!1))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8715])).
% 1.53/1.73 tff(8717,plain,
% 1.53/1.73 (r(z, s(elem!1)) <=> r(z, s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8716])).
% 1.53/1.73 tff(8718,plain,
% 1.53/1.73 (r(z, s(s(elem!1))) <=> r(z, s(elem!1))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8717])).
% 1.53/1.73 tff(8719,plain,
% 1.53/1.73 (r(z, s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8641, 8718])).
% 1.53/1.73 tff(8720,plain,
% 1.53/1.73 (~r(s(s(z)), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8461, 8632, 4569, 8715, 8719])).
% 1.53/1.73 tff(8721,plain,
% 1.53/1.73 (b(s(s(z)), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1135, 8720, 8639])).
% 1.53/1.73 tff(8722,plain,
% 1.53/1.73 (b(s(s(z)), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8721, 8636])).
% 1.53/1.73 tff(8723,plain,
% 1.53/1.73 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5850, 224, 8602, 8600])).
% 1.53/1.73 tff(8724,plain,
% 1.53/1.73 (~b(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8723, 8722])).
% 1.53/1.73 tff(8725,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[213, 68, 210, 8724, 8633])).
% 1.53/1.73 tff(8726,plain,((elem!1 = s(z)) | (~r(s(z), z)) | (~r(z, s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(8727,plain,
% 1.53/1.73 (elem!1 = s(z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8726, 8583, 4569, 7733, 688, 7732, 170])).
% 1.53/1.73 tff(8728,plain,
% 1.53/1.73 (s(elem!1) = s(s(z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8727])).
% 1.53/1.73 tff(8729,plain,
% 1.53/1.73 (s(s(elem!1)) = s(s(s(z)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8728])).
% 1.53/1.73 tff(8730,plain,
% 1.53/1.73 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8729])).
% 1.53/1.73 tff(8731,plain,
% 1.53/1.73 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8730])).
% 1.53/1.73 tff(8732,plain,
% 1.53/1.73 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8731])).
% 1.53/1.73 tff(8733,plain,
% 1.53/1.73 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8732])).
% 1.53/1.73 tff(8734,plain,
% 1.53/1.73 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8733])).
% 1.53/1.73 tff(8735,plain,
% 1.53/1.73 (s(z) = elem!1),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2654, 8727])).
% 1.53/1.73 tff(8736,plain,
% 1.53/1.73 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[7751, 8735])).
% 1.53/1.73 tff(8737,plain,
% 1.53/1.73 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1306, 8736])).
% 1.53/1.73 tff(8738,plain,
% 1.53/1.73 (~(s(elem!1) = s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[318, 8737])).
% 1.53/1.73 tff(8739,plain,
% 1.53/1.73 (~(s(s(elem!1)) = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[525, 8738])).
% 1.53/1.73 tff(8740,plain,
% 1.53/1.73 (~(s(elem!1) = elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[302, 8737])).
% 1.53/1.73 tff(8741,plain,
% 1.53/1.73 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8727])).
% 1.53/1.73 tff(8742,plain,
% 1.53/1.73 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8741])).
% 1.53/1.73 tff(8743,plain,
% 1.53/1.73 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8729])).
% 1.53/1.73 tff(8744,plain,
% 1.53/1.73 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8743])).
% 1.53/1.73 tff(8745,plain,
% 1.53/1.73 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[8744, 8742])).
% 1.53/1.73 tff(8746,plain,
% 1.53/1.73 (r(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[176, 8745])).
% 1.53/1.73 tff(8747,plain,
% 1.53/1.73 (r(s(z), s(s(elem!1)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[176, 8744])).
% 1.53/1.73 tff(8748,plain,
% 1.53/1.73 (~r(z, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[6325, 8747, 4569])).
% 1.53/1.73 tff(8749,plain,
% 1.53/1.73 (b(z, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[752, 8748])).
% 1.53/1.73 tff(8750,plain,
% 1.53/1.73 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8729])).
% 1.53/1.73 tff(8751,plain,
% 1.53/1.73 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.53/1.73 inference(symmetry,[status(thm)],[8750])).
% 1.53/1.73 tff(8752,plain,
% 1.53/1.73 (~r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[187, 8583, 176])).
% 1.53/1.73 tff(8753,plain,
% 1.53/1.73 (b(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[72, 8752])).
% 1.53/1.73 tff(8754,plain,
% 1.53/1.73 (b(s(s(elem!1)), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8753, 8751])).
% 1.53/1.73 tff(8755,plain,
% 1.53/1.73 (~r(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[7865, 8754, 4569, 8727, 8749, 8746])).
% 1.53/1.73 tff(8756,plain,
% 1.53/1.73 (b(s(elem!1), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[939, 8755, 8740])).
% 1.53/1.73 tff(8757,plain,
% 1.53/1.73 (~r(elem!1, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8293, 8727, 176, 4569, 7733])).
% 1.53/1.73 tff(8758,plain,
% 1.53/1.73 (~(elem!1 = s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[326, 8740])).
% 1.53/1.73 tff(8759,plain,
% 1.53/1.73 (b(elem!1, s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[515, 8758, 8757])).
% 1.53/1.73 tff(8760,plain,
% 1.53/1.73 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8727])).
% 1.53/1.73 tff(8761,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.53/1.73 inference(symmetry,[status(thm)],[8760])).
% 1.53/1.73 tff(8762,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8729])).
% 1.53/1.73 tff(8763,plain,
% 1.53/1.73 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8762])).
% 1.53/1.73 tff(8764,plain,
% 1.53/1.73 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.53/1.73 inference(transitivity,[status(thm)],[8763, 8761])).
% 1.53/1.73 tff(8765,plain,
% 1.53/1.73 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[8727])).
% 1.53/1.73 tff(8766,plain,
% 1.53/1.74 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8765])).
% 1.53/1.74 tff(8767,plain,
% 1.53/1.74 (r(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[176, 8766])).
% 1.53/1.74 tff(8768,plain,
% 1.53/1.74 (~r(z, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2420, 8767, 688])).
% 1.53/1.74 tff(8769,plain,
% 1.53/1.74 (b(z, s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[100, 8768])).
% 1.53/1.74 tff(8770,plain,
% 1.53/1.74 (elem!1 = s(s(s(s(z))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[3104])).
% 1.53/1.74 tff(8771,plain,
% 1.53/1.74 (s(z) = s(s(s(s(z))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[7742, 8770])).
% 1.53/1.74 tff(8772,plain,
% 1.53/1.74 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8771])).
% 1.53/1.74 tff(8773,plain,
% 1.53/1.74 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8772])).
% 1.53/1.74 tff(8774,plain,
% 1.53/1.74 (s(s(s(z))) = z),
% 1.53/1.74 inference(transitivity,[status(thm)],[1679, 8773, 27])).
% 1.53/1.74 tff(8775,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[58, 8774])).
% 1.53/1.74 tff(8776,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8777,plain,
% 1.53/1.74 (~(s(s(s(s(z)))) = elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8776, 8727])).
% 1.53/1.74 tff(8778,plain,
% 1.53/1.74 (s(z) = elem!1),
% 1.53/1.74 inference(symmetry,[status(thm)],[8727])).
% 1.53/1.74 tff(8779,plain,
% 1.53/1.74 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8778, 8732])).
% 1.53/1.74 tff(8780,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8779])).
% 1.53/1.74 tff(8781,plain,
% 1.53/1.74 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1407, 8736])).
% 1.53/1.74 tff(8782,plain,
% 1.53/1.74 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8006])).
% 1.53/1.74 tff(8783,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.74 tff(8784,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.53/1.74 tff(8785,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8129, 112, 178, 8783, 8784])).
% 1.53/1.74 tff(8786,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8787,plain,
% 1.53/1.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8786, 8783, 178])).
% 1.53/1.74 tff(8788,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8787, 8782])).
% 1.53/1.74 tff(8789,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1884, 8788])).
% 1.53/1.74 tff(8790,plain,
% 1.53/1.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8789, 7818])).
% 1.53/1.74 tff(8791,plain,
% 1.53/1.74 (~r(s(s(s(z))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[187, 179, 178])).
% 1.53/1.74 tff(8792,plain,
% 1.53/1.74 (b(s(s(s(z))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[72, 8791])).
% 1.53/1.74 tff(8793,plain,
% 1.53/1.74 (~b(s(s(s(s(s(z))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7825, 224, 6255, 8792, 8790])).
% 1.53/1.74 tff(8794,plain,
% 1.53/1.74 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8795,plain,
% 1.53/1.74 (~(s(s(s(s(s(z))))) = z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8794, 40])).
% 1.53/1.74 tff(8796,plain,
% 1.53/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8797,plain,
% 1.53/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8798,plain,
% 1.53/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8797, 8796])).
% 1.53/1.74 tff(8799,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 8793])).
% 1.53/1.74 tff(8800,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8801,plain,
% 1.53/1.74 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8802,plain,
% 1.53/1.74 (((~![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))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), 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), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8801])).
% 1.53/1.74 tff(8803,plain,
% 1.53/1.74 (((~![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))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), 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), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[8802, 8800])).
% 1.53/1.74 tff(8804,plain,
% 1.53/1.74 ((~![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))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8805,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8804, 8803])).
% 1.53/1.74 tff(8806,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8805, 112, 179, 8783, 8799])).
% 1.53/1.74 tff(8807,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8808,plain,
% 1.53/1.74 (~r(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8807, 8583, 8769, 8727, 176])).
% 1.53/1.74 tff(8809,plain,
% 1.53/1.74 (r(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8067, 8111])).
% 1.53/1.74 tff(8810,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.74 tff(8811,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8810, 8809])).
% 1.53/1.74 tff(8812,plain,(r(s(z), s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8813,plain,
% 1.53/1.74 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8812, 8808, 8727])).
% 1.53/1.74 tff(8814,plain,
% 1.53/1.74 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1439, 8813, 8781])).
% 1.53/1.74 tff(8815,plain,
% 1.53/1.74 (b(s(z), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8814, 8780])).
% 1.53/1.74 tff(8816,plain,
% 1.53/1.74 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8732, 8778])).
% 1.53/1.74 tff(8817,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8816])).
% 1.53/1.74 tff(8818,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7830, 8753, 8727, 8769, 4569, 8767])).
% 1.53/1.74 tff(8819,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1294, 8818, 8736])).
% 1.53/1.74 tff(8820,plain,
% 1.53/1.74 (b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8819, 8817])).
% 1.53/1.74 tff(8821,plain,
% 1.53/1.74 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8778])).
% 1.53/1.74 tff(8822,plain,
% 1.53/1.74 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8821])).
% 1.53/1.74 tff(8823,plain,
% 1.53/1.74 (b(s(s(z)), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7872, 8756, 8735])).
% 1.53/1.74 tff(8824,plain,
% 1.53/1.74 (b(s(s(z)), s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8823, 8822])).
% 1.53/1.74 tff(8825,plain,
% 1.53/1.74 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8728])).
% 1.53/1.74 tff(8826,plain,
% 1.53/1.74 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8727])).
% 1.53/1.74 tff(8827,plain,
% 1.53/1.74 (b(s(z), s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8759, 8826])).
% 1.53/1.74 tff(8828,plain,
% 1.53/1.74 (b(s(z), s(s(z)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8827, 8825])).
% 1.53/1.74 tff(8829,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.74 tff(8830,plain,
% 1.53/1.74 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8829])).
% 1.53/1.74 tff(8831,plain,
% 1.53/1.74 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1679, 8830, 2326, 8829, 7737])).
% 1.53/1.74 tff(8832,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1165, 8831])).
% 1.53/1.74 tff(8833,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8834,plain,
% 1.53/1.74 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8833, 8727])).
% 1.53/1.74 tff(8835,plain,
% 1.53/1.74 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8732])).
% 1.53/1.74 tff(8836,plain,
% 1.53/1.74 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8835])).
% 1.53/1.74 tff(8837,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8728])).
% 1.53/1.74 tff(8838,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[8837, 8836])).
% 1.53/1.74 tff(8839,plain,
% 1.53/1.74 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1143, 7773])).
% 1.53/1.74 tff(8840,plain,
% 1.53/1.74 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1675, 8839])).
% 1.53/1.74 tff(8841,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7788, 8840])).
% 1.53/1.74 tff(8842,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(8843,plain,
% 1.53/1.74 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8842, 8735])).
% 1.53/1.74 tff(8844,plain,
% 1.53/1.74 (s(s(z)) = s(elem!1)),
% 1.53/1.74 inference(symmetry,[status(thm)],[8728])).
% 1.53/1.74 tff(8845,plain,
% 1.53/1.74 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8844, 8732])).
% 1.53/1.74 tff(8846,plain,
% 1.53/1.74 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8845])).
% 1.53/1.74 tff(8847,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8848,plain,
% 1.53/1.74 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(s(z)), s(z)))) <=> ((~b(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))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8849,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8848])).
% 1.53/1.74 tff(8850,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[8849, 8847])).
% 1.53/1.74 tff(8851,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(s(z)), s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8852,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8851, 8850])).
% 1.53/1.74 tff(8853,plain,
% 1.53/1.74 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8852, 224, 8824, 8820, 8815])).
% 1.53/1.74 tff(8854,plain,
% 1.53/1.74 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8853, 8846])).
% 1.53/1.74 tff(8855,plain,
% 1.53/1.74 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1869, 8854, 8843])).
% 1.53/1.74 tff(8856,plain,
% 1.53/1.74 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8855, 8838])).
% 1.53/1.74 tff(8857,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5194, 224, 5187, 1570, 2844])).
% 1.53/1.74 tff(8858,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 8857])).
% 1.53/1.74 tff(8859,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8860,plain,
% 1.53/1.74 (((~b(s(s(s(s(s(z))))), 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(z)))), s(z)))) <=> ((~b(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(z)))), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8861,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8860])).
% 1.53/1.74 tff(8862,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[8861, 8859])).
% 1.53/1.74 tff(8863,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8864,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8863, 8862])).
% 1.53/1.74 tff(8865,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8864, 224, 1570, 4495, 4494])).
% 1.53/1.74 tff(8866,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.74 tff(8867,plain,
% 1.53/1.74 (((~![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)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8868,plain,
% 1.53/1.74 ((~![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)))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(8869,plain,
% 1.53/1.74 ((~![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))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[8868, 8867])).
% 1.53/1.74 tff(8870,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8869, 68, 8866, 8865])).
% 1.53/1.74 tff(8871,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.74 tff(8872,plain,
% 1.53/1.74 (((~![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(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(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8873,plain,
% 1.53/1.74 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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(s(z))))) <=> ((~r(s(s(s(s(z)))), 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))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(8874,plain,
% 1.53/1.74 (((~![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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[8873])).
% 1.53/1.74 tff(8875,plain,
% 1.53/1.74 (((~![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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[8874, 8872])).
% 1.53/1.74 tff(8876,plain,
% 1.53/1.74 ((~![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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(8877,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8876, 8875])).
% 1.53/1.75 tff(8878,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8877, 112, 8871, 8870, 8858])).
% 1.53/1.75 tff(8879,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(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(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8880,plain,
% 1.53/1.75 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8879, 8856, 8834, 8828, 8824, 8820, 8815])).
% 1.53/1.75 tff(8881,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[78])).
% 1.53/1.75 tff(8882,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[5274, 8881])).
% 1.53/1.75 tff(8883,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3163, 8882])).
% 1.53/1.75 tff(8884,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8885,plain,
% 1.53/1.75 (~b(s(s(s(s(z)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8884, 8880, 8727])).
% 1.53/1.75 tff(8886,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3183, 8885, 8777])).
% 1.53/1.75 tff(8887,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[78])).
% 1.53/1.75 tff(8888,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2274, 8887])).
% 1.53/1.75 tff(8889,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3162, 8888])).
% 1.53/1.75 tff(8890,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8891,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8890, 8886, 8727])).
% 1.53/1.75 tff(8892,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 6092])).
% 1.53/1.75 tff(8893,plain,
% 1.53/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3326, 3317, 3188])).
% 1.53/1.75 tff(8894,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3252, 8893])).
% 1.53/1.75 tff(8895,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8896,plain,
% 1.53/1.75 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8897,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8896])).
% 1.53/1.75 tff(8898,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8897, 8895])).
% 1.53/1.75 tff(8899,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(8900,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8899, 8898])).
% 1.53/1.75 tff(8901,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8900, 224, 6255, 7672, 8894, 8892])).
% 1.53/1.75 tff(8902,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8903,plain,
% 1.53/1.75 (~r(s(s(s(z))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8902, 8891, 8753, 4569, 8769])).
% 1.53/1.75 tff(8904,plain,
% 1.53/1.75 (b(s(s(s(z))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[925, 8903])).
% 1.53/1.75 tff(8905,plain,
% 1.53/1.75 (b(s(s(elem!1)), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8904, 8764])).
% 1.53/1.75 tff(8906,plain,
% 1.53/1.75 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1496, 8905, 8759, 8756])).
% 1.53/1.75 tff(8907,plain,
% 1.53/1.75 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[530, 8906, 8739])).
% 1.53/1.75 tff(8908,plain,
% 1.53/1.75 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8303, 8907, 8727])).
% 1.53/1.75 tff(8909,plain,
% 1.53/1.75 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[7790, 8735])).
% 1.53/1.75 tff(8910,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8731, 8728])).
% 1.53/1.75 tff(8911,plain,
% 1.53/1.75 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(symmetry,[status(thm)],[8910])).
% 1.53/1.75 tff(8912,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8911])).
% 1.53/1.75 tff(8913,plain,
% 1.53/1.75 ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8001, 224, 8828])).
% 1.53/1.75 tff(8914,plain,
% 1.53/1.75 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8913, 8824, 8820])).
% 1.53/1.75 tff(8915,plain,
% 1.53/1.75 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8914, 8912])).
% 1.53/1.75 tff(8916,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1345, 8915, 8909])).
% 1.53/1.75 tff(8917,plain,
% 1.53/1.75 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8351, 8916, 8727])).
% 1.53/1.75 tff(8918,plain,
% 1.53/1.75 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8358, 112, 8917, 8908])).
% 1.53/1.75 tff(8919,plain,
% 1.53/1.75 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8918, 8734])).
% 1.53/1.75 tff(8920,plain,
% 1.53/1.75 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8732])).
% 1.53/1.75 tff(8921,plain,
% 1.53/1.75 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8920])).
% 1.53/1.75 tff(8922,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8923,plain,
% 1.53/1.75 (((~b(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(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(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8924,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8923])).
% 1.53/1.75 tff(8925,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8924, 8922])).
% 1.53/1.75 tff(8926,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(8927,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8926, 8925])).
% 1.53/1.75 tff(8928,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8927, 224, 8904, 8820, 8815])).
% 1.53/1.75 tff(8929,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8928, 8921])).
% 1.53/1.75 tff(8930,plain,
% 1.53/1.75 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5426, 8929])).
% 1.53/1.75 tff(8931,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8930, 8919])).
% 1.53/1.75 tff(8932,plain,((s(elem!1) = s(s(s(z)))) | (~r(z, s(z))) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8933,plain,
% 1.53/1.75 (s(elem!1) = s(s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8932, 170, 688, 7732, 4569, 4538])).
% 1.53/1.75 tff(8934,plain,
% 1.53/1.75 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8933])).
% 1.53/1.75 tff(8935,plain,
% 1.53/1.75 (elem!1 = s(s(z))),
% 1.53/1.75 inference(transitivity,[status(thm)],[155, 8934, 31])).
% 1.53/1.75 tff(8936,plain,
% 1.53/1.75 ((s(z) = elem!1) <=> (s(z) = s(s(z)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8935])).
% 1.53/1.75 tff(8937,plain,
% 1.53/1.75 ((s(z) = elem!1) <=> (s(s(z)) = s(z))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8936, 1063])).
% 1.53/1.75 tff(8938,plain,
% 1.53/1.75 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 1.53/1.75 inference(symmetry,[status(thm)],[8937])).
% 1.53/1.75 tff(8939,plain,
% 1.53/1.75 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8938])).
% 1.53/1.75 tff(8940,plain,
% 1.53/1.75 (~(s(z) = elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[210, 8939])).
% 1.53/1.75 tff(8941,plain,
% 1.53/1.75 (b(s(z), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[454, 8940, 7731])).
% 1.53/1.75 tff(8942,plain,
% 1.53/1.75 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.53/1.75 inference(symmetry,[status(thm)],[8934])).
% 1.53/1.75 tff(8943,plain,
% 1.53/1.75 (s(s(z)) = elem!1),
% 1.53/1.75 inference(transitivity,[status(thm)],[32, 8942, 121])).
% 1.53/1.75 tff(8944,plain,
% 1.53/1.75 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8943])).
% 1.53/1.75 tff(8945,plain,
% 1.53/1.75 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.75 inference(transitivity,[status(thm)],[8944, 284])).
% 1.53/1.75 tff(8946,plain,
% 1.53/1.75 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8945])).
% 1.53/1.75 tff(8947,plain,
% 1.53/1.75 (~(s(s(s(z))) = elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[55, 8946])).
% 1.53/1.75 tff(8948,plain,
% 1.53/1.75 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8938, 85])).
% 1.53/1.75 tff(8949,plain,
% 1.53/1.75 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8948])).
% 1.53/1.75 tff(8950,plain,
% 1.53/1.75 (~(elem!1 = s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[210, 8949])).
% 1.53/1.75 tff(8951,plain,
% 1.53/1.75 (b(elem!1, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1277, 8950, 8368])).
% 1.53/1.75 tff(8952,plain,
% 1.53/1.75 (~r(s(s(s(z))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5504, 8951, 8947, 8941, 688, 4569])).
% 1.53/1.75 tff(8953,plain,
% 1.53/1.75 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8944])).
% 1.53/1.75 tff(8954,plain,
% 1.53/1.75 (~(elem!1 = s(s(s(z))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[55, 8953])).
% 1.53/1.75 tff(8955,plain,
% 1.53/1.75 (r(elem!1, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[388, 8954, 7732])).
% 1.53/1.75 tff(8956,plain,
% 1.53/1.75 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8933])).
% 1.53/1.75 tff(8957,plain,
% 1.53/1.75 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.53/1.75 inference(symmetry,[status(thm)],[8956])).
% 1.53/1.75 tff(8958,plain,
% 1.53/1.75 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8957])).
% 1.53/1.75 tff(8959,plain,
% 1.53/1.75 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8958])).
% 1.53/1.75 tff(8960,plain,
% 1.53/1.75 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[3246, 8959])).
% 1.53/1.75 tff(8961,plain,
% 1.53/1.75 ((elem!1 = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8935, 8956])).
% 1.53/1.75 tff(8962,plain,
% 1.53/1.75 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8961, 5537])).
% 1.53/1.75 tff(8963,plain,
% 1.53/1.75 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 1.53/1.75 inference(symmetry,[status(thm)],[8962])).
% 1.53/1.75 tff(8964,plain,
% 1.53/1.75 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 1.53/1.75 inference(transitivity,[status(thm)],[8963, 76])).
% 1.53/1.75 tff(8965,plain,
% 1.53/1.75 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8964])).
% 1.53/1.75 tff(8966,plain,
% 1.53/1.75 (~(s(s(elem!1)) = elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1229, 8965])).
% 1.53/1.75 tff(8967,plain,
% 1.53/1.75 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8230, 8940, 688, 4569, 7732, 170])).
% 1.53/1.75 tff(8968,plain,
% 1.53/1.75 (r(s(s(elem!1)), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[360, 8967, 8966])).
% 1.53/1.75 tff(8969,plain,
% 1.53/1.75 (~b(s(s(s(z))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[7684, 8968, 8960, 8955, 688])).
% 1.53/1.75 tff(8970,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[72, 8969, 8952])).
% 1.53/1.75 tff(8971,plain,(b(s(z), s(s(s(z)))) | (~r(z, elem!1)) | (~r(z, s(z))) | b(elem!1, s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8972,plain,
% 1.53/1.75 (b(elem!1, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8971, 7728, 170, 688, 4538])).
% 1.53/1.75 tff(8973,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8974,plain,
% 1.53/1.75 (((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(8975,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[8974])).
% 1.53/1.75 tff(8976,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[8975, 8973])).
% 1.53/1.75 tff(8977,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(8978,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[8977, 8976])).
% 1.53/1.75 tff(8979,plain,
% 1.53/1.75 (~b(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8978, 224, 8972, 7730, 7672])).
% 1.53/1.75 tff(8980,plain,
% 1.53/1.75 (r(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[403, 8979, 157])).
% 1.53/1.75 tff(8981,plain,
% 1.53/1.75 (~b(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4322, 8980, 3340, 7660, 526, 7686])).
% 1.53/1.75 tff(8982,plain,
% 1.53/1.75 (~r(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[604, 8980, 7686])).
% 1.53/1.75 tff(8983,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[625, 8982, 8981])).
% 1.53/1.75 tff(8984,plain,(b(elem!1, s(elem!1)) | (elem!1 = z) | (~b(s(s(s(z))), z)) | b(s(z), s(s(s(z)))) | (~r(z, elem!1)) | b(z, elem!1) | (~r(elem!1, s(s(elem!1)))) | r(elem!1, s(s(s(z)))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(8985,plain,
% 1.53/1.75 (b(elem!1, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8984, 545, 7644, 170, 688, 4538, 157, 7685, 91, 3, 354])).
% 1.53/1.75 tff(8986,plain,
% 1.53/1.75 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2287, 7373])).
% 1.53/1.75 tff(8987,plain,
% 1.53/1.75 (b(s(z), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[454, 7731, 91])).
% 1.53/1.75 tff(8988,plain,
% 1.53/1.75 (~b(s(z), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4221, 8987, 501, 1488])).
% 1.53/1.75 tff(8989,plain,
% 1.53/1.75 (r(s(z), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[670, 8988, 415])).
% 1.53/1.75 tff(8990,plain,
% 1.53/1.75 (~r(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5470, 4569, 176])).
% 1.53/1.75 tff(8991,plain,
% 1.53/1.75 (b(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[100, 8990])).
% 1.53/1.75 tff(8992,plain,
% 1.53/1.75 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[7680, 224, 5604, 8991, 7672])).
% 1.53/1.75 tff(8993,plain,
% 1.53/1.75 (r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[147, 8992, 2])).
% 1.53/1.75 tff(8994,plain,
% 1.53/1.75 (~r(s(z), s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[835, 8993, 176])).
% 1.53/1.75 tff(8995,plain,
% 1.53/1.75 (b(s(z), s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[653, 8994])).
% 1.53/1.75 tff(8996,plain,
% 1.53/1.75 (~b(s(z), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4051, 8995, 4106, 5604])).
% 1.53/1.75 tff(8997,plain,
% 1.53/1.75 (r(s(z), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[194, 8996])).
% 1.53/1.75 tff(8998,plain,
% 1.53/1.75 (~r(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4231, 8997, 8989])).
% 1.53/1.75 tff(8999,plain,
% 1.53/1.75 (b(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[625, 8998])).
% 1.53/1.75 tff(9000,plain,
% 1.53/1.75 (b(elem!1, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1277, 8368, 83])).
% 1.53/1.75 tff(9001,plain,
% 1.53/1.75 (~b(s(elem!1), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2662, 224, 1488, 8987, 9000])).
% 1.53/1.75 tff(9002,plain,
% 1.53/1.75 (r(s(elem!1), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1476, 9001, 166])).
% 1.53/1.75 tff(9003,plain,
% 1.53/1.75 (~r(s(elem!1), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5625, 112, 4569, 9002])).
% 1.53/1.75 tff(9004,plain,
% 1.53/1.75 (b(s(elem!1), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[498, 9003])).
% 1.53/1.75 tff(9005,plain,
% 1.53/1.75 (~b(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4320, 9004, 8999, 5604])).
% 1.53/1.75 tff(9006,plain,
% 1.53/1.75 (r(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[530, 9005, 2505])).
% 1.53/1.75 tff(9007,plain,
% 1.53/1.75 (~(elem!1 = s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2477, 8987, 170])).
% 1.53/1.75 tff(9008,plain,
% 1.53/1.75 (~(s(s(s(z))) = elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2487, 9007])).
% 1.53/1.75 tff(9009,plain,
% 1.53/1.75 (b(s(s(s(z))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[374, 9008, 2932])).
% 1.53/1.75 tff(9010,plain,
% 1.53/1.75 (((~b(s(z), elem!1)) | (~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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9011,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9010])).
% 1.53/1.75 tff(9012,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9011, 5497])).
% 1.53/1.75 tff(9013,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9014,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9013, 9012])).
% 1.53/1.75 tff(9015,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9014, 224, 8987, 9000, 9009])).
% 1.53/1.75 tff(9016,plain,
% 1.53/1.75 (r(s(s(s(z))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[925, 9015])).
% 1.53/1.75 tff(9017,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), 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(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9018,plain,
% 1.53/1.75 (((~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(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9019,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(z))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9018])).
% 1.53/1.76 tff(9020,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9019, 9017])).
% 1.53/1.76 tff(9021,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9022,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9021, 9020])).
% 1.53/1.76 tff(9023,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9022, 112, 9002, 9016])).
% 1.53/1.76 tff(9024,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9025,plain,
% 1.53/1.76 (((~b(s(elem!1), 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(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9026,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9025])).
% 1.53/1.76 tff(9027,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9026, 9024])).
% 1.53/1.76 tff(9028,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9029,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9028, 9027])).
% 1.53/1.76 tff(9030,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9029, 224, 501, 1488, 9009])).
% 1.53/1.76 tff(9031,plain,
% 1.53/1.76 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[816, 68, 9030])).
% 1.53/1.76 tff(9032,plain,
% 1.53/1.76 (s(s(s(z))) = s(elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9031, 9023])).
% 1.53/1.76 tff(9033,plain,
% 1.53/1.76 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9032])).
% 1.53/1.76 tff(9034,plain,
% 1.53/1.76 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9033, 1143])).
% 1.53/1.76 tff(9035,plain,
% 1.53/1.76 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9034])).
% 1.53/1.76 tff(9036,plain,
% 1.53/1.76 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1165, 9035])).
% 1.53/1.76 tff(9037,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3939, 112, 544, 7315])).
% 1.53/1.76 tff(9038,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1401, 68, 2287, 9037])).
% 1.53/1.76 tff(9039,plain,
% 1.53/1.76 (((~![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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9040,plain,
% 1.53/1.76 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9041,plain,
% 1.53/1.76 (((~![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(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9040])).
% 1.53/1.76 tff(9042,plain,
% 1.53/1.76 (((~![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(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9041, 9039])).
% 1.53/1.76 tff(9043,plain,
% 1.53/1.76 ((~![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(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9044,plain,
% 1.53/1.76 ((~![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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9043, 9042])).
% 1.53/1.76 tff(9045,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9044, 112, 178, 655, 7315])).
% 1.53/1.76 tff(9046,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 9045])).
% 1.53/1.76 tff(9047,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), 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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9048,plain,
% 1.53/1.76 (((~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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9049,plain,
% 1.53/1.76 (((~![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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9048])).
% 1.53/1.76 tff(9050,plain,
% 1.53/1.76 (((~![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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9049, 9047])).
% 1.53/1.76 tff(9051,plain,
% 1.53/1.76 ((~![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))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9052,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9051, 9050])).
% 1.53/1.76 tff(9053,plain,
% 1.53/1.76 (~r(s(s(elem!1)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9052, 112, 544, 655])).
% 1.53/1.76 tff(9054,plain,
% 1.53/1.76 (b(s(s(elem!1)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[901, 9053])).
% 1.53/1.76 tff(9055,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9056,plain,
% 1.53/1.76 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9057,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9056])).
% 1.53/1.76 tff(9058,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9057, 9055])).
% 1.53/1.76 tff(9059,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9060,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9059, 9058])).
% 1.53/1.76 tff(9061,plain,
% 1.53/1.76 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9060, 224, 3919, 684, 9054])).
% 1.53/1.76 tff(9062,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9061, 9046, 9038])).
% 1.53/1.76 tff(9063,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9064,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9063, 9036, 176, 8987, 8989, 2287, 9006, 501, 1488])).
% 1.53/1.76 tff(9065,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.53/1.76 tff(9066,plain,
% 1.53/1.76 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9065])).
% 1.53/1.76 tff(9067,plain,
% 1.53/1.76 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[32, 9066, 121, 2768])).
% 1.53/1.76 tff(9068,plain,
% 1.53/1.76 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9067])).
% 1.53/1.76 tff(9069,plain,
% 1.53/1.76 (s(z) = s(s(s(elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[50, 9068, 989])).
% 1.53/1.76 tff(9070,plain,
% 1.53/1.76 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9069])).
% 1.53/1.76 tff(9071,plain,
% 1.53/1.76 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.53/1.76 inference(symmetry,[status(thm)],[9070])).
% 1.53/1.76 tff(9072,plain,
% 1.53/1.76 (s(s(elem!1)) = z),
% 1.53/1.76 inference(transitivity,[status(thm)],[1376, 9071, 27])).
% 1.53/1.76 tff(9073,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[566, 9072])).
% 1.53/1.76 tff(9074,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~(s(s(s(z))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9075,plain,
% 1.53/1.76 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9074, 9032])).
% 1.53/1.76 tff(9076,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1294, 9075, 9064])).
% 1.53/1.76 tff(9077,plain,
% 1.53/1.76 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5903, 112, 9076, 1181])).
% 1.53/1.76 tff(9078,plain,
% 1.53/1.76 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1422, 68, 9077, 8986])).
% 1.53/1.76 tff(9079,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9080,plain,
% 1.53/1.76 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9081,plain,
% 1.53/1.76 (((~![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(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9080])).
% 1.53/1.76 tff(9082,plain,
% 1.53/1.76 (((~![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(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9081, 9079])).
% 1.53/1.76 tff(9083,plain,
% 1.53/1.76 ((~![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(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9084,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9083, 9082])).
% 1.53/1.76 tff(9085,plain,
% 1.53/1.76 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9084, 112, 9076, 688])).
% 1.53/1.76 tff(9086,plain,
% 1.53/1.76 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4412, 9085])).
% 1.53/1.76 tff(9087,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9088,plain,
% 1.53/1.76 (((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9089,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9088])).
% 1.53/1.76 tff(9090,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9089, 9087])).
% 1.53/1.76 tff(9091,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9092,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9091, 9090])).
% 1.53/1.76 tff(9093,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9092, 112, 9076, 4569, 688])).
% 1.53/1.76 tff(9094,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1338, 9093])).
% 1.53/1.76 tff(9095,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4427, 224, 5604, 9094, 9086, 9078])).
% 1.53/1.76 tff(9096,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | r(s(s(s(z))), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9097,plain,
% 1.53/1.76 (~r(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9096, 8985, 3340, 7240, 688, 7671, 526, 409, 2, 7644, 7669, 170])).
% 1.53/1.76 tff(9098,plain,
% 1.53/1.76 (b(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5459, 9097])).
% 1.53/1.76 tff(9099,plain,
% 1.53/1.76 (~r(s(z), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1205, 9098, 7658, 3340])).
% 1.53/1.76 tff(9100,plain,
% 1.53/1.76 (b(s(z), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[454, 9099, 91])).
% 1.53/1.76 tff(9101,plain,
% 1.53/1.76 (~(elem!1 = s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2477, 9100, 170])).
% 1.53/1.76 tff(9102,plain,
% 1.53/1.76 (~(s(s(s(z))) = elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2487, 9101])).
% 1.53/1.76 tff(9103,plain,
% 1.53/1.76 (b(s(s(s(z))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[374, 9102, 7669])).
% 1.53/1.76 tff(9104,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[706, 224, 9098, 9100, 9103, 7644])).
% 1.53/1.76 tff(9105,plain,
% 1.53/1.76 (r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[925, 9104])).
% 1.53/1.76 tff(9106,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5271, 112, 656, 3188, 6847])).
% 1.53/1.76 tff(9107,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9108,plain,
% 1.53/1.76 (~r(s(z), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9107, 9105, 7662])).
% 1.53/1.76 tff(9109,plain,
% 1.53/1.76 (b(s(z), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[653, 9108])).
% 1.53/1.76 tff(9110,plain,
% 1.53/1.76 (~b(s(z), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4051, 9109, 7658, 7660])).
% 1.53/1.76 tff(9111,plain,
% 1.53/1.76 (r(s(z), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[194, 9110])).
% 1.53/1.76 tff(9112,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9113,plain,
% 1.53/1.76 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9114,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9113])).
% 1.53/1.76 tff(9115,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9114, 9112])).
% 1.53/1.76 tff(9116,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9117,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9116, 9115])).
% 1.53/1.77 tff(9118,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9117, 112, 179, 178, 689])).
% 1.53/1.77 tff(9119,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9120,plain,
% 1.53/1.77 (~r(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9119, 9111, 176])).
% 1.53/1.77 tff(9121,plain,
% 1.53/1.77 (b(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[100, 9120])).
% 1.53/1.77 tff(9122,plain,
% 1.53/1.77 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7680, 224, 7660, 9121, 7644])).
% 1.53/1.77 tff(9123,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[147, 9122, 2])).
% 1.53/1.77 tff(9124,plain,
% 1.53/1.77 (~r(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4039, 9123, 176])).
% 1.53/1.77 tff(9125,plain,
% 1.53/1.77 (b(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[901, 9124])).
% 1.53/1.77 tff(9126,plain,
% 1.53/1.77 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9127,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9126])).
% 1.53/1.77 tff(9128,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9127, 1198])).
% 1.53/1.77 tff(9129,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9130,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9129, 9128])).
% 1.53/1.77 tff(9131,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9130, 224, 9098, 9109, 9125, 7658])).
% 1.53/1.77 tff(9132,plain,((~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (~r(z, elem!1)) | b(z, elem!1) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9133,plain,
% 1.53/1.77 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9132, 354, 170, 7067, 4538, 11, 3, 2])).
% 1.53/1.77 tff(9134,plain,
% 1.53/1.77 (b(elem!1, s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[558, 9133, 3])).
% 1.53/1.77 tff(9135,plain,
% 1.53/1.77 (~b(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[613, 9134, 7646, 7648])).
% 1.53/1.77 tff(9136,plain,
% 1.53/1.77 (r(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[403, 9135, 11])).
% 1.53/1.77 tff(9137,plain,
% 1.53/1.77 (~r(elem!1, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7684, 3340, 7644, 2, 7067])).
% 1.53/1.77 tff(9138,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.53/1.77 tff(9139,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.53/1.77 tff(9140,plain,
% 1.53/1.77 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[306])).
% 1.53/1.77 tff(9141,plain,
% 1.53/1.77 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.53/1.77 inference(symmetry,[status(thm)],[9140])).
% 1.53/1.77 tff(9142,plain,
% 1.53/1.77 (b(s(s(elem!1)), z)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[7672, 9141])).
% 1.53/1.77 tff(9143,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9139, 9142])).
% 1.53/1.77 tff(9144,plain,((~(s(s(elem!1)) = s(s(s(z))))) | b(s(s(elem!1)), z) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9145,plain,
% 1.53/1.77 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9144, 9139, 7672])).
% 1.53/1.77 tff(9146,plain,
% 1.53/1.77 (r(s(s(elem!1)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[593, 9139])).
% 1.53/1.77 tff(9147,plain,
% 1.53/1.77 (r(z, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5459, 9138])).
% 1.53/1.77 tff(9148,plain,
% 1.53/1.77 (~(s(s(z)) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2788, 3111])).
% 1.53/1.77 tff(9149,plain,
% 1.53/1.77 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.77 tff(9150,plain,
% 1.53/1.77 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9149])).
% 1.53/1.77 tff(9151,plain,
% 1.53/1.77 (~(s(z) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7751, 3110])).
% 1.53/1.77 tff(9152,plain,
% 1.53/1.77 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[131, 9151])).
% 1.53/1.77 tff(9153,plain,
% 1.53/1.77 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[310, 9152])).
% 1.53/1.77 tff(9154,plain,
% 1.53/1.77 (~(elem!1 = s(s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9153, 9150])).
% 1.53/1.77 tff(9155,plain,
% 1.53/1.77 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.77 inference(transitivity,[status(thm)],[9149, 284])).
% 1.53/1.77 tff(9156,plain,
% 1.53/1.77 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9155])).
% 1.53/1.77 tff(9157,plain,
% 1.53/1.77 (~(s(s(s(z))) = elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9153, 9156])).
% 1.53/1.77 tff(9158,plain,
% 1.53/1.77 (~(elem!1 = s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2654, 9151])).
% 1.53/1.77 tff(9159,plain,
% 1.53/1.77 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.77 tff(9160,plain,
% 1.53/1.77 (r(elem!1, z)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[102, 9159])).
% 1.53/1.77 tff(9161,plain,
% 1.53/1.77 (~r(elem!1, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5749, 9160, 4569])).
% 1.53/1.77 tff(9162,plain,
% 1.53/1.77 (b(elem!1, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1277, 9161, 9158])).
% 1.53/1.77 tff(9163,plain,
% 1.53/1.77 (~r(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5764, 1090, 9160, 9154, 9162, 4569])).
% 1.53/1.77 tff(9164,plain,
% 1.53/1.77 (b(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[100, 9163])).
% 1.53/1.77 tff(9165,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.77 tff(9166,plain,
% 1.53/1.77 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9165])).
% 1.53/1.77 tff(9167,plain,
% 1.53/1.77 ((~r(elem!1, s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9166])).
% 1.53/1.77 tff(9168,plain,
% 1.53/1.77 (~r(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9161, 9167])).
% 1.53/1.77 tff(9169,plain,
% 1.53/1.77 (b(s(s(elem!1)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[901, 9168])).
% 1.53/1.77 tff(9170,plain,
% 1.53/1.77 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.77 tff(9171,plain,
% 1.53/1.77 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9170])).
% 1.53/1.77 tff(9172,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9173,plain,
% 1.53/1.77 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9174,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9173])).
% 1.53/1.77 tff(9175,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9174, 9172])).
% 1.53/1.77 tff(9176,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9177,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9176, 9175])).
% 1.53/1.77 tff(9178,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9177, 224, 1, 1090, 6255, 7672])).
% 1.53/1.77 tff(9179,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9180,plain,
% 1.53/1.77 (~b(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9179, 9164, 1090, 7672])).
% 1.53/1.77 tff(9181,plain,
% 1.53/1.77 (r(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[194, 9180])).
% 1.53/1.77 tff(9182,plain,
% 1.53/1.77 (~r(s(z), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2841, 9181, 9160])).
% 1.53/1.77 tff(9183,plain,
% 1.53/1.77 (b(s(z), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[454, 9182, 9151])).
% 1.53/1.77 tff(9184,plain,
% 1.53/1.77 (b(s(z), s(s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9183, 9171])).
% 1.53/1.77 tff(9185,plain,
% 1.53/1.77 (~r(s(s(z)), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[274, 112, 102, 268])).
% 1.53/1.77 tff(9186,plain,
% 1.53/1.77 (~r(s(s(z)), elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9185, 8615])).
% 1.53/1.77 tff(9187,plain,
% 1.53/1.77 (b(s(s(z)), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1135, 9186, 2796])).
% 1.53/1.77 tff(9188,plain,
% 1.53/1.77 (b(s(s(z)), s(s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9187, 8611])).
% 1.53/1.77 tff(9189,plain,
% 1.53/1.77 (~b(s(s(z)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 1241, 9188])).
% 1.53/1.77 tff(9190,plain,
% 1.53/1.77 (r(s(s(z)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[213, 68, 210, 9189])).
% 1.53/1.77 tff(9191,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[6165, 112, 4569, 268, 9190])).
% 1.53/1.77 tff(9192,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (s(s(z)) = elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9193,plain,
% 1.53/1.77 (~r(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9192, 9184, 4569, 102, 3109, 9169, 9148])).
% 1.53/1.77 tff(9194,plain,
% 1.53/1.77 (b(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[281, 9193])).
% 1.53/1.77 tff(9195,plain,
% 1.53/1.77 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9196,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9195])).
% 1.53/1.77 tff(9197,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9196, 8417])).
% 1.53/1.77 tff(9198,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9199,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9198, 9197])).
% 1.53/1.77 tff(9200,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9199, 224, 2212, 6255, 7672, 1118])).
% 1.53/1.77 tff(9201,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9202,plain,
% 1.53/1.77 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9201, 9194, 7672, 9164])).
% 1.53/1.77 tff(9203,plain,
% 1.53/1.77 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[249, 9202])).
% 1.53/1.77 tff(9204,plain,
% 1.53/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3120, 349])).
% 1.53/1.77 tff(9205,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.53/1.77 tff(9206,plain,
% 1.53/1.77 (~b(s(s(s(z))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2941, 685, 684, 1090])).
% 1.53/1.77 tff(9207,plain,
% 1.53/1.77 (r(s(s(s(z))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[374, 9206, 362])).
% 1.53/1.77 tff(9208,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2767])).
% 1.53/1.77 tff(9209,plain,
% 1.53/1.77 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9208])).
% 1.53/1.77 tff(9210,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9207, 9209])).
% 1.53/1.77 tff(9211,plain,
% 1.53/1.77 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5413, 9210, 196])).
% 1.53/1.77 tff(9212,plain,
% 1.53/1.77 (~r(s(s(z)), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5403, 9211, 2767])).
% 1.53/1.77 tff(9213,plain,
% 1.53/1.77 (b(s(s(z)), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1135, 9212, 2796])).
% 1.53/1.77 tff(9214,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9215,plain,
% 1.53/1.77 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9216,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9215])).
% 1.53/1.77 tff(9217,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9216, 9214])).
% 1.53/1.77 tff(9218,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9219,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9218, 9217])).
% 1.53/1.77 tff(9220,plain,
% 1.53/1.77 (~b(s(z), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9219, 224, 684, 685, 1090, 1109])).
% 1.53/1.77 tff(9221,plain,
% 1.53/1.77 (r(s(z), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1071, 9220])).
% 1.53/1.77 tff(9222,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9223,plain,
% 1.53/1.77 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9224,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9223])).
% 1.53/1.77 tff(9225,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9224, 9222])).
% 1.53/1.77 tff(9226,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9227,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9226, 9225])).
% 1.53/1.78 tff(9228,plain,
% 1.53/1.78 (~b(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9227, 224, 344, 685, 1109, 6255])).
% 1.53/1.78 tff(9229,plain,
% 1.53/1.78 (r(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1088, 9228])).
% 1.53/1.78 tff(9230,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[6682, 112, 4569, 9229, 9221])).
% 1.53/1.78 tff(9231,plain,((~b(s(s(z)), elem!1)) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9232,plain,
% 1.53/1.78 (~b(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9231, 9213, 4569, 685, 6255, 684, 1090])).
% 1.53/1.78 tff(9233,plain,
% 1.53/1.78 (r(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[289, 9232, 4])).
% 1.53/1.78 tff(9234,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), 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(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9235,plain,
% 1.53/1.78 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9236,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9235])).
% 1.53/1.78 tff(9237,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9236, 9234])).
% 1.53/1.78 tff(9238,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9239,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9238, 9237])).
% 1.53/1.78 tff(9240,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9239, 112, 4569, 688, 2274])).
% 1.53/1.78 tff(9241,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 9240])).
% 1.53/1.78 tff(9242,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9243,plain,
% 1.53/1.78 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9244,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9243])).
% 1.53/1.78 tff(9245,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9244, 9242])).
% 1.53/1.78 tff(9246,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9247,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9246, 9245])).
% 1.53/1.78 tff(9248,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9247, 112, 690, 2274])).
% 1.53/1.78 tff(9249,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3252, 9248])).
% 1.53/1.78 tff(9250,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8900, 224, 6255, 7672, 9249, 9241])).
% 1.53/1.78 tff(9251,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9252,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9251, 9233, 7672, 6255, 4569, 9207])).
% 1.53/1.78 tff(9253,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3183, 9252, 9205])).
% 1.53/1.78 tff(9254,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9255,plain,
% 1.53/1.78 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), 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)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9256,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9255])).
% 1.53/1.78 tff(9257,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9256, 9254])).
% 1.53/1.78 tff(9258,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9259,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9258, 9257])).
% 1.53/1.78 tff(9260,plain,
% 1.53/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9259, 224, 684, 2896, 9253])).
% 1.53/1.78 tff(9261,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3166, 68, 9260, 3161])).
% 1.53/1.78 tff(9262,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8902, 9261, 7672, 4569, 6255])).
% 1.53/1.78 tff(9263,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[925, 9262])).
% 1.53/1.78 tff(9264,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5792, 224, 2896, 685, 1090, 9263])).
% 1.53/1.78 tff(9265,plain,((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (z = elem!1) | (s(s(z)) = elem!1) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9266,plain,
% 1.53/1.78 (~b(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9265, 1090, 9162, 7672, 4569, 9164, 9183, 9204, 4, 9148, 3110, 9203, 9157])).
% 1.53/1.78 tff(9267,plain,
% 1.53/1.78 (r(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[388, 9266, 9154])).
% 1.53/1.78 tff(9268,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(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(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9269,plain,
% 1.53/1.78 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9270,plain,
% 1.53/1.78 (((~![X0: $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(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(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9269])).
% 1.53/1.78 tff(9271,plain,
% 1.53/1.78 (((~![X0: $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(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(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9270, 9268])).
% 1.53/1.78 tff(9272,plain,
% 1.53/1.78 ((~![X0: $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(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9273,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9272, 9271])).
% 1.53/1.78 tff(9274,plain,
% 1.53/1.78 (~r(s(s(z)), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9273, 112, 9203, 9267])).
% 1.53/1.78 tff(9275,plain,
% 1.53/1.78 (b(s(s(z)), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1135, 9274, 9148])).
% 1.53/1.78 tff(9276,plain,
% 1.53/1.78 (~b(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5613, 224, 9183, 9162, 9275])).
% 1.53/1.78 tff(9277,plain,
% 1.53/1.78 (r(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[213, 68, 210, 9276])).
% 1.53/1.78 tff(9278,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(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(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9279,plain,
% 1.53/1.78 (((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9280,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9279])).
% 1.53/1.78 tff(9281,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9280, 9278])).
% 1.53/1.78 tff(9282,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9283,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9282, 9281])).
% 1.53/1.78 tff(9284,plain,
% 1.53/1.78 (~r(elem!1, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9283, 112, 9203, 9267])).
% 1.53/1.78 tff(9285,plain,
% 1.53/1.78 (b(elem!1, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2874, 9284, 3111])).
% 1.53/1.78 tff(9286,plain,
% 1.53/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9259, 224, 684, 2896, 5274])).
% 1.53/1.78 tff(9287,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3166, 68, 9286, 3161])).
% 1.53/1.78 tff(9288,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9289,plain,
% 1.53/1.78 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9290,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9289])).
% 1.53/1.78 tff(9291,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9290, 9288])).
% 1.53/1.78 tff(9292,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9293,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9292, 9291])).
% 1.53/1.78 tff(9294,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9293, 112, 196, 9287, 5702, 5282])).
% 1.53/1.78 tff(9295,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9296,plain,
% 1.53/1.78 (~b(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9295, 9285, 9203, 9275, 9183, 9162])).
% 1.53/1.78 tff(9297,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3183, 9296, 9204])).
% 1.53/1.78 tff(9298,plain,
% 1.53/1.78 (~r(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[6072, 112, 4569, 9277])).
% 1.53/1.78 tff(9299,plain,
% 1.53/1.78 (b(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1088, 9298])).
% 1.53/1.78 tff(9300,plain,
% 1.53/1.78 (~b(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2869, 9299, 9285, 9275])).
% 1.53/1.78 tff(9301,plain,
% 1.53/1.78 (r(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[289, 9300, 4])).
% 1.53/1.78 tff(9302,plain,
% 1.53/1.78 (~r(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9251, 9301, 7672, 9164, 4569, 9297])).
% 1.53/1.78 tff(9303,plain,
% 1.53/1.78 (b(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[374, 9302, 9157])).
% 1.53/1.78 tff(9304,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9014, 224, 9183, 9162, 9303])).
% 1.53/1.78 tff(9305,plain,
% 1.53/1.78 (r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[925, 9304])).
% 1.53/1.78 tff(9306,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3194, 112, 9203, 9305, 9277])).
% 1.53/1.78 tff(9307,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (z = elem!1) | (~r(s(s(elem!1)), z)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9308,plain,
% 1.53/1.78 (~b(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9307, 349, 4569, 4, 102, 7672])).
% 1.53/1.78 tff(9309,plain,
% 1.53/1.78 (r(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[175, 9308])).
% 1.53/1.78 tff(9310,plain,
% 1.53/1.78 (~r(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5470, 9309, 4569])).
% 1.53/1.78 tff(9311,plain,
% 1.53/1.78 (b(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[100, 9310])).
% 1.53/1.78 tff(9312,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3110])).
% 1.53/1.78 tff(9313,plain,
% 1.53/1.78 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.78 tff(9314,plain,
% 1.53/1.78 (~r(s(z), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2639, 112, 9160, 179])).
% 1.53/1.78 tff(9315,plain,
% 1.53/1.78 (b(s(z), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[454, 9314, 9151])).
% 1.53/1.78 tff(9316,plain,
% 1.53/1.78 (b(s(z), s(s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9315, 9171])).
% 1.53/1.78 tff(9317,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9192, 9316, 4569, 102, 3109, 1546, 9148])).
% 1.53/1.78 tff(9318,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[281, 9317])).
% 1.53/1.78 tff(9319,plain,
% 1.53/1.78 (b(s(z), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[454, 2640, 9151])).
% 1.53/1.78 tff(9320,plain,
% 1.53/1.78 (b(s(z), s(s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9319, 9171])).
% 1.53/1.78 tff(9321,plain,
% 1.53/1.78 (~b(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8630, 827, 178, 179, 1241, 3109, 9320, 7672, 1118])).
% 1.53/1.78 tff(9322,plain,
% 1.53/1.78 (r(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[100, 9321])).
% 1.53/1.78 tff(9323,plain,
% 1.53/1.78 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[349])).
% 1.53/1.78 tff(9324,plain,
% 1.53/1.78 (r(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[827, 9323])).
% 1.53/1.78 tff(9325,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5762, 112, 4569, 363, 9324, 9322])).
% 1.53/1.78 tff(9326,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9327,plain,
% 1.53/1.78 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9326, 179, 9160, 349, 178, 4569, 1546, 7672, 9318])).
% 1.53/1.78 tff(9328,plain,
% 1.53/1.78 (b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[147, 9327, 9153])).
% 1.53/1.78 tff(9329,plain,
% 1.53/1.78 (b(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9328, 9313])).
% 1.53/1.78 tff(9330,plain,
% 1.53/1.78 (~r(elem!1, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1259, 179, 9160])).
% 1.53/1.78 tff(9331,plain,
% 1.53/1.78 (b(elem!1, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1277, 9330, 9158])).
% 1.53/1.78 tff(9332,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2767])).
% 1.53/1.78 tff(9333,plain,
% 1.53/1.78 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9201, 6255, 7672, 1118])).
% 1.53/1.78 tff(9334,plain,
% 1.53/1.78 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[249, 9333])).
% 1.53/1.78 tff(9335,plain,
% 1.53/1.78 (~r(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8608, 112, 179, 9334, 178])).
% 1.53/1.78 tff(9336,plain,
% 1.53/1.78 (b(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[213, 68, 210, 9335])).
% 1.53/1.78 tff(9337,plain,
% 1.53/1.78 (~b(s(s(z)), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4521, 224, 684, 2896, 9336])).
% 1.53/1.78 tff(9338,plain,
% 1.53/1.78 (r(s(s(z)), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1135, 9337, 2796])).
% 1.53/1.78 tff(9339,plain,
% 1.53/1.78 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9338, 5399])).
% 1.53/1.78 tff(9340,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5413, 9339, 9334])).
% 1.53/1.78 tff(9341,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[5426, 9340])).
% 1.53/1.78 tff(9342,plain,
% 1.53/1.78 (b(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9341, 9332])).
% 1.53/1.78 tff(9343,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9014, 224, 684, 2896, 9342])).
% 1.53/1.78 tff(9344,plain,
% 1.53/1.78 (r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[925, 9343])).
% 1.53/1.78 tff(9345,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8902, 9344, 7672, 4569, 6255])).
% 1.53/1.78 tff(9346,plain,
% 1.53/1.78 (~b(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[6432, 224, 685, 9342, 6255])).
% 1.53/1.78 tff(9347,plain,
% 1.53/1.78 (r(z, elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[289, 9346, 4])).
% 1.53/1.78 tff(9348,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9349,plain,
% 1.53/1.79 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9350,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~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(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9349])).
% 1.53/1.79 tff(9351,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~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(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9350, 9348])).
% 1.53/1.79 tff(9352,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9353,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9352, 9351])).
% 1.53/1.79 tff(9354,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9353, 112, 196, 1047, 2274])).
% 1.53/1.79 tff(9355,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 9354])).
% 1.53/1.79 tff(9356,plain,
% 1.53/1.79 (~r(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3758, 688, 1047])).
% 1.53/1.79 tff(9357,plain,
% 1.53/1.79 (b(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1088, 9356])).
% 1.53/1.79 tff(9358,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3298, 224, 9357, 1118, 9355, 9241])).
% 1.53/1.79 tff(9359,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9360,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9359, 9334, 1118, 9338, 4569, 9347])).
% 1.53/1.79 tff(9361,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3183, 9360, 9205])).
% 1.53/1.79 tff(9362,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9259, 224, 684, 2896, 9361])).
% 1.53/1.79 tff(9363,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3166, 68, 9362, 9345, 3161])).
% 1.53/1.79 tff(9364,plain,((~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~b(elem!1, s(s(s(z))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(z)) = elem!1) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9365,plain,
% 1.53/1.79 (~b(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9364, 9315, 9331, 9204, 9318, 4569, 7672, 4, 9329, 3110, 9148, 179, 178])).
% 1.53/1.79 tff(9366,plain,
% 1.53/1.79 (r(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[100, 9365])).
% 1.53/1.79 tff(9367,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9117, 112, 179, 178, 9366])).
% 1.53/1.79 tff(9368,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9369,plain,
% 1.53/1.79 (~r(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9368, 9309, 4569, 7672, 4, 349, 102])).
% 1.53/1.79 tff(9370,plain,
% 1.53/1.79 (b(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[194, 9369])).
% 1.53/1.79 tff(9371,plain,
% 1.53/1.79 (~b(s(z), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9177, 224, 1, 6255, 7672])).
% 1.53/1.79 tff(9372,plain,
% 1.53/1.79 (r(s(z), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[175, 9371])).
% 1.53/1.79 tff(9373,plain,
% 1.53/1.79 (~r(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[835, 9372, 827])).
% 1.53/1.79 tff(9374,plain,
% 1.53/1.79 (b(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[653, 9373])).
% 1.53/1.79 tff(9375,plain,
% 1.53/1.79 (~r(elem!1, s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1028, 9372, 9324])).
% 1.53/1.79 tff(9376,plain,
% 1.53/1.79 (~r(s(s(elem!1)), s(z))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9375, 9167])).
% 1.53/1.79 tff(9377,plain,
% 1.53/1.79 (b(s(s(elem!1)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[901, 9376])).
% 1.53/1.79 tff(9378,plain,
% 1.53/1.79 (~r(s(s(z)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9192, 9377, 4569, 102, 3109, 9374, 9148])).
% 1.53/1.79 tff(9379,plain,
% 1.53/1.79 (b(s(s(z)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[281, 9378])).
% 1.53/1.79 tff(9380,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6296, 8424, 9372, 2303])).
% 1.53/1.79 tff(9381,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9382,plain,
% 1.53/1.79 (~r(s(z), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9381, 9379, 6255, 7672, 1])).
% 1.53/1.79 tff(9383,plain,
% 1.53/1.79 (b(s(z), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1071, 9382])).
% 1.53/1.79 tff(9384,plain,
% 1.53/1.79 (~r(s(s(z)), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8623, 9379, 6255, 7672, 827])).
% 1.53/1.79 tff(9385,plain,
% 1.53/1.79 (~r(s(s(z)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2801, 9384, 349])).
% 1.53/1.79 tff(9386,plain,
% 1.53/1.79 (b(s(s(z)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1135, 9385, 9148])).
% 1.53/1.79 tff(9387,plain,
% 1.53/1.79 (b(elem!1, s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1277, 9375, 9158])).
% 1.53/1.79 tff(9388,plain,
% 1.53/1.79 (b(s(z), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9374, 9170])).
% 1.53/1.79 tff(9389,plain,
% 1.53/1.79 (~b(s(s(z)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5613, 224, 9388, 9387, 9386])).
% 1.53/1.79 tff(9390,plain,
% 1.53/1.79 (r(s(s(z)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[213, 68, 210, 9389])).
% 1.53/1.79 tff(9391,plain,
% 1.53/1.79 (~r(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6072, 112, 4569, 9390])).
% 1.53/1.79 tff(9392,plain,
% 1.53/1.79 (b(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1088, 9391])).
% 1.53/1.79 tff(9393,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9394,plain,
% 1.53/1.79 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9395,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9394])).
% 1.53/1.79 tff(9396,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9395, 9393])).
% 1.53/1.79 tff(9397,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9398,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9397, 9396])).
% 1.53/1.79 tff(9399,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9398, 224, 1, 9388, 9386, 9392, 9383])).
% 1.53/1.79 tff(9400,plain,((~b(s(z), z)) | (~r(z, s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9401,plain,
% 1.53/1.79 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9400, 9370, 349, 4569, 7672, 9311, 102])).
% 1.53/1.79 tff(9402,plain,
% 1.53/1.79 (b(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[147, 9401, 9153])).
% 1.53/1.79 tff(9403,plain,
% 1.53/1.79 (b(elem!1, s(s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9402, 9313])).
% 1.53/1.79 tff(9404,plain,
% 1.53/1.79 (~r(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5470, 178, 4569])).
% 1.53/1.79 tff(9405,plain,
% 1.53/1.79 (b(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[100, 9404])).
% 1.53/1.79 tff(9406,plain,
% 1.53/1.79 (~r(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2374, 416, 178])).
% 1.53/1.79 tff(9407,plain,
% 1.53/1.79 (b(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[374, 9406, 362])).
% 1.53/1.79 tff(9408,plain,
% 1.53/1.79 (~r(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5480, 416, 4569])).
% 1.53/1.79 tff(9409,plain,
% 1.53/1.79 (b(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[289, 9408, 4])).
% 1.53/1.79 tff(9410,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6432, 224, 9409, 685, 9407, 9405])).
% 1.53/1.79 tff(9411,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (z = elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9412,plain,
% 1.53/1.79 (~r(s(z), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9411, 9403, 9157, 9309, 4, 4569])).
% 1.53/1.79 tff(9413,plain,
% 1.53/1.79 (b(s(z), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[454, 9412, 9151])).
% 1.53/1.79 tff(9414,plain,
% 1.53/1.79 (b(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9413, 9171])).
% 1.53/1.79 tff(9415,plain,
% 1.53/1.79 (~r(s(s(z)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9192, 9414, 4569, 102, 3109, 9169, 9148])).
% 1.53/1.79 tff(9416,plain,
% 1.53/1.79 (b(s(s(z)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[281, 9415])).
% 1.53/1.79 tff(9417,plain,
% 1.53/1.79 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9201, 9416, 7672, 9311])).
% 1.53/1.79 tff(9418,plain,
% 1.53/1.79 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[249, 9417])).
% 1.53/1.79 tff(9419,plain,
% 1.53/1.79 (~r(s(s(z)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[202, 112, 9418, 9309])).
% 1.53/1.79 tff(9420,plain,
% 1.53/1.79 (b(s(s(z)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[213, 68, 210, 9419])).
% 1.53/1.79 tff(9421,plain,
% 1.53/1.79 (~b(s(s(z)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4521, 224, 9413, 9162, 9420])).
% 1.53/1.79 tff(9422,plain,
% 1.53/1.79 (r(s(s(z)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1135, 9421, 9148])).
% 1.53/1.79 tff(9423,plain,
% 1.53/1.79 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5403, 9422, 3110])).
% 1.53/1.79 tff(9424,plain,
% 1.53/1.79 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5413, 9423, 9418])).
% 1.53/1.79 tff(9425,plain,
% 1.53/1.79 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5426, 9424])).
% 1.53/1.79 tff(9426,plain,
% 1.53/1.79 (b(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9425, 9312])).
% 1.53/1.79 tff(9427,plain,
% 1.53/1.79 (~b(s(s(s(z))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9014, 224, 9413, 9162, 9426])).
% 1.53/1.79 tff(9428,plain,
% 1.53/1.79 (r(s(s(s(z))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[925, 9427])).
% 1.53/1.79 tff(9429,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8902, 9428, 7672, 4569, 9311])).
% 1.53/1.79 tff(9430,plain,
% 1.53/1.79 (~b(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6432, 224, 9403, 9426, 9311])).
% 1.53/1.79 tff(9431,plain,
% 1.53/1.79 (r(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[289, 9430, 4])).
% 1.53/1.79 tff(9432,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9359, 9431, 9416, 9418, 4569, 9422])).
% 1.53/1.79 tff(9433,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3183, 9432, 9204])).
% 1.53/1.79 tff(9434,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9259, 224, 9413, 9162, 9433])).
% 1.53/1.79 tff(9435,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3166, 68, 9434, 9429, 3161])).
% 1.53/1.79 tff(9436,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (z = elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9437,plain,
% 1.53/1.79 (~(s(s(elem!1)) = elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9436, 9146, 9147, 4, 7672])).
% 1.53/1.79 tff(9438,plain,
% 1.53/1.79 (r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[360, 9437, 354])).
% 1.53/1.79 tff(9439,plain,
% 1.53/1.79 (~r(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2346, 9438, 9146])).
% 1.53/1.79 tff(9440,plain,
% 1.53/1.79 (b(z, elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[289, 9439, 4])).
% 1.53/1.79 tff(9441,plain,
% 1.53/1.79 (~r(elem!1, z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2076, 9438, 9146])).
% 1.53/1.79 tff(9442,plain,
% 1.53/1.79 (b(elem!1, z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[403, 9441, 11])).
% 1.53/1.79 tff(9443,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9444,plain,
% 1.53/1.79 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9445,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9444])).
% 1.53/1.79 tff(9446,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9445, 9443])).
% 1.53/1.79 tff(9447,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9448,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9447, 9446])).
% 1.53/1.79 tff(9449,plain,
% 1.53/1.79 (~b(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9448, 224, 9442, 9440, 7672])).
% 1.53/1.79 tff(9450,plain,
% 1.53/1.79 (~r(s(s(elem!1)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5928, 9146, 9147])).
% 1.53/1.79 tff(9451,plain,
% 1.53/1.79 (b(s(s(elem!1)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[901, 9450])).
% 1.53/1.79 tff(9452,plain,
% 1.53/1.79 (b(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5814, 9145, 9451, 9438, 9449, 9147, 9440])).
% 1.53/1.79 tff(9453,plain,
% 1.53/1.79 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[75])).
% 1.53/1.79 tff(9454,plain,
% 1.53/1.79 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9437, 9453])).
% 1.53/1.79 tff(9455,plain,
% 1.53/1.79 (b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[558, 9454, 2597])).
% 1.53/1.79 tff(9456,plain,
% 1.53/1.79 (b(z, s(z)) <=> b(z, elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[86])).
% 1.53/1.79 tff(9457,plain,
% 1.53/1.79 (b(z, elem!1) <=> b(z, s(z))),
% 1.53/1.79 inference(symmetry,[status(thm)],[9456])).
% 1.53/1.79 tff(9458,plain,
% 1.53/1.79 (b(z, s(z))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[344, 9457])).
% 1.53/1.79 tff(9459,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9138, 9458])).
% 1.53/1.79 tff(9460,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9461,plain,
% 1.53/1.79 (~(s(z) = elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9460, 9440, 9138])).
% 1.53/1.79 tff(9462,plain,
% 1.53/1.79 (~(elem!1 = s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2654, 9461])).
% 1.53/1.79 tff(9463,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9464,plain,
% 1.53/1.79 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9465,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9464])).
% 1.53/1.79 tff(9466,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9465, 9463])).
% 1.53/1.79 tff(9467,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9468,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9467, 9466])).
% 1.53/1.79 tff(9469,plain,
% 1.53/1.79 ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9468, 224])).
% 1.53/1.79 tff(9470,plain,
% 1.53/1.79 (~b(z, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9469, 2896, 405, 1241, 682])).
% 1.53/1.79 tff(9471,plain,
% 1.53/1.79 (r(z, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[752, 9470])).
% 1.53/1.79 tff(9472,plain,
% 1.53/1.79 (~r(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6325, 9471, 4569])).
% 1.53/1.79 tff(9473,plain,
% 1.53/1.79 (b(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[653, 9472])).
% 1.53/1.79 tff(9474,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9475,plain,
% 1.53/1.79 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9476,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9475])).
% 1.53/1.79 tff(9477,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9476, 9474])).
% 1.53/1.79 tff(9478,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9479,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9478, 9477])).
% 1.53/1.79 tff(9480,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9479, 224, 682, 9473, 1241, 2896])).
% 1.53/1.79 tff(9481,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9482,plain,
% 1.53/1.79 (~b(elem!1, s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9481, 9455, 9451, 9147, 9442])).
% 1.53/1.79 tff(9483,plain,
% 1.53/1.79 (r(elem!1, s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1277, 9482, 9462])).
% 1.53/1.79 tff(9484,plain,
% 1.53/1.79 (~b(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9448, 224, 405, 344, 7672])).
% 1.53/1.79 tff(9485,plain,
% 1.53/1.79 (~b(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9179, 1090, 6255, 7672])).
% 1.53/1.79 tff(9486,plain,
% 1.53/1.79 (r(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[194, 9485])).
% 1.63/1.80 tff(9487,plain,
% 1.63/1.80 (~r(s(z), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2096, 112, 1181, 102, 9486])).
% 1.63/1.80 tff(9488,plain,
% 1.63/1.80 (b(s(z), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[653, 9487])).
% 1.63/1.80 tff(9489,plain,
% 1.63/1.80 (~r(s(s(s(z))), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5988, 9488, 1090, 2, 1181])).
% 1.63/1.80 tff(9490,plain,
% 1.63/1.80 (s(s(s(z))) = elem!1),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[374, 9489, 9484])).
% 1.63/1.80 tff(9491,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9490])).
% 1.63/1.80 tff(9492,plain,
% 1.63/1.80 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(symmetry,[status(thm)],[9491])).
% 1.63/1.80 tff(9493,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1181, 9492])).
% 1.63/1.80 tff(9494,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9490])).
% 1.63/1.80 tff(9495,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9494, 2587])).
% 1.63/1.80 tff(9496,plain,
% 1.63/1.80 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9495])).
% 1.63/1.80 tff(9497,plain,
% 1.63/1.80 (~(elem!1 = s(s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[55, 9496])).
% 1.63/1.80 tff(9498,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9499,plain,
% 1.63/1.80 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~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(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9500,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~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(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9499])).
% 1.63/1.80 tff(9501,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~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(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9500, 9498])).
% 1.63/1.80 tff(9502,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(9503,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9502, 9501])).
% 1.63/1.80 tff(9504,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9503, 112, 1181, 102, 268])).
% 1.63/1.80 tff(9505,plain,
% 1.63/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[265, 9504, 259])).
% 1.63/1.80 tff(9506,plain,
% 1.63/1.80 (~b(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 1241, 9505])).
% 1.63/1.80 tff(9507,plain,
% 1.63/1.80 (r(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[213, 68, 210, 9506])).
% 1.63/1.80 tff(9508,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9509,plain,
% 1.63/1.80 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9510,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9509])).
% 1.63/1.80 tff(9511,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9510, 9508])).
% 1.63/1.80 tff(9512,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(9513,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9512, 9511])).
% 1.63/1.80 tff(9514,plain,
% 1.63/1.80 (~r(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9513, 112, 102, 268])).
% 1.63/1.80 tff(9515,plain,
% 1.63/1.80 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3547, 68, 9514])).
% 1.63/1.80 tff(9516,plain,
% 1.63/1.80 (b(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9515, 3659])).
% 1.63/1.80 tff(9517,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9518,plain,
% 1.63/1.80 (((~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9519,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9518])).
% 1.63/1.80 tff(9520,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9519, 9517])).
% 1.63/1.80 tff(9521,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(9522,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9521, 9520])).
% 1.63/1.80 tff(9523,plain,
% 1.63/1.80 (~b(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9522, 224, 682, 9505, 9516])).
% 1.63/1.80 tff(9524,plain,
% 1.63/1.80 (r(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2874, 9523, 2786])).
% 1.63/1.80 tff(9525,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2978, 112, 9524, 993, 9507])).
% 1.63/1.80 tff(9526,plain,((~r(s(s(z)), z)) | (~r(elem!1, s(z))) | (elem!1 = s(s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(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(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9527,plain,
% 1.63/1.80 (~r(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9526, 9497, 993, 682, 9488, 1241, 259, 1181, 102])).
% 1.63/1.80 tff(9528,plain,
% 1.63/1.80 (b(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[281, 9527])).
% 1.63/1.80 tff(9529,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8623, 9528, 9493, 7672, 6255])).
% 1.63/1.80 tff(9530,plain,
% 1.63/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[265, 9529, 259])).
% 1.63/1.80 tff(9531,plain,
% 1.63/1.80 (~b(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5850, 224, 9488, 1241, 9530])).
% 1.63/1.80 tff(9532,plain,
% 1.63/1.80 (r(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[213, 68, 210, 9531])).
% 1.63/1.80 tff(9533,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.63/1.80 inference(transitivity,[status(thm)],[9495, 2588])).
% 1.63/1.80 tff(9534,plain,
% 1.63/1.80 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9533])).
% 1.63/1.80 tff(9535,plain,
% 1.63/1.80 (~(s(s(z)) = elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[55, 9534])).
% 1.63/1.80 tff(9536,plain,
% 1.63/1.80 (~b(s(s(z)), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1126, 9528, 405, 344])).
% 1.63/1.80 tff(9537,plain,
% 1.63/1.80 (r(s(s(z)), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1135, 9536, 9535])).
% 1.63/1.80 tff(9538,plain,
% 1.63/1.80 (~r(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3582, 112, 1181, 9537])).
% 1.63/1.80 tff(9539,plain,
% 1.63/1.80 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3547, 68, 9538])).
% 1.63/1.80 tff(9540,plain,
% 1.63/1.80 (b(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9539, 3659])).
% 1.63/1.80 tff(9541,plain,
% 1.63/1.80 (~b(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9522, 224, 682, 9530, 9540])).
% 1.63/1.80 tff(9542,plain,
% 1.63/1.80 (r(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2874, 9541, 9497])).
% 1.63/1.80 tff(9543,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2978, 112, 9542, 993, 9532])).
% 1.63/1.80 tff(9544,plain,((~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9545,plain,
% 1.63/1.80 (~b(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9544, 9483, 9455, 9451, 169, 9438, 7672, 9452, 9442, 9440, 9146, 9145])).
% 1.63/1.80 tff(9546,plain,
% 1.63/1.80 (r(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[175, 9545])).
% 1.63/1.80 tff(9547,plain,
% 1.63/1.80 (s(s(s(z))) = elem!1),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[374, 9406, 9484])).
% 1.63/1.80 tff(9548,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9547])).
% 1.63/1.80 tff(9549,plain,
% 1.63/1.80 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(symmetry,[status(thm)],[9548])).
% 1.63/1.80 tff(9550,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1181, 9549])).
% 1.63/1.80 tff(9551,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9547])).
% 1.63/1.80 tff(9552,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9551, 2587])).
% 1.63/1.80 tff(9553,plain,
% 1.63/1.80 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9552])).
% 1.63/1.80 tff(9554,plain,
% 1.63/1.80 (~(elem!1 = s(s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[55, 9553])).
% 1.63/1.80 tff(9555,plain,
% 1.63/1.80 (~b(elem!1, s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9479, 224, 682, 1197, 1241])).
% 1.63/1.80 tff(9556,plain,
% 1.63/1.80 (r(elem!1, s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1277, 9555, 88])).
% 1.63/1.80 tff(9557,plain,
% 1.63/1.80 (~r(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9526, 9556, 9554, 682, 1197, 1241, 259, 1181, 102])).
% 1.63/1.80 tff(9558,plain,
% 1.63/1.80 (b(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[281, 9557])).
% 1.63/1.80 tff(9559,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8623, 9558, 9550, 7672, 6255])).
% 1.63/1.80 tff(9560,plain,
% 1.63/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[265, 9559, 259])).
% 1.63/1.80 tff(9561,plain,
% 1.63/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.63/1.80 inference(transitivity,[status(thm)],[9552, 2588])).
% 1.63/1.80 tff(9562,plain,
% 1.63/1.80 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9561])).
% 1.63/1.80 tff(9563,plain,
% 1.63/1.80 (~(s(s(z)) = elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[55, 9562])).
% 1.63/1.80 tff(9564,plain,
% 1.63/1.80 (~b(s(s(z)), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1126, 9558, 405, 344])).
% 1.63/1.80 tff(9565,plain,
% 1.63/1.80 (r(s(s(z)), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1135, 9564, 9563])).
% 1.63/1.80 tff(9566,plain,
% 1.63/1.80 (~r(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1053, 112, 416, 9565])).
% 1.63/1.80 tff(9567,plain,
% 1.63/1.80 (b(s(s(z)), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[213, 68, 210, 9566])).
% 1.63/1.80 tff(9568,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5850, 224, 1197, 1241, 9567, 9560])).
% 1.63/1.80 tff(9569,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9570,plain,
% 1.63/1.80 (~r(s(z), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9569, 9546, 169, 7672, 9452, 9442, 9440, 9455, 9438, 9146, 9462, 9451])).
% 1.63/1.80 tff(9571,plain,
% 1.63/1.80 (b(s(z), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[454, 9570, 9461])).
% 1.63/1.80 tff(9572,plain,
% 1.63/1.80 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9573,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9572])).
% 1.63/1.80 tff(9574,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9573, 8973])).
% 1.63/1.80 tff(9575,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(9576,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9575, 9574])).
% 1.63/1.80 tff(9577,plain,
% 1.63/1.80 (~b(elem!1, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9576, 224, 9442, 9452, 7672])).
% 1.63/1.80 tff(9578,plain,
% 1.63/1.80 (~r(elem!1, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1028, 9546, 9483])).
% 1.63/1.80 tff(9579,plain,
% 1.63/1.80 (elem!1 = s(s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[388, 9578, 9577])).
% 1.63/1.80 tff(9580,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2477, 9579, 9571, 9545])).
% 1.63/1.80 tff(9581,plain,(b(s(s(elem!1)), z) | (~b(s(s(s(z))), z)) | b(z, s(z)) | r(elem!1, s(s(elem!1))) | (z = elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9582,plain,
% 1.63/1.80 (b(s(s(elem!1)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9581, 354, 9138, 2597, 4, 7672])).
% 1.63/1.80 tff(9583,plain,
% 1.63/1.80 (b(elem!1, z)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[7672, 2433])).
% 1.63/1.80 tff(9584,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[341])).
% 1.63/1.80 tff(9585,plain,
% 1.63/1.80 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9584])).
% 1.63/1.80 tff(9586,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.63/1.80 tff(9587,plain,
% 1.63/1.80 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9586, 9585])).
% 1.63/1.80 tff(9588,plain,
% 1.63/1.80 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[341])).
% 1.63/1.80 tff(9589,plain,
% 1.63/1.80 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.80 inference(transitivity,[status(thm)],[9588, 1403])).
% 1.63/1.80 tff(9590,plain,
% 1.63/1.80 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9589])).
% 1.63/1.80 tff(9591,plain,
% 1.63/1.80 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[1165, 9590])).
% 1.63/1.80 tff(9592,plain,
% 1.63/1.80 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1306, 9591])).
% 1.63/1.80 tff(9593,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[558, 9592, 9587, 2597])).
% 1.63/1.80 tff(9594,plain,((~(s(s(s(z))) = elem!1)) | r(elem!1, s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9595,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9594, 341, 2597])).
% 1.63/1.80 tff(9596,plain,
% 1.63/1.80 (b(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9595, 9584])).
% 1.63/1.80 tff(9597,plain,
% 1.63/1.80 (~b(z, s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[613, 9596, 1240, 9583])).
% 1.63/1.80 tff(9598,plain,
% 1.63/1.80 (r(z, s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[752, 9597])).
% 1.63/1.80 tff(9599,plain,
% 1.63/1.80 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[4257])).
% 1.63/1.80 tff(9600,plain,
% 1.63/1.80 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[354, 9599])).
% 1.63/1.80 tff(9601,plain,
% 1.63/1.80 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 1.63/1.80 inference(monotonicity,[status(thm)],[341])).
% 1.63/1.80 tff(9602,plain,
% 1.63/1.80 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9601])).
% 1.63/1.80 tff(9603,plain,
% 1.63/1.80 (~(s(z) = elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[45, 9602])).
% 1.63/1.80 tff(9604,plain,
% 1.63/1.80 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[131, 9603])).
% 1.63/1.80 tff(9605,plain,
% 1.63/1.80 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[310, 9604])).
% 1.63/1.80 tff(9606,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[147, 9605, 9600])).
% 1.63/1.80 tff(9607,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3074, 9606, 9598, 689])).
% 1.63/1.80 tff(9608,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9609,plain,
% 1.63/1.80 (~(s(s(s(z))) = elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9608, 689, 9582, 7672, 354, 2597])).
% 1.63/1.80 tff(9610,plain,
% 1.63/1.80 (r(s(s(s(z))), elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[374, 5799, 362])).
% 1.63/1.80 tff(9611,plain,
% 1.63/1.80 (~r(z, elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[698, 9610, 689])).
% 1.63/1.80 tff(9612,plain,
% 1.63/1.80 (b(z, elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[289, 9611, 4])).
% 1.63/1.80 tff(9613,plain,
% 1.63/1.80 (~(s(z) = elem!1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9460, 9612, 9138])).
% 1.63/1.80 tff(9614,plain,
% 1.63/1.80 (~(elem!1 = s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2654, 9613])).
% 1.63/1.80 tff(9615,plain,
% 1.63/1.80 (~r(elem!1, z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5767, 9614, 689, 377, 9147])).
% 1.63/1.80 tff(9616,plain,
% 1.63/1.80 (b(elem!1, z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[403, 9615, 11])).
% 1.63/1.80 tff(9617,plain,
% 1.63/1.80 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[131, 9613])).
% 1.63/1.80 tff(9618,plain,
% 1.63/1.80 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[310, 9617])).
% 1.63/1.80 tff(9619,plain,
% 1.63/1.80 (~r(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5470, 689, 9147])).
% 1.63/1.80 tff(9620,plain,
% 1.63/1.80 (b(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[175, 9619])).
% 1.63/1.80 tff(9621,plain,
% 1.63/1.80 (~r(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6165, 112, 4569, 2851])).
% 1.63/1.80 tff(9622,plain,
% 1.63/1.80 (b(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[281, 9621])).
% 1.63/1.80 tff(9623,plain,
% 1.63/1.80 (~r(z, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6072, 112, 4569, 2851])).
% 1.63/1.80 tff(9624,plain,
% 1.63/1.80 (b(z, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1088, 9623])).
% 1.63/1.80 tff(9625,plain,
% 1.63/1.80 (~b(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3766, 224, 1240, 9624, 9622])).
% 1.63/1.80 tff(9626,plain,
% 1.63/1.80 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3547, 68, 9625])).
% 1.63/1.80 tff(9627,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9626, 3659])).
% 1.63/1.80 tff(9628,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9629,plain,
% 1.63/1.80 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(9630,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[9629])).
% 1.63/1.80 tff(9631,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[9630, 9628])).
% 1.63/1.81 tff(9632,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9633,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9632, 9631])).
% 1.63/1.81 tff(9634,plain,
% 1.63/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9633, 224, 7672, 9624, 9622])).
% 1.63/1.81 tff(9635,plain,
% 1.63/1.81 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3535, 68, 9634])).
% 1.63/1.81 tff(9636,plain,
% 1.63/1.81 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9635, 56])).
% 1.63/1.81 tff(9637,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9638,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9639,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9638, 9637])).
% 1.63/1.81 tff(9640,plain,
% 1.63/1.81 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9639, 112, 690, 9636, 9627])).
% 1.63/1.81 tff(9641,plain,
% 1.63/1.81 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[147, 9640, 2])).
% 1.63/1.81 tff(9642,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9643,plain,
% 1.63/1.81 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9644,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9643])).
% 1.63/1.81 tff(9645,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[9644, 9642])).
% 1.63/1.81 tff(9646,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9647,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9646, 9645])).
% 1.63/1.81 tff(9648,plain,
% 1.63/1.81 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9647, 224, 1240, 1090, 7672])).
% 1.63/1.81 tff(9649,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9648, 9641])).
% 1.63/1.81 tff(9650,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[901, 9649])).
% 1.63/1.81 tff(9651,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3679, 112, 9650, 2851, 9627])).
% 1.63/1.81 tff(9652,plain,((~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9653,plain,
% 1.63/1.81 (~r(s(s(z)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9652, 9618, 9620, 7672, 1240, 9610, 169, 9147])).
% 1.63/1.81 tff(9654,plain,
% 1.63/1.81 (b(s(s(z)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[213, 68, 210, 9653])).
% 1.63/1.81 tff(9655,plain,
% 1.63/1.81 (~r(s(s(s(z))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4621, 689, 9147])).
% 1.63/1.81 tff(9656,plain,
% 1.63/1.81 (b(s(s(s(z))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[925, 9655])).
% 1.63/1.81 tff(9657,plain,
% 1.63/1.81 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1096, 224, 9620, 9656, 9654])).
% 1.63/1.81 tff(9658,plain,
% 1.63/1.81 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[249, 9657])).
% 1.63/1.81 tff(9659,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9660,plain,
% 1.63/1.81 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9661,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9660])).
% 1.63/1.81 tff(9662,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[9661, 9659])).
% 1.63/1.81 tff(9663,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9664,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9663, 9662])).
% 1.63/1.81 tff(9665,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9664, 112, 4569, 196, 689, 268])).
% 1.63/1.81 tff(9666,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9667,plain,
% 1.63/1.81 (~r(s(s(z)), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9666, 9658, 689, 9147])).
% 1.63/1.81 tff(9668,plain,
% 1.63/1.81 (b(s(s(z)), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[281, 9667])).
% 1.63/1.81 tff(9669,plain,
% 1.63/1.81 (~r(z, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1104, 112, 9658, 689])).
% 1.63/1.81 tff(9670,plain,
% 1.63/1.81 (b(z, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1088, 9669])).
% 1.63/1.81 tff(9671,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3766, 224, 1240, 9670, 9668])).
% 1.63/1.81 tff(9672,plain,
% 1.63/1.81 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3547, 68, 9671])).
% 1.63/1.81 tff(9673,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9672, 3623])).
% 1.63/1.81 tff(9674,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9675,plain,
% 1.63/1.81 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9676,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9675])).
% 1.63/1.81 tff(9677,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[9676, 9674])).
% 1.63/1.81 tff(9678,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9679,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9678, 9677])).
% 1.63/1.81 tff(9680,plain,
% 1.63/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9679, 224, 7672, 9670, 9656, 9654])).
% 1.63/1.81 tff(9681,plain,
% 1.63/1.81 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3535, 68, 9680])).
% 1.63/1.81 tff(9682,plain,
% 1.63/1.81 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9681, 56])).
% 1.63/1.81 tff(9683,plain,
% 1.63/1.81 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9639, 112, 9610, 9682, 9673])).
% 1.63/1.81 tff(9684,plain,
% 1.63/1.81 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[147, 9683, 9618])).
% 1.63/1.81 tff(9685,plain,
% 1.63/1.81 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9647, 224, 1240, 9620, 7672])).
% 1.63/1.81 tff(9686,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9685, 9684])).
% 1.63/1.81 tff(9687,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[901, 9686])).
% 1.63/1.81 tff(9688,plain,
% 1.63/1.81 (~r(z, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5570, 112, 9147, 9687])).
% 1.63/1.81 tff(9689,plain,
% 1.63/1.81 (b(z, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[752, 9688])).
% 1.63/1.81 tff(9690,plain,
% 1.63/1.81 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[613, 9689, 1240, 9616])).
% 1.63/1.81 tff(9691,plain,
% 1.63/1.81 (elem!1 = s(s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[558, 9690, 2597])).
% 1.63/1.81 tff(9692,plain,
% 1.63/1.81 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9691])).
% 1.63/1.81 tff(9693,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[9692])).
% 1.63/1.81 tff(9694,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9695,plain,
% 1.63/1.81 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(9696,plain,
% 1.63/1.81 (((~![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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9695])).
% 1.63/1.81 tff(9697,plain,
% 1.63/1.81 (((~![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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[9696, 9694])).
% 1.63/1.81 tff(9698,plain,
% 1.63/1.81 ((~![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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(9699,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9698, 9697])).
% 1.63/1.81 tff(9700,plain,
% 1.63/1.81 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9699, 112, 9682, 9673])).
% 1.63/1.81 tff(9701,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[135, 68, 9617, 9700])).
% 1.63/1.81 tff(9702,plain,
% 1.63/1.81 (b(s(s(s(z))), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9701, 9693])).
% 1.63/1.81 tff(9703,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5799, 9702])).
% 1.63/1.81 tff(9704,plain,(b(s(s(s(z))), elem!1) | r(elem!1, s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | b(z, s(z)) | (z = elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9705,plain,
% 1.63/1.81 (b(s(s(s(z))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9704, 689, 9582, 7672, 2597, 9138, 4, 9609])).
% 1.63/1.81 tff(9706,plain,
% 1.63/1.81 (~r(s(s(s(z))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[698, 688, 689])).
% 1.63/1.81 tff(9707,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2951, 9706, 3335, 354, 5752, 362, 5481])).
% 1.63/1.81 tff(9708,plain,((~r(z, elem!1)) | b(s(s(elem!1)), elem!1) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9709,plain,
% 1.63/1.81 (~r(z, elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9708, 9609, 354, 689, 9147])).
% 1.63/1.81 tff(9710,plain,
% 1.63/1.81 (b(z, elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[289, 9709, 4])).
% 1.63/1.81 tff(9711,plain,
% 1.63/1.81 (~(elem!1 = s(s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9609, 376])).
% 1.63/1.81 tff(9712,plain,
% 1.63/1.81 (~(s(z) = elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9460, 9710, 9138])).
% 1.63/1.81 tff(9713,plain,
% 1.63/1.81 (~(elem!1 = s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2654, 9712])).
% 1.63/1.81 tff(9714,plain,
% 1.63/1.81 (~r(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5767, 9713, 689, 9711, 9147])).
% 1.63/1.81 tff(9715,plain,
% 1.63/1.81 (b(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[403, 9714, 11])).
% 1.63/1.81 tff(9716,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9448, 224, 9715, 9710, 9705, 7672])).
% 1.63/1.81 tff(9717,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(z, s(z)) | (z = elem!1) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9718,plain,
% 1.63/1.81 (~r(z, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9717, 354, 9138, 4, 7672, 2597])).
% 1.63/1.81 tff(9719,plain,
% 1.63/1.81 (b(z, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[100, 9718])).
% 1.63/1.81 tff(9720,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[7680, 224, 9582, 9719, 7672])).
% 1.63/1.81 tff(9721,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[7680, 224, 1240, 6255, 7672])).
% 1.63/1.81 tff(9722,plain,
% 1.63/1.81 (r(z, elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[289, 4538, 4])).
% 1.63/1.81 tff(9723,plain,
% 1.63/1.81 (b(elem!1, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8971, 9722, 4569, 170, 4538])).
% 1.63/1.81 tff(9724,plain,
% 1.63/1.81 (~b(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8978, 224, 9723, 6255, 7672])).
% 1.63/1.81 tff(9725,plain,
% 1.63/1.81 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3641, 9724, 1240])).
% 1.63/1.81 tff(9726,plain,
% 1.63/1.81 (b(elem!1, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[558, 9725, 2597])).
% 1.63/1.81 tff(9727,plain,
% 1.63/1.81 (~r(elem!1, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5490, 9722, 4569])).
% 1.63/1.81 tff(9728,plain,
% 1.63/1.81 (~r(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4037, 112, 178, 827])).
% 1.63/1.81 tff(9729,plain,
% 1.63/1.81 (b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[901, 9728])).
% 1.63/1.81 tff(9730,plain,
% 1.63/1.81 (~r(s(z), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[835, 827, 178])).
% 1.63/1.81 tff(9731,plain,
% 1.63/1.81 (b(s(z), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[653, 9730])).
% 1.63/1.81 tff(9732,plain,
% 1.63/1.81 (~b(elem!1, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9479, 224, 682, 9731, 9729])).
% 1.63/1.81 tff(9733,plain,
% 1.63/1.81 (elem!1 = s(z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1277, 9732, 1271])).
% 1.63/1.81 tff(9734,plain,
% 1.63/1.81 (s(z) = elem!1),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2654, 9733])).
% 1.63/1.81 tff(9735,plain,
% 1.63/1.81 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9734])).
% 1.63/1.81 tff(9736,plain,
% 1.63/1.81 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(symmetry,[status(thm)],[9735])).
% 1.63/1.81 tff(9737,plain,
% 1.63/1.81 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9736])).
% 1.63/1.81 tff(9738,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[354, 9737])).
% 1.63/1.81 tff(9739,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9729, 9738])).
% 1.63/1.81 tff(9740,plain,((~r(s(s(elem!1)), s(s(s(z))))) | b(s(s(elem!1)), elem!1) | r(elem!1, s(z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9741,plain,
% 1.63/1.81 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9740, 9727, 354, 9726, 176])).
% 1.63/1.81 tff(9742,plain,
% 1.63/1.81 (s(s(elem!1)) = s(s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[147, 9741, 9721])).
% 1.63/1.81 tff(9743,plain,
% 1.63/1.81 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[310, 9742])).
% 1.63/1.81 tff(9744,plain,
% 1.63/1.81 (s(z) = elem!1),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[131, 9743])).
% 1.63/1.81 tff(9745,plain,
% 1.63/1.81 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[9744])).
% 1.63/1.81 tff(9746,plain,
% 1.63/1.81 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[9745])).
% 1.63/1.81 tff(9747,plain,
% 1.63/1.81 (b(s(z), s(s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[9723, 9746])).
% 1.63/1.81 tff(9748,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[170, 9747])).
% 1.63/1.81 tff(9749,plain,(b(z, elem!1) | b(s(z), s(s(s(z)))) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9750,plain,
% 1.63/1.81 (b(z, elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9749, 170, 354, 2597, 9582, 9719, 7672, 9147, 4])).
% 1.63/1.81 tff(9751,plain,
% 1.63/1.81 (~(s(z) = elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9460, 9750, 9138])).
% 1.63/1.81 tff(9752,plain,
% 1.63/1.81 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[131, 9751])).
% 1.63/1.81 tff(9753,plain,
% 1.63/1.81 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[310, 9752])).
% 1.63/1.81 tff(9754,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[147, 9753, 9720])).
% 1.63/1.81 tff(9755,plain,
% 1.63/1.81 (b(elem!1, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[558, 3642, 2597])).
% 1.63/1.81 tff(9756,plain,
% 1.63/1.81 (r(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[403, 3633, 157])).
% 1.63/1.81 tff(9757,plain,
% 1.63/1.81 (~r(elem!1, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5749, 9756, 4569])).
% 1.63/1.81 tff(9758,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9740, 9757, 9755, 354, 827, 178])).
% 1.63/1.81 tff(9759,plain,(b(elem!1, z) | b(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | r(elem!1, s(s(elem!1))) | (elem!1 = z) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(9760,plain,
% 1.63/1.81 (b(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9759, 9754, 354, 176, 9147, 2597, 11, 9582])).
% 1.63/1.81 tff(9761,plain,
% 1.63/1.81 (~b(elem!1, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9576, 224, 9760, 9719, 7672])).
% 1.63/1.81 tff(9762,plain,
% 1.63/1.81 (~b(s(s(s(z))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9448, 224, 9760, 9750, 7672])).
% 1.63/1.81 tff(9763,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3122])).
% 1.63/1.81 tff(9764,plain,
% 1.63/1.81 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2826])).
% 1.63/1.81 tff(9765,plain,
% 1.63/1.81 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5799, 9764])).
% 1.63/1.81 tff(9766,plain,
% 1.63/1.81 (r(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[135, 68, 308, 9765])).
% 1.63/1.81 tff(9767,plain,
% 1.63/1.81 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[310, 308])).
% 1.63/1.82 tff(9768,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[147, 9767, 9721])).
% 1.63/1.82 tff(9769,plain,
% 1.63/1.82 (~r(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[835, 9768, 178])).
% 1.63/1.82 tff(9770,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[653, 9769])).
% 1.63/1.82 tff(9771,plain,
% 1.63/1.82 (~r(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4037, 112, 178, 9768])).
% 1.63/1.82 tff(9772,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[901, 9771])).
% 1.63/1.82 tff(9773,plain,
% 1.63/1.82 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1296])).
% 1.63/1.82 tff(9774,plain,
% 1.63/1.82 (b(z, s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[344, 9773])).
% 1.63/1.82 tff(9775,plain,
% 1.63/1.82 (~b(s(z), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5368, 224, 1240, 9770, 9774])).
% 1.63/1.82 tff(9776,plain,
% 1.63/1.82 (r(s(z), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[194, 9775])).
% 1.63/1.82 tff(9777,plain,
% 1.63/1.82 (~b(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8630, 9776, 6255, 178, 9772, 9768, 9770, 7672, 1296])).
% 1.63/1.82 tff(9778,plain,
% 1.63/1.82 (r(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[281, 9777])).
% 1.63/1.82 tff(9779,plain,
% 1.63/1.82 (~r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6167, 9778, 4569])).
% 1.63/1.82 tff(9780,plain,
% 1.63/1.82 (b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2726, 9779])).
% 1.63/1.82 tff(9781,plain,
% 1.63/1.82 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9782,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9781])).
% 1.63/1.82 tff(9783,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[9782, 5845])).
% 1.63/1.82 tff(9784,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9785,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9784, 9783])).
% 1.63/1.82 tff(9786,plain,
% 1.63/1.82 (~b(s(s(z)), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9785, 224, 9770, 9772, 9780])).
% 1.63/1.82 tff(9787,plain,
% 1.63/1.82 (r(s(s(z)), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[265, 9786, 259])).
% 1.63/1.82 tff(9788,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6051, 112, 9787, 9766])).
% 1.63/1.82 tff(9789,plain,
% 1.63/1.82 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3535, 68, 9788])).
% 1.63/1.82 tff(9790,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9789, 56])).
% 1.63/1.82 tff(9791,plain,
% 1.63/1.82 (~r(s(z), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5137, 112, 9776, 9778])).
% 1.63/1.82 tff(9792,plain,
% 1.63/1.82 (b(s(z), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1071, 9791])).
% 1.63/1.82 tff(9793,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4989, 224, 9792, 9780, 9790])).
% 1.63/1.82 tff(9794,plain,
% 1.63/1.82 (r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[925, 9793])).
% 1.63/1.82 tff(9795,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8902, 9794, 7672, 4569, 6255])).
% 1.63/1.82 tff(9796,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3168, 9795])).
% 1.63/1.82 tff(9797,plain,
% 1.63/1.82 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6101, 224, 9770, 9772, 9796])).
% 1.63/1.82 tff(9798,plain,
% 1.63/1.82 (~b(s(s(s(s(z)))), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9797, 6043])).
% 1.63/1.82 tff(9799,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3183, 9798, 3121])).
% 1.63/1.82 tff(9800,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9799, 9763])).
% 1.63/1.82 tff(9801,plain,
% 1.63/1.82 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5194, 224, 9792, 9796, 9780])).
% 1.63/1.82 tff(9802,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 9801])).
% 1.63/1.82 tff(9803,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1300])).
% 1.63/1.82 tff(9804,plain,
% 1.63/1.82 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9803])).
% 1.63/1.82 tff(9805,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9806,plain,
% 1.63/1.82 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9807,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9806])).
% 1.63/1.82 tff(9808,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[9807, 9805])).
% 1.63/1.82 tff(9809,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9810,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9809, 9808])).
% 1.63/1.82 tff(9811,plain,
% 1.63/1.82 (~b(s(s(elem!1)), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9810, 224, 9772, 9792, 9780])).
% 1.63/1.82 tff(9812,plain,
% 1.63/1.82 (~b(elem!1, s(s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9811, 9804])).
% 1.63/1.82 tff(9813,plain,
% 1.63/1.82 (r(elem!1, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2874, 9812, 2832])).
% 1.63/1.82 tff(9814,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9813, 2830])).
% 1.63/1.82 tff(9815,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9816,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9817,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9816, 9815])).
% 1.63/1.82 tff(9818,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9817, 112, 9768, 9814, 9802])).
% 1.63/1.82 tff(9819,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9818, 9800])).
% 1.63/1.82 tff(9820,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | b(s(s(s(z))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(9821,plain,
% 1.63/1.82 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9820, 176, 9147, 9719, 169, 7672, 9752, 9582, 9762, 9750])).
% 1.63/1.82 tff(9822,plain,
% 1.63/1.82 (b(elem!1, s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[558, 9821, 2597])).
% 1.63/1.82 tff(9823,plain,
% 1.63/1.82 (r(elem!1, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9740, 9822, 354, 9754, 176])).
% 1.63/1.82 tff(9824,plain,
% 1.63/1.82 (~r(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1028, 9823, 176])).
% 1.63/1.82 tff(9825,plain,
% 1.63/1.82 (elem!1 = s(s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[388, 9824, 9761])).
% 1.63/1.82 tff(9826,plain,
% 1.63/1.82 (~b(z, s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[613, 9822, 9582, 9760])).
% 1.63/1.82 tff(9827,plain,
% 1.63/1.82 (r(z, s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[752, 9826])).
% 1.63/1.82 tff(9828,plain,
% 1.63/1.82 (r(z, s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3033, 9827, 9825])).
% 1.63/1.82 tff(9829,plain,
% 1.63/1.82 (s(elem!1) = s(s(s(s(z))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9825])).
% 1.63/1.82 tff(9830,plain,
% 1.63/1.82 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9829])).
% 1.63/1.82 tff(9831,plain,
% 1.63/1.82 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.63/1.82 inference(symmetry,[status(thm)],[9830])).
% 1.63/1.82 tff(9832,plain,
% 1.63/1.82 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9831])).
% 1.63/1.82 tff(9833,plain,
% 1.63/1.82 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.63/1.82 inference(symmetry,[status(thm)],[9832])).
% 1.63/1.82 tff(9834,plain,
% 1.63/1.82 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9833])).
% 1.63/1.82 tff(9835,plain,
% 1.63/1.82 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[169, 9834])).
% 1.63/1.82 tff(9836,plain,
% 1.63/1.82 (~r(s(s(z)), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8623, 1118, 827, 7672, 6255])).
% 1.63/1.82 tff(9837,plain,
% 1.63/1.82 (b(s(s(z)), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[265, 9836, 259])).
% 1.63/1.82 tff(9838,plain,
% 1.63/1.82 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9837, 3446])).
% 1.63/1.82 tff(9839,plain,
% 1.63/1.82 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9201, 1118, 7672, 6255])).
% 1.63/1.82 tff(9840,plain,
% 1.63/1.82 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[249, 9839])).
% 1.63/1.82 tff(9841,plain,
% 1.63/1.82 (~r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[202, 112, 9840, 178])).
% 1.63/1.82 tff(9842,plain,
% 1.63/1.82 (b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2726, 9841])).
% 1.63/1.82 tff(9843,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3026])).
% 1.63/1.82 tff(9844,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9731, 9843])).
% 1.63/1.82 tff(9845,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3026])).
% 1.63/1.82 tff(9846,plain,
% 1.63/1.82 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9729, 9845])).
% 1.63/1.82 tff(9847,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8852, 224, 9846, 9844, 9842, 9838])).
% 1.63/1.82 tff(9848,plain,((~b(s(s(z)), z)) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(9849,plain,
% 1.63/1.82 (~b(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9848, 9825, 176, 169, 9754, 7672, 9719])).
% 1.63/1.82 tff(9850,plain,
% 1.63/1.82 (r(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[281, 9849])).
% 1.63/1.82 tff(9851,plain,
% 1.63/1.82 (~r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6167, 9850, 9147])).
% 1.63/1.82 tff(9852,plain,
% 1.63/1.82 (b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2726, 9851])).
% 1.63/1.82 tff(9853,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9830])).
% 1.63/1.82 tff(9854,plain,
% 1.63/1.82 (~r(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[835, 9754, 176])).
% 1.63/1.82 tff(9855,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[653, 9854])).
% 1.63/1.82 tff(9856,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9855, 9853])).
% 1.63/1.82 tff(9857,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9830])).
% 1.63/1.82 tff(9858,plain,
% 1.63/1.82 (~r(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4037, 112, 176, 9754])).
% 1.63/1.82 tff(9859,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[901, 9858])).
% 1.63/1.82 tff(9860,plain,
% 1.63/1.82 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9859, 9857])).
% 1.63/1.82 tff(9861,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.82 tff(9862,plain,
% 1.63/1.82 (((~b(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(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))))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9863,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9862])).
% 1.63/1.82 tff(9864,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[9863, 8847])).
% 1.63/1.82 tff(9865,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9866,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9865, 9864])).
% 1.63/1.82 tff(9867,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9866, 224, 4495, 4494, 2844, 9861])).
% 1.63/1.82 tff(9868,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(9869,plain,
% 1.63/1.82 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9868, 9860, 9856, 9852])).
% 1.63/1.82 tff(9870,plain,
% 1.63/1.82 (((~![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)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9871,plain,
% 1.63/1.82 ((~![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)))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9872,plain,
% 1.63/1.82 ((~![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))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9871, 9870])).
% 1.63/1.82 tff(9873,plain,
% 1.63/1.82 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9872, 68, 9869])).
% 1.63/1.82 tff(9874,plain,
% 1.63/1.82 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9873, 9835])).
% 1.63/1.82 tff(9875,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(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(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9876,plain,
% 1.63/1.82 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9877,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9876])).
% 1.63/1.82 tff(9878,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[9877, 9875])).
% 1.63/1.82 tff(9879,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(9880,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9879, 9878])).
% 1.63/1.82 tff(9881,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9880, 112, 9147, 9850, 9874, 9828])).
% 1.63/1.82 tff(9882,plain,(b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), z)) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1))) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(9883,plain,
% 1.63/1.82 (b(z, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9882, 9133, 170, 7644, 354, 4])).
% 1.63/1.82 tff(9884,plain,
% 1.63/1.82 (~r(s(z), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1205, 9883, 7646, 3340])).
% 1.63/1.82 tff(9885,plain,
% 1.63/1.82 (b(s(z), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[454, 9884, 91])).
% 1.63/1.82 tff(9886,plain,
% 1.63/1.82 (~(elem!1 = s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2477, 9885, 170])).
% 1.63/1.82 tff(9887,plain,
% 1.63/1.82 (b(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[388, 9886, 9137])).
% 1.63/1.82 tff(9888,plain,
% 1.63/1.82 (~b(s(z), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4051, 2252, 1180, 1240])).
% 1.63/1.82 tff(9889,plain,
% 1.63/1.82 (r(s(z), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[194, 9888])).
% 1.63/1.82 tff(9890,plain,
% 1.63/1.82 (~r(elem!1, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1259, 9889, 363])).
% 1.63/1.82 tff(9891,plain,
% 1.63/1.82 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9740, 9890, 354, 178, 682])).
% 1.63/1.82 tff(9892,plain,
% 1.63/1.82 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[147, 9891, 2])).
% 1.63/1.82 tff(9893,plain,
% 1.63/1.82 (b(elem!1, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1277, 9890, 83])).
% 1.63/1.82 tff(9894,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9895,plain,
% 1.63/1.82 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(9896,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9895])).
% 1.63/1.82 tff(9897,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[9896, 9894])).
% 1.63/1.82 tff(9898,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(9899,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[9898, 9897])).
% 1.63/1.83 tff(9900,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9899, 224, 682, 2252, 9893, 685, 9892])).
% 1.63/1.83 tff(9901,plain,((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9902,plain,
% 1.63/1.83 (~b(s(z), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9901, 9134, 9887, 2, 354, 176, 9136, 7646, 7648])).
% 1.63/1.83 tff(9903,plain,
% 1.63/1.83 (r(s(z), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[653, 9902])).
% 1.63/1.83 tff(9904,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6382, 112, 9903, 176, 7656])).
% 1.63/1.83 tff(9905,plain,(b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (z = elem!1) | (elem!1 = s(s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9906,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9905, 4, 170, 2, 3, 4538])).
% 1.63/1.83 tff(9907,plain,
% 1.63/1.83 (b(s(s(s(z))), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[7205, 102, 176, 6255, 3, 2])).
% 1.63/1.83 tff(9908,plain,
% 1.63/1.83 (~b(s(s(z)), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9201, 2212, 6255, 9907])).
% 1.63/1.83 tff(9909,plain,
% 1.63/1.83 (r(s(s(z)), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[281, 9908])).
% 1.63/1.83 tff(9910,plain,
% 1.63/1.83 (~r(s(s(elem!1)), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9513, 112, 102, 9909])).
% 1.63/1.83 tff(9911,plain,
% 1.63/1.83 (~(s(s(elem!1)) = s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3490, 1108])).
% 1.63/1.83 tff(9912,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3547, 68, 9911, 9910])).
% 1.63/1.83 tff(9913,plain,
% 1.63/1.83 (~r(s(s(z)), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[276, 9909, 102])).
% 1.63/1.83 tff(9914,plain,
% 1.63/1.83 (b(s(s(z)), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[265, 9913, 1108])).
% 1.63/1.83 tff(9915,plain,
% 1.63/1.83 (~r(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5928, 9147, 102])).
% 1.63/1.83 tff(9916,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[901, 9915])).
% 1.63/1.83 tff(9917,plain,
% 1.63/1.83 (~r(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6167, 9909, 9147])).
% 1.63/1.83 tff(9918,plain,
% 1.63/1.83 (b(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2726, 9917])).
% 1.63/1.83 tff(9919,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 1241, 2844, 2596])).
% 1.63/1.83 tff(9920,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9921,plain,
% 1.63/1.83 (~b(s(z), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9920, 9918, 9916, 9914])).
% 1.63/1.83 tff(9922,plain,
% 1.63/1.83 (r(s(z), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[653, 9921])).
% 1.63/1.83 tff(9923,plain,
% 1.63/1.83 (~r(z, s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6325, 9922, 9147])).
% 1.63/1.83 tff(9924,plain,
% 1.63/1.83 (b(z, s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[752, 9923])).
% 1.63/1.83 tff(9925,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9926,plain,
% 1.63/1.83 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9927,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[9926])).
% 1.63/1.83 tff(9928,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[9927, 9925])).
% 1.63/1.83 tff(9929,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(9930,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[9929, 9928])).
% 1.63/1.83 tff(9931,plain,
% 1.63/1.83 ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9930, 224, 2212, 6255, 9912])).
% 1.63/1.83 tff(9932,plain,
% 1.63/1.83 (~b(z, s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9931, 9924])).
% 1.63/1.83 tff(9933,plain,
% 1.63/1.83 (r(z, s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1088, 9932])).
% 1.63/1.83 tff(9934,plain,
% 1.63/1.83 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[835, 9922, 176])).
% 1.63/1.83 tff(9935,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[147, 9934, 2])).
% 1.63/1.83 tff(9936,plain,
% 1.63/1.83 (b(elem!1, s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8971, 9722, 170, 4569, 4538])).
% 1.63/1.83 tff(9937,plain,
% 1.63/1.83 (~(s(s(z)) = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3574, 9936, 523, 176, 2596, 656, 152])).
% 1.63/1.83 tff(9938,plain,
% 1.63/1.83 (~r(s(s(z)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3758, 9722, 3750])).
% 1.63/1.83 tff(9939,plain,
% 1.63/1.83 (b(s(s(z)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1135, 9938, 9937])).
% 1.63/1.83 tff(9940,plain,
% 1.63/1.83 (~r(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5480, 9722, 4569])).
% 1.63/1.83 tff(9941,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[454, 9940, 129])).
% 1.63/1.83 tff(9942,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9943,plain,
% 1.63/1.83 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9944,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[9943])).
% 1.63/1.83 tff(9945,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[9944, 9942])).
% 1.63/1.83 tff(9946,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(9947,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[9946, 9945])).
% 1.63/1.83 tff(9948,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9947, 224, 9941, 2212, 9936, 9939, 2844])).
% 1.63/1.83 tff(9949,plain,(b(z, elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (s(z) = elem!1) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | b(s(z), s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9950,plain,
% 1.63/1.83 (b(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9949, 2212, 9918, 91, 319, 9914, 9922, 9935, 9933, 9147, 170, 511])).
% 1.63/1.83 tff(9951,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2573, 112, 6502, 656, 416])).
% 1.63/1.83 tff(9952,plain,((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9953,plain,
% 1.63/1.83 (~r(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9952, 9922, 3, 9924, 9950])).
% 1.63/1.83 tff(9954,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[454, 9953, 91])).
% 1.63/1.83 tff(9955,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9882, 2597, 170, 7672, 9138, 4])).
% 1.63/1.83 tff(9956,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[743, 9955, 4261, 1180, 344])).
% 1.63/1.83 tff(9957,plain,(r(elem!1, s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), z)) | b(z, s(z)) | (z = elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9958,plain,
% 1.63/1.83 (r(elem!1, s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9957, 9924, 9950, 170, 9907, 9138, 511, 3])).
% 1.63/1.83 tff(9959,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9960,plain,
% 1.63/1.83 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9961,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[9960])).
% 1.63/1.83 tff(9962,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[9961, 9959])).
% 1.63/1.83 tff(9963,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(9964,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[9963, 9962])).
% 1.63/1.83 tff(9965,plain,
% 1.63/1.83 (~r(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9964, 112, 9958, 9922])).
% 1.63/1.83 tff(9966,plain,
% 1.63/1.83 (b(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1277, 9965, 83])).
% 1.63/1.83 tff(9967,plain,
% 1.63/1.83 (~b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5584, 224, 9954, 9916, 9966])).
% 1.63/1.83 tff(9968,plain,
% 1.63/1.83 (r(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[360, 9967, 353])).
% 1.63/1.83 tff(9969,plain,
% 1.63/1.83 (~r(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2076, 9968, 102])).
% 1.63/1.83 tff(9970,plain,
% 1.63/1.83 (b(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[403, 9969, 157])).
% 1.63/1.83 tff(9971,plain,
% 1.63/1.83 (~b(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6730, 9970, 9954, 9950])).
% 1.63/1.83 tff(9972,plain,
% 1.63/1.83 (r(s(z), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[194, 9971])).
% 1.63/1.83 tff(9973,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5137, 112, 179, 2303, 268])).
% 1.63/1.83 tff(9974,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9975,plain,
% 1.63/1.83 (~r(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9974, 9972, 9909])).
% 1.63/1.83 tff(9976,plain,
% 1.63/1.83 (b(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1071, 9975])).
% 1.63/1.83 tff(9977,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9978,plain,
% 1.63/1.83 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9979,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[9978])).
% 1.63/1.83 tff(9980,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[9979, 9977])).
% 1.63/1.83 tff(9981,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(9982,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[9981, 9980])).
% 1.63/1.83 tff(9983,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9982, 224, 9916, 2212, 9935, 9976, 9912])).
% 1.63/1.83 tff(9984,plain,((~b(s(s(z)), s(s(s(z))))) | (elem!1 = z) | (~r(s(s(elem!1)), z)) | b(s(z), s(s(s(z)))) | b(z, s(z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(9985,plain,
% 1.63/1.83 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9984, 9138, 102, 170, 157, 3, 6255, 2])).
% 1.63/1.83 tff(9986,plain,
% 1.63/1.83 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[249, 9985])).
% 1.63/1.83 tff(9987,plain,
% 1.63/1.83 (~r(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6257, 9986, 176])).
% 1.63/1.83 tff(9988,plain,
% 1.63/1.83 (b(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2726, 9987])).
% 1.63/1.83 tff(9989,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9882, 2597, 170, 9907, 9138, 511])).
% 1.63/1.83 tff(9990,plain,
% 1.63/1.83 (r(z, elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[289, 4538, 511])).
% 1.63/1.83 tff(9991,plain,
% 1.63/1.83 (~r(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5480, 9990, 4569])).
% 1.63/1.83 tff(9992,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[454, 9991, 91])).
% 1.63/1.83 tff(9993,plain,
% 1.63/1.83 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2346, 9990, 102])).
% 1.63/1.83 tff(9994,plain,
% 1.63/1.83 (b(elem!1, s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8971, 9990, 170, 4569, 4538])).
% 1.63/1.83 tff(9995,plain,
% 1.63/1.83 (~b(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8978, 224, 9994, 6255, 9907])).
% 1.63/1.83 tff(9996,plain,
% 1.63/1.83 (r(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[403, 9995, 157])).
% 1.63/1.83 tff(9997,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9998,plain,
% 1.63/1.83 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(9999,plain,
% 1.63/1.83 (((~![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)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[9998])).
% 1.63/1.84 tff(10000,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[9999, 9997])).
% 1.63/1.84 tff(10001,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10002,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10001, 10000])).
% 1.63/1.84 tff(10003,plain,
% 1.63/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10002, 112, 9996, 102])).
% 1.63/1.84 tff(10004,plain,
% 1.63/1.84 (~b(s(z), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3687, 10003, 3, 9993, 9992])).
% 1.63/1.84 tff(10005,plain,
% 1.63/1.84 (r(s(z), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[653, 10004])).
% 1.63/1.84 tff(10006,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[835, 10005, 176])).
% 1.63/1.84 tff(10007,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[147, 10006, 2])).
% 1.63/1.84 tff(10008,plain,
% 1.63/1.84 (b(s(s(elem!1)), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[360, 9993, 353])).
% 1.63/1.84 tff(10009,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5928, 4569, 102])).
% 1.63/1.84 tff(10010,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[901, 10009])).
% 1.63/1.84 tff(10011,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10012,plain,
% 1.63/1.84 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10013,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10012])).
% 1.63/1.84 tff(10014,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10013, 10011])).
% 1.63/1.84 tff(10015,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10016,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10015, 10014])).
% 1.63/1.84 tff(10017,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10016, 224, 9992, 10010, 10008, 9994, 10007])).
% 1.63/1.84 tff(10018,plain,(b(z, elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10019,plain,
% 1.63/1.84 (b(z, elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10018, 9147, 3, 102, 157, 6255, 2, 170])).
% 1.63/1.84 tff(10020,plain,
% 1.63/1.84 (~b(z, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9957, 2597, 10019, 170, 9907, 9138, 511, 3])).
% 1.63/1.84 tff(10021,plain,
% 1.63/1.84 (r(z, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[752, 10020])).
% 1.63/1.84 tff(10022,plain,
% 1.63/1.84 (~r(s(z), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6325, 10021, 9147])).
% 1.63/1.84 tff(10023,plain,
% 1.63/1.84 (b(s(z), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[653, 10022])).
% 1.63/1.84 tff(10024,plain,
% 1.63/1.84 (~b(s(z), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3685, 10023, 9989, 4261])).
% 1.63/1.84 tff(10025,plain,
% 1.63/1.84 (r(s(z), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[454, 10024, 91])).
% 1.63/1.84 tff(10026,plain,
% 1.63/1.84 (~r(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2374, 10025, 176])).
% 1.63/1.84 tff(10027,plain,
% 1.63/1.84 (~b(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9479, 224, 4261, 10023, 9916])).
% 1.63/1.84 tff(10028,plain,
% 1.63/1.84 (r(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1277, 10027, 83])).
% 1.63/1.84 tff(10029,plain,
% 1.63/1.84 (~r(elem!1, z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5749, 10028, 9147])).
% 1.63/1.84 tff(10030,plain,
% 1.63/1.84 (b(elem!1, z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[403, 10029, 157])).
% 1.63/1.84 tff(10031,plain,
% 1.63/1.84 (~b(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9448, 224, 10030, 10019, 9907])).
% 1.63/1.84 tff(10032,plain,
% 1.63/1.84 (s(s(s(z))) = elem!1),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[374, 10031, 10026])).
% 1.63/1.84 tff(10033,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[4505])).
% 1.63/1.84 tff(10034,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10033])).
% 1.63/1.84 tff(10035,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1241, 10034])).
% 1.63/1.84 tff(10036,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.63/1.84 tff(10037,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10036, 10035])).
% 1.63/1.84 tff(10038,plain,((~b(s(s(elem!1)), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10039,plain,
% 1.63/1.84 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10038, 10032, 9916])).
% 1.63/1.84 tff(10040,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9594, 10032, 2597])).
% 1.63/1.84 tff(10041,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6853, 10040, 9916, 10023])).
% 1.63/1.84 tff(10042,plain,
% 1.63/1.84 (r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[925, 10041])).
% 1.63/1.84 tff(10043,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8902, 10042, 9907, 9147, 6255])).
% 1.63/1.84 tff(10044,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3168, 10043])).
% 1.63/1.84 tff(10045,plain,
% 1.63/1.84 (~r(s(z), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6296, 9986, 176])).
% 1.63/1.84 tff(10046,plain,
% 1.63/1.84 (b(s(z), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1071, 10045])).
% 1.63/1.84 tff(10047,plain,
% 1.63/1.84 (b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4511, 10032, 10023])).
% 1.63/1.84 tff(10048,plain,
% 1.63/1.84 (~r(elem!1, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1028, 10028, 176])).
% 1.63/1.84 tff(10049,plain,
% 1.63/1.84 (~b(s(s(z)), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9920, 10023, 9916, 9988])).
% 1.63/1.84 tff(10050,plain,
% 1.63/1.84 (r(s(s(z)), s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[265, 10049, 1108])).
% 1.63/1.84 tff(10051,plain,
% 1.63/1.84 (~r(s(s(z)), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[276, 10050, 102])).
% 1.63/1.84 tff(10052,plain,
% 1.63/1.84 (b(s(s(z)), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[281, 10051])).
% 1.63/1.84 tff(10053,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8623, 10052, 6255, 9907, 10050])).
% 1.63/1.84 tff(10054,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[147, 10053, 2])).
% 1.63/1.84 tff(10055,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10056,plain,
% 1.63/1.84 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10057,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10056])).
% 1.63/1.84 tff(10058,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10057, 10055])).
% 1.63/1.84 tff(10059,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10060,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10059, 10058])).
% 1.63/1.84 tff(10061,plain,
% 1.63/1.84 (~b(elem!1, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10060, 224, 4261, 10030, 10054, 9907])).
% 1.63/1.84 tff(10062,plain,
% 1.63/1.84 (elem!1 = s(s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[388, 10061, 10048])).
% 1.63/1.84 tff(10063,plain,
% 1.63/1.84 (s(elem!1) = s(s(s(s(z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10062])).
% 1.63/1.84 tff(10064,plain,
% 1.63/1.84 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10063])).
% 1.63/1.84 tff(10065,plain,
% 1.63/1.84 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10064])).
% 1.63/1.84 tff(10066,plain,
% 1.63/1.84 (s(s(s(s(z)))) = s(elem!1)),
% 1.63/1.84 inference(symmetry,[status(thm)],[10063])).
% 1.63/1.84 tff(10067,plain,
% 1.63/1.84 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10066, 10065])).
% 1.63/1.84 tff(10068,plain,
% 1.63/1.84 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10067, 519])).
% 1.63/1.84 tff(10069,plain,
% 1.63/1.84 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10068])).
% 1.63/1.84 tff(10070,plain,
% 1.63/1.84 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10069])).
% 1.63/1.84 tff(10071,plain,
% 1.63/1.84 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[526, 10070])).
% 1.63/1.84 tff(10072,plain,
% 1.63/1.84 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10064])).
% 1.63/1.84 tff(10073,plain,
% 1.63/1.84 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10050, 10072])).
% 1.63/1.84 tff(10074,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8879, 10073, 10071, 10047, 10046, 10044, 10039, 9988])).
% 1.63/1.84 tff(10075,plain,(r(elem!1, s(s(elem!1))) | (~b(z, s(s(s(z))))) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | b(s(z), s(s(s(z)))) | b(z, s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10076,plain,
% 1.63/1.84 (~b(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10075, 9138, 157, 2, 102, 170, 2597, 3])).
% 1.63/1.84 tff(10077,plain,
% 1.63/1.84 (~r(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5470, 9147, 176])).
% 1.63/1.84 tff(10078,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[100, 10077, 10076])).
% 1.63/1.84 tff(10079,plain,(b(z, s(z)) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | b(s(z), s(s(s(z)))) | r(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10080,plain,
% 1.63/1.84 (b(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10079, 2597, 2, 102, 170, 157, 3])).
% 1.63/1.84 tff(10081,plain,
% 1.63/1.84 (r(s(elem!1), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[939, 1287, 303])).
% 1.63/1.84 tff(10082,plain,
% 1.63/1.84 (~r(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2499, 10081, 688])).
% 1.63/1.84 tff(10083,plain,
% 1.63/1.84 (b(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[625, 10082])).
% 1.63/1.84 tff(10084,plain,
% 1.63/1.84 (~r(s(elem!1), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[722, 112, 10081, 688])).
% 1.63/1.84 tff(10085,plain,
% 1.63/1.84 (b(s(elem!1), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[498, 10084])).
% 1.63/1.84 tff(10086,plain,
% 1.63/1.84 (~r(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3061, 293, 688, 656])).
% 1.63/1.84 tff(10087,plain,
% 1.63/1.84 (b(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[194, 10086])).
% 1.63/1.84 tff(10088,plain,
% 1.63/1.84 (~r(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6325, 293, 656])).
% 1.63/1.84 tff(10089,plain,
% 1.63/1.84 (b(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5459, 10088])).
% 1.63/1.84 tff(10090,plain,
% 1.63/1.84 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10091,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10090])).
% 1.63/1.84 tff(10092,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10091, 764])).
% 1.63/1.84 tff(10093,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10094,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10093, 10092])).
% 1.63/1.84 tff(10095,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10094, 224, 10089, 10087, 7672])).
% 1.63/1.84 tff(10096,plain,
% 1.63/1.84 (r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[925, 10095])).
% 1.63/1.84 tff(10097,plain,
% 1.63/1.84 (~b(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6470, 10087, 10085, 10089])).
% 1.63/1.84 tff(10098,plain,
% 1.63/1.84 (r(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1476, 10097, 409])).
% 1.63/1.84 tff(10099,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9022, 112, 10098, 10096])).
% 1.63/1.84 tff(10100,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10101,plain,
% 1.63/1.84 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10102,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10101])).
% 1.63/1.84 tff(10103,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10102, 10100])).
% 1.63/1.84 tff(10104,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10105,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10104, 10103])).
% 1.63/1.84 tff(10106,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10105, 224, 10085, 10083, 7672])).
% 1.63/1.84 tff(10107,plain,
% 1.63/1.84 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[816, 68, 10106])).
% 1.63/1.84 tff(10108,plain,
% 1.63/1.84 (s(s(s(z))) = s(elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10107, 10099])).
% 1.63/1.84 tff(10109,plain,
% 1.63/1.84 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10108])).
% 1.63/1.84 tff(10110,plain,
% 1.63/1.84 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10109, 1143])).
% 1.63/1.84 tff(10111,plain,
% 1.63/1.84 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10110])).
% 1.63/1.84 tff(10112,plain,
% 1.63/1.84 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1165, 10111])).
% 1.63/1.84 tff(10113,plain,
% 1.63/1.84 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[9074, 10108])).
% 1.63/1.84 tff(10114,plain,
% 1.63/1.84 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10115,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10114])).
% 1.63/1.84 tff(10116,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10115, 725])).
% 1.63/1.84 tff(10117,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10118,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10117, 10116])).
% 1.63/1.84 tff(10119,plain,
% 1.63/1.84 (~b(s(z), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10118, 224, 10087, 10085, 10083])).
% 1.63/1.84 tff(10120,plain,
% 1.63/1.84 (r(s(z), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[670, 10119, 561])).
% 1.63/1.84 tff(10121,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[664, 10120, 656])).
% 1.63/1.84 tff(10122,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.63/1.84 tff(10123,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[530, 10122, 526])).
% 1.63/1.84 tff(10124,plain,
% 1.63/1.84 (~r(s(z), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[449, 407, 77, 409, 408])).
% 1.63/1.84 tff(10125,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10126,plain,
% 1.63/1.84 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10127,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10126])).
% 1.63/1.85 tff(10128,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10127, 10125])).
% 1.63/1.85 tff(10129,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10130,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10129, 10128])).
% 1.63/1.85 tff(10131,plain,
% 1.63/1.85 (~b(z, elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10130, 224, 501, 77, 684, 407])).
% 1.63/1.85 tff(10132,plain,
% 1.63/1.85 (r(z, elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[289, 10131, 511])).
% 1.63/1.85 tff(10133,plain,
% 1.63/1.85 (~r(s(elem!1), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[722, 112, 408, 10132])).
% 1.63/1.85 tff(10134,plain,
% 1.63/1.85 (b(s(elem!1), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[498, 10133])).
% 1.63/1.85 tff(10135,plain,
% 1.63/1.85 (~b(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[4320, 10134, 1391, 407])).
% 1.63/1.85 tff(10136,plain,
% 1.63/1.85 (r(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[593, 10135])).
% 1.63/1.85 tff(10137,plain,
% 1.63/1.85 (~b(elem!1, z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[507, 224, 501, 10134, 407])).
% 1.63/1.85 tff(10138,plain,
% 1.63/1.85 (r(elem!1, z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[403, 10137, 157])).
% 1.63/1.85 tff(10139,plain,
% 1.63/1.85 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2074, 112, 10138, 10136])).
% 1.63/1.85 tff(10140,plain,
% 1.63/1.85 (b(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[358, 68, 10139, 353])).
% 1.63/1.85 tff(10141,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10142,plain,
% 1.63/1.85 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10143,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10142])).
% 1.63/1.85 tff(10144,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10143, 10141])).
% 1.63/1.85 tff(10145,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10146,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10145, 10144])).
% 1.63/1.85 tff(10147,plain,
% 1.63/1.85 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10146, 224, 501, 1391, 684])).
% 1.63/1.85 tff(10148,plain,
% 1.63/1.85 (~b(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10147, 10140])).
% 1.63/1.85 tff(10149,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[901, 10148])).
% 1.63/1.85 tff(10150,plain,
% 1.63/1.85 (~r(s(z), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[895, 10149, 10136])).
% 1.63/1.85 tff(10151,plain,
% 1.63/1.85 (b(s(z), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[194, 10150])).
% 1.63/1.85 tff(10152,plain,
% 1.63/1.85 (~b(s(elem!1), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6468, 224, 77, 10151, 10134])).
% 1.63/1.85 tff(10153,plain,
% 1.63/1.85 (r(s(elem!1), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[440, 68, 409, 10152])).
% 1.63/1.85 tff(10154,plain,
% 1.63/1.85 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10002, 112, 10138, 10136])).
% 1.63/1.85 tff(10155,plain,
% 1.63/1.85 (b(elem!1, s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[558, 10154, 3])).
% 1.63/1.85 tff(10156,plain,
% 1.63/1.85 (~b(s(z), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[634, 224, 10155, 684, 10140])).
% 1.63/1.85 tff(10157,plain,
% 1.63/1.85 (r(s(z), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[653, 10156])).
% 1.63/1.85 tff(10158,plain,
% 1.63/1.85 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3570, 10155, 1391, 501])).
% 1.63/1.85 tff(10159,plain,
% 1.63/1.85 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1521, 10158, 319])).
% 1.63/1.85 tff(10160,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2649, 112, 10159, 10157, 10153])).
% 1.63/1.85 tff(10161,plain,((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10162,plain,
% 1.63/1.85 (~b(s(z), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10161, 407, 501, 1391, 3, 157, 77, 408])).
% 1.63/1.85 tff(10163,plain,
% 1.63/1.85 (s(z) = elem!1),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[454, 10162, 10124])).
% 1.63/1.85 tff(10164,plain,
% 1.63/1.85 (b(z, s(z)) <=> b(z, elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10163])).
% 1.63/1.85 tff(10165,plain,
% 1.63/1.85 (b(z, elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[77, 10164])).
% 1.63/1.85 tff(10166,plain,
% 1.63/1.85 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[7751, 10163])).
% 1.63/1.85 tff(10167,plain,
% 1.63/1.85 (b(s(z), z) <=> b(elem!1, z)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10163])).
% 1.63/1.85 tff(10168,plain,
% 1.63/1.85 (~r(s(elem!1), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[491, 179, 77, 409, 407, 408])).
% 1.63/1.85 tff(10169,plain,
% 1.63/1.85 (b(s(elem!1), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[498, 10168])).
% 1.63/1.85 tff(10170,plain,
% 1.63/1.85 (~b(elem!1, z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[507, 224, 501, 10169, 407])).
% 1.63/1.85 tff(10171,plain,
% 1.63/1.85 (r(elem!1, z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[403, 10170, 157])).
% 1.63/1.85 tff(10172,plain,
% 1.63/1.85 (~r(s(z), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2639, 112, 10171, 179])).
% 1.63/1.85 tff(10173,plain,
% 1.63/1.85 (s(z) = elem!1),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[454, 10172, 2337])).
% 1.63/1.85 tff(10174,plain,
% 1.63/1.85 (s(s(z)) = s(elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10173])).
% 1.63/1.85 tff(10175,plain,
% 1.63/1.85 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10174])).
% 1.63/1.85 tff(10176,plain,
% 1.63/1.85 (s(s(elem!1)) = s(s(s(z)))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10175])).
% 1.63/1.85 tff(10177,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10176])).
% 1.63/1.85 tff(10178,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10177])).
% 1.63/1.85 tff(10179,plain,
% 1.63/1.85 (elem!1 = s(z)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10173, 85])).
% 1.63/1.85 tff(10180,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.85 tff(10181,plain,
% 1.63/1.85 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10180])).
% 1.63/1.85 tff(10182,plain,
% 1.63/1.85 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10181])).
% 1.63/1.85 tff(10183,plain,
% 1.63/1.85 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10182])).
% 1.63/1.85 tff(10184,plain,
% 1.63/1.85 (s(s(z)) = s(s(s(s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[32, 10183, 989, 7777])).
% 1.63/1.85 tff(10185,plain,
% 1.63/1.85 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10184])).
% 1.63/1.85 tff(10186,plain,
% 1.63/1.85 (s(z) = s(s(s(z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[50, 10185, 1223])).
% 1.63/1.85 tff(10187,plain,
% 1.63/1.85 ((s(z) = s(s(s(z)))) <=> (s(z) = s(s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[7775])).
% 1.63/1.85 tff(10188,plain,
% 1.63/1.85 ((s(z) = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10187])).
% 1.63/1.85 tff(10189,plain,
% 1.63/1.85 ((~(s(z) = s(s(elem!1)))) <=> (~(s(z) = s(s(s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10188])).
% 1.63/1.85 tff(10190,plain,
% 1.63/1.85 (~(s(z) = s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[648, 10189])).
% 1.63/1.85 tff(10191,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10190, 10186])).
% 1.63/1.85 tff(10192,plain,((~(s(s(s(z))) = s(s(s(s(elem!1)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10193,plain,
% 1.63/1.85 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10192, 10179])).
% 1.63/1.85 tff(10194,plain,
% 1.63/1.85 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10175])).
% 1.63/1.85 tff(10195,plain,
% 1.63/1.85 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10175])).
% 1.63/1.85 tff(10196,plain,
% 1.63/1.85 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10195])).
% 1.63/1.85 tff(10197,plain,
% 1.63/1.85 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10196])).
% 1.63/1.85 tff(10198,plain,
% 1.63/1.85 (~b(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[4320, 10169, 1391, 407])).
% 1.63/1.85 tff(10199,plain,
% 1.63/1.85 (r(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[593, 10198])).
% 1.63/1.85 tff(10200,plain,
% 1.63/1.85 (~r(s(z), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[983, 112, 10199, 179])).
% 1.63/1.85 tff(10201,plain,
% 1.63/1.85 (b(s(z), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[653, 10200])).
% 1.63/1.85 tff(10202,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10203,plain,
% 1.63/1.85 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10204,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10203])).
% 1.63/1.85 tff(10205,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10204, 10202])).
% 1.63/1.85 tff(10206,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10207,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10206, 10205])).
% 1.63/1.85 tff(10208,plain,
% 1.63/1.85 (~b(z, s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10207, 224, 77, 1391, 10201, 407])).
% 1.63/1.85 tff(10209,plain,
% 1.63/1.85 (~b(z, s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10208, 10197])).
% 1.63/1.85 tff(10210,plain,
% 1.63/1.85 (r(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[100, 10209])).
% 1.63/1.85 tff(10211,plain,
% 1.63/1.85 (r(z, s(s(elem!1)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10210, 10194])).
% 1.63/1.85 tff(10212,plain,
% 1.63/1.85 (b(z, s(z)) <=> b(z, elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10173])).
% 1.63/1.85 tff(10213,plain,
% 1.63/1.85 (b(z, elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[77, 10212])).
% 1.63/1.85 tff(10214,plain,
% 1.63/1.85 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[7751, 10173])).
% 1.63/1.85 tff(10215,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10173])).
% 1.63/1.85 tff(10216,plain,
% 1.63/1.85 (~r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[895, 10199, 179])).
% 1.63/1.85 tff(10217,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[901, 10216])).
% 1.63/1.85 tff(10218,plain,
% 1.63/1.85 (b(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10217, 10215])).
% 1.63/1.85 tff(10219,plain,
% 1.63/1.85 (s(s(s(z))) = s(s(elem!1))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[7770])).
% 1.63/1.85 tff(10220,plain,
% 1.63/1.85 (s(s(elem!1)) = s(s(s(z)))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10219])).
% 1.63/1.85 tff(10221,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10220])).
% 1.63/1.85 tff(10222,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10221])).
% 1.63/1.85 tff(10223,plain,
% 1.63/1.85 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10192, 87])).
% 1.63/1.85 tff(10224,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.85 tff(10225,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.85 tff(10226,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10227,plain,
% 1.63/1.85 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10228,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10227])).
% 1.63/1.85 tff(10229,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10228, 10226])).
% 1.63/1.85 tff(10230,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10231,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10230, 10229])).
% 1.63/1.85 tff(10232,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10231, 224, 501, 344, 407, 10224, 10225])).
% 1.63/1.85 tff(10233,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10234,plain,
% 1.63/1.85 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10233, 10224, 344, 407, 501])).
% 1.63/1.85 tff(10235,plain,
% 1.63/1.85 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[4412, 10234])).
% 1.63/1.85 tff(10236,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10220])).
% 1.63/1.85 tff(10237,plain,
% 1.63/1.85 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10236])).
% 1.63/1.85 tff(10238,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5397, 10237])).
% 1.63/1.85 tff(10239,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10240,plain,
% 1.63/1.85 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10241,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10240])).
% 1.63/1.85 tff(10242,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10241, 10239])).
% 1.63/1.85 tff(10243,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10244,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10243, 10242])).
% 1.63/1.85 tff(10245,plain,
% 1.63/1.85 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10244, 112, 293, 7578])).
% 1.63/1.85 tff(10246,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10245, 10238])).
% 1.63/1.85 tff(10247,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(s(z) = elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10248,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10247, 10235, 293, 86])).
% 1.63/1.85 tff(10249,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5425, 10248, 10223])).
% 1.63/1.85 tff(10250,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10249, 10222])).
% 1.63/1.85 tff(10251,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10252,plain,
% 1.63/1.85 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10253,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10252])).
% 1.63/1.86 tff(10254,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10253, 10251])).
% 1.63/1.86 tff(10255,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10256,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10255, 10254])).
% 1.63/1.86 tff(10257,plain,
% 1.63/1.86 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10256, 224, 501, 1391, 390, 10224])).
% 1.63/1.86 tff(10258,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10257, 10250])).
% 1.63/1.86 tff(10259,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~(s(z) = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10260,plain,
% 1.63/1.86 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10259, 10173, 501, 1391, 10218, 10211, 10213, 407])).
% 1.63/1.86 tff(10261,plain,
% 1.63/1.86 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8842, 10173])).
% 1.63/1.86 tff(10262,plain,
% 1.63/1.86 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1869, 10261, 10260])).
% 1.63/1.86 tff(10263,plain,
% 1.63/1.86 (((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10264,plain,
% 1.63/1.86 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10265,plain,
% 1.63/1.86 (((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10264])).
% 1.63/1.86 tff(10266,plain,
% 1.63/1.86 (((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10265, 10263])).
% 1.63/1.86 tff(10267,plain,
% 1.63/1.86 ((~![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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10268,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10267, 10266])).
% 1.63/1.86 tff(10269,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10268, 112, 408, 1798, 4716])).
% 1.63/1.86 tff(10270,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10271,plain,
% 1.63/1.86 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10270, 10262, 408])).
% 1.63/1.86 tff(10272,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1294, 10271, 10214])).
% 1.63/1.86 tff(10273,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10274,plain,
% 1.63/1.86 (((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10275,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10274])).
% 1.63/1.86 tff(10276,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10275, 10273])).
% 1.63/1.86 tff(10277,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10278,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10277, 10276])).
% 1.63/1.86 tff(10279,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10278, 224, 501, 3919, 344, 407, 10225])).
% 1.63/1.86 tff(10280,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10281,plain,
% 1.63/1.86 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10280, 10272, 10213, 407, 501])).
% 1.63/1.86 tff(10282,plain,
% 1.63/1.86 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4412, 10281])).
% 1.63/1.86 tff(10283,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10247, 10282, 10211, 10173])).
% 1.63/1.86 tff(10284,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5425, 10283, 10193])).
% 1.63/1.86 tff(10285,plain,
% 1.63/1.86 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10284, 10178])).
% 1.63/1.86 tff(10286,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10287,plain,
% 1.63/1.86 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10288,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10287])).
% 1.63/1.86 tff(10289,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10288, 10286])).
% 1.63/1.86 tff(10290,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10291,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10290, 10289])).
% 1.63/1.86 tff(10292,plain,
% 1.63/1.86 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10291, 224, 501, 10272, 1391, 10218])).
% 1.63/1.86 tff(10293,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10292, 10285])).
% 1.63/1.86 tff(10294,plain,((~r(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(z, s(z))) | b(s(z), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10295,plain,
% 1.63/1.86 (~r(s(z), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10294, 10162, 1391, 407, 408, 77, 501, 157])).
% 1.63/1.86 tff(10296,plain,
% 1.63/1.86 (b(s(z), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[194, 10295])).
% 1.63/1.86 tff(10297,plain,
% 1.63/1.86 (b(elem!1, z)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10296, 10167])).
% 1.63/1.86 tff(10298,plain,
% 1.63/1.86 (~b(s(elem!1), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[509, 10297, 501, 407])).
% 1.63/1.86 tff(10299,plain,
% 1.63/1.86 (r(s(elem!1), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[498, 10298])).
% 1.63/1.86 tff(10300,plain,
% 1.63/1.86 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10219])).
% 1.63/1.86 tff(10301,plain,
% 1.63/1.86 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10219])).
% 1.63/1.86 tff(10302,plain,
% 1.63/1.86 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[10301])).
% 1.63/1.86 tff(10303,plain,
% 1.63/1.86 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(z)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10302])).
% 1.63/1.86 tff(10304,plain,
% 1.63/1.86 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4010, 1700, 408])).
% 1.63/1.86 tff(10305,plain,
% 1.63/1.86 (b(elem!1, s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[558, 10304, 3])).
% 1.63/1.86 tff(10306,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10307,plain,
% 1.63/1.86 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10308,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10307])).
% 1.63/1.86 tff(10309,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10308, 10306])).
% 1.63/1.86 tff(10310,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10311,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10310, 10309])).
% 1.63/1.86 tff(10312,plain,
% 1.63/1.86 (~b(z, s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10311, 224, 10305, 1391, 344, 407])).
% 1.63/1.86 tff(10313,plain,
% 1.63/1.86 (~b(z, s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10312, 10303])).
% 1.63/1.86 tff(10314,plain,
% 1.63/1.86 (r(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[100, 10313])).
% 1.63/1.86 tff(10315,plain,
% 1.63/1.86 (r(z, s(s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10314, 10300])).
% 1.63/1.86 tff(10316,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10317,plain,
% 1.63/1.86 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10318,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10317])).
% 1.63/1.86 tff(10319,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10318, 10316])).
% 1.63/1.86 tff(10320,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10321,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10320, 10319])).
% 1.63/1.86 tff(10322,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10321, 112, 1700, 467, 10315])).
% 1.63/1.86 tff(10323,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10324,plain,
% 1.63/1.86 (~r(s(elem!1), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10323, 10299, 10163, 1391, 10165, 407, 3, 408])).
% 1.63/1.86 tff(10325,plain,
% 1.63/1.86 (b(s(elem!1), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1521, 10324, 319])).
% 1.63/1.86 tff(10326,plain,
% 1.63/1.86 (s(elem!1) = s(s(z))),
% 1.63/1.86 inference(symmetry,[status(thm)],[7770])).
% 1.63/1.86 tff(10327,plain,
% 1.63/1.86 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10326])).
% 1.63/1.86 tff(10328,plain,
% 1.63/1.86 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[10327])).
% 1.63/1.86 tff(10329,plain,
% 1.63/1.86 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10328])).
% 1.63/1.86 tff(10330,plain,
% 1.63/1.86 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[7788, 10329])).
% 1.63/1.86 tff(10331,plain,
% 1.63/1.86 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10268, 112, 408, 1798])).
% 1.63/1.87 tff(10332,plain,
% 1.63/1.87 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1868, 68, 10331])).
% 1.63/1.87 tff(10333,plain,
% 1.63/1.87 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10332, 10330])).
% 1.63/1.87 tff(10334,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10326])).
% 1.63/1.87 tff(10335,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10334, 1686])).
% 1.63/1.87 tff(10336,plain,
% 1.63/1.87 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.87 inference(symmetry,[status(thm)],[10335])).
% 1.63/1.87 tff(10337,plain,
% 1.63/1.87 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10336])).
% 1.63/1.87 tff(10338,plain,
% 1.63/1.87 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[7788, 10337])).
% 1.63/1.87 tff(10339,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1315, 112, 408, 1798])).
% 1.63/1.87 tff(10340,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1344, 68, 10339])).
% 1.63/1.87 tff(10341,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10340, 10338])).
% 1.63/1.87 tff(10342,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10343,plain,
% 1.63/1.87 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10344,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10343])).
% 1.63/1.87 tff(10345,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10344, 10342])).
% 1.63/1.87 tff(10346,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10347,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10346, 10345])).
% 1.63/1.87 tff(10348,plain,
% 1.63/1.87 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10347, 224, 407, 10341, 10333])).
% 1.63/1.87 tff(10349,plain,
% 1.63/1.87 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4410, 68, 10348])).
% 1.63/1.87 tff(10350,plain,
% 1.63/1.87 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10349, 4407])).
% 1.63/1.87 tff(10351,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10220])).
% 1.63/1.87 tff(10352,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10351, 1147])).
% 1.63/1.87 tff(10353,plain,
% 1.63/1.87 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.63/1.87 inference(symmetry,[status(thm)],[10352])).
% 1.63/1.87 tff(10354,plain,
% 1.63/1.87 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10353])).
% 1.63/1.87 tff(10355,plain,
% 1.63/1.87 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10223, 10354])).
% 1.63/1.87 tff(10356,plain,
% 1.63/1.87 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 1390, 10341])).
% 1.63/1.87 tff(10357,plain,
% 1.63/1.87 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1401, 68, 10356])).
% 1.63/1.87 tff(10358,plain,
% 1.63/1.87 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10357, 10355])).
% 1.63/1.87 tff(10359,plain,
% 1.63/1.87 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10360,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10359])).
% 1.63/1.87 tff(10361,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10360, 4117])).
% 1.63/1.87 tff(10362,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10363,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10362, 10361])).
% 1.63/1.87 tff(10364,plain,
% 1.63/1.87 (~b(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10363, 224, 1391, 1390, 407])).
% 1.63/1.87 tff(10365,plain,
% 1.63/1.87 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[580, 68, 10364])).
% 1.63/1.87 tff(10366,plain,
% 1.63/1.87 (r(z, s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10365, 567])).
% 1.63/1.87 tff(10367,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10368,plain,
% 1.63/1.87 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10369,plain,
% 1.63/1.87 (((~![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(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10368])).
% 1.63/1.87 tff(10370,plain,
% 1.63/1.87 (((~![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(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10369, 10367])).
% 1.63/1.87 tff(10371,plain,
% 1.63/1.87 ((~![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(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10372,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10371, 10370])).
% 1.63/1.87 tff(10373,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10372, 112, 10366, 10358, 10350])).
% 1.63/1.87 tff(10374,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(10375,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10374, 10325, 408, 1391, 407, 10163])).
% 1.63/1.87 tff(10376,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1294, 10375, 10166])).
% 1.63/1.87 tff(10377,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10220])).
% 1.63/1.87 tff(10378,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(symmetry,[status(thm)],[10377])).
% 1.63/1.87 tff(10379,plain,
% 1.63/1.87 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 1.63/1.87 tff(10380,assumption,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.87 tff(10381,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10380, 10379])).
% 1.63/1.87 tff(10382,plain,((~(s(s(s(s(elem!1)))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(10383,plain,
% 1.63/1.87 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10382, 10223])).
% 1.63/1.87 tff(10384,plain,
% 1.63/1.87 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10220])).
% 1.63/1.87 tff(10385,plain,
% 1.63/1.87 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10384])).
% 1.63/1.87 tff(10386,plain,
% 1.63/1.87 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[7751, 86])).
% 1.63/1.87 tff(10387,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10374, 1390, 408, 1391, 407, 86])).
% 1.63/1.87 tff(10388,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1294, 10387, 10386])).
% 1.63/1.87 tff(10389,plain,
% 1.63/1.87 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1324, 224, 10388, 405, 344])).
% 1.63/1.87 tff(10390,plain,
% 1.63/1.87 (r(s(s(s(s(elem!1)))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1338, 10389])).
% 1.63/1.87 tff(10391,plain,
% 1.63/1.87 (~b(z, s(s(s(z))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10364, 10303])).
% 1.63/1.87 tff(10392,plain,
% 1.63/1.87 (r(z, s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[100, 10391])).
% 1.63/1.87 tff(10393,plain,
% 1.63/1.87 (r(z, s(s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10392, 10300])).
% 1.63/1.87 tff(10394,plain,
% 1.63/1.87 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10247, 10393, 7578, 86])).
% 1.63/1.87 tff(10395,plain,
% 1.63/1.87 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5425, 10394, 10223])).
% 1.63/1.87 tff(10396,plain,
% 1.63/1.87 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10395, 10222])).
% 1.63/1.87 tff(10397,plain,
% 1.63/1.87 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[8842, 86])).
% 1.63/1.87 tff(10398,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10399,plain,
% 1.63/1.87 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10400,plain,
% 1.63/1.87 (((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10399])).
% 1.63/1.87 tff(10401,plain,
% 1.63/1.87 (((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10400, 10398])).
% 1.63/1.87 tff(10402,plain,
% 1.63/1.87 ((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10403,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10402, 10401])).
% 1.63/1.87 tff(10404,plain,
% 1.63/1.87 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10403, 112, 467, 10390])).
% 1.63/1.87 tff(10405,plain,
% 1.63/1.87 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1869, 10404, 10397])).
% 1.63/1.87 tff(10406,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10407,plain,
% 1.63/1.87 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10408,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10407])).
% 1.63/1.87 tff(10409,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10408, 10406])).
% 1.63/1.87 tff(10410,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10411,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10410, 10409])).
% 1.63/1.87 tff(10412,plain,
% 1.63/1.87 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10411, 224, 1391, 407, 10405])).
% 1.63/1.87 tff(10413,plain,
% 1.63/1.87 (~b(s(s(elem!1)), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10412, 10396])).
% 1.63/1.87 tff(10414,plain,
% 1.63/1.87 (r(s(s(elem!1)), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[593, 10413])).
% 1.63/1.87 tff(10415,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10416,plain,
% 1.63/1.87 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10417,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10416])).
% 1.63/1.87 tff(10418,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10417, 10415])).
% 1.63/1.87 tff(10419,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10420,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10419, 10418])).
% 1.63/1.87 tff(10421,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10420, 112, 10414, 10390])).
% 1.63/1.87 tff(10422,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10421, 10385])).
% 1.63/1.87 tff(10423,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1883, 10422, 10383])).
% 1.63/1.87 tff(10424,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10423, 10378])).
% 1.63/1.87 tff(10425,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10426,plain,
% 1.63/1.87 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10427,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10426])).
% 1.63/1.87 tff(10428,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10427, 10425])).
% 1.63/1.88 tff(10429,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10430,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[10429, 10428])).
% 1.63/1.88 tff(10431,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10430, 224, 1390, 10405, 10396, 10424])).
% 1.63/1.88 tff(10432,plain,((~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10433,plain,
% 1.63/1.88 (~r(z, s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10432, 10325, 1391, 407, 10163, 10299, 10297, 10165, 408])).
% 1.63/1.88 tff(10434,plain,
% 1.63/1.88 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4412, 10433])).
% 1.63/1.88 tff(10435,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10280, 10434, 10376, 10165, 407, 501])).
% 1.63/1.88 tff(10436,plain,((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10437,plain,
% 1.63/1.88 (~b(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10436, 501, 10123, 408, 3, 77, 157])).
% 1.63/1.88 tff(10438,plain,
% 1.63/1.88 (r(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[625, 10437])).
% 1.63/1.88 tff(10439,plain,
% 1.63/1.88 (~r(z, elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2499, 10438, 408])).
% 1.63/1.88 tff(10440,plain,
% 1.63/1.88 (b(z, elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[289, 10439, 511])).
% 1.63/1.88 tff(10441,plain,
% 1.63/1.88 (((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10442,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[10441])).
% 1.63/1.88 tff(10443,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[10442, 1478])).
% 1.63/1.88 tff(10444,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10445,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[10444, 10443])).
% 1.63/1.88 tff(10446,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10445, 224, 1391, 441, 427])).
% 1.63/1.88 tff(10447,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10446])).
% 1.63/1.88 tff(10448,plain,
% 1.63/1.88 (((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10449,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[10448])).
% 1.63/1.88 tff(10450,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[10449, 5965])).
% 1.63/1.88 tff(10451,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10452,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[10451, 10450])).
% 1.63/1.88 tff(10453,plain,
% 1.63/1.88 (~b(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10452, 224, 501, 441, 427])).
% 1.63/1.88 tff(10454,plain,
% 1.63/1.88 (r(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1275, 68, 10453, 88])).
% 1.63/1.88 tff(10455,plain,
% 1.63/1.88 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3397, 112, 10447, 10454])).
% 1.63/1.88 tff(10456,plain,
% 1.63/1.88 (b(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[358, 68, 10455, 355])).
% 1.63/1.88 tff(10457,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10458,plain,
% 1.63/1.88 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10459,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[10458])).
% 1.63/1.88 tff(10460,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[10459, 10457])).
% 1.63/1.88 tff(10461,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10462,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[10461, 10460])).
% 1.63/1.88 tff(10463,plain,
% 1.63/1.88 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10462, 224, 501, 1391, 344])).
% 1.63/1.88 tff(10464,plain,
% 1.63/1.88 (~b(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10463, 10456])).
% 1.63/1.88 tff(10465,plain,
% 1.63/1.88 (r(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[593, 10464])).
% 1.63/1.88 tff(10466,plain,
% 1.63/1.88 (~r(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[895, 10465, 10447])).
% 1.63/1.88 tff(10467,plain,
% 1.63/1.88 (b(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[194, 10466])).
% 1.63/1.88 tff(10468,plain,
% 1.63/1.88 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10469,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[10468])).
% 1.63/1.88 tff(10470,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[10469, 6463])).
% 1.63/1.88 tff(10471,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10472,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[10471, 10470])).
% 1.63/1.88 tff(10473,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10472, 224, 77, 10467, 500, 441])).
% 1.63/1.88 tff(10474,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (s(s(elem!1)) = elem!1) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10475,plain,
% 1.63/1.88 (~r(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10474, 500, 77, 501, 1391, 344, 353, 2655, 166, 408])).
% 1.63/1.88 tff(10476,plain,
% 1.63/1.88 (b(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[454, 10475, 129])).
% 1.63/1.88 tff(10477,plain,
% 1.63/1.88 (~b(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2904, 10476, 77, 344])).
% 1.63/1.88 tff(10478,plain,
% 1.63/1.88 (r(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1275, 68, 10477, 2655])).
% 1.63/1.88 tff(10479,plain,
% 1.63/1.88 (~r(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1259, 10478, 363])).
% 1.63/1.88 tff(10480,plain,
% 1.63/1.88 (b(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[194, 10479])).
% 1.63/1.88 tff(10481,plain,
% 1.63/1.88 (~b(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6468, 224, 77, 10480, 500])).
% 1.63/1.88 tff(10482,plain,
% 1.63/1.88 (r(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[440, 68, 166, 10481])).
% 1.63/1.88 tff(10483,plain,
% 1.63/1.88 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2074, 112, 363, 102])).
% 1.63/1.88 tff(10484,plain,
% 1.63/1.88 (b(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[358, 68, 10483, 353])).
% 1.63/1.88 tff(10485,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10147, 10484])).
% 1.63/1.88 tff(10486,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10485])).
% 1.63/1.88 tff(10487,plain,
% 1.63/1.88 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10002, 112, 363, 102])).
% 1.63/1.88 tff(10488,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[558, 10487, 3])).
% 1.63/1.88 tff(10489,plain,
% 1.63/1.88 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3570, 10488, 1391, 501])).
% 1.63/1.88 tff(10490,plain,
% 1.63/1.88 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1521, 10489, 319])).
% 1.63/1.88 tff(10491,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5554, 112, 10490, 10486, 428])).
% 1.63/1.88 tff(10492,plain,((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10493,plain,
% 1.63/1.88 (~r(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10492, 10482, 501, 1391, 10476, 3, 363])).
% 1.63/1.88 tff(10494,plain,
% 1.63/1.88 (b(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[593, 10493])).
% 1.63/1.88 tff(10495,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1249, 10494, 77, 10480])).
% 1.63/1.88 tff(10496,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10495])).
% 1.63/1.88 tff(10497,plain,
% 1.63/1.88 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1001, 10496, 10478])).
% 1.63/1.88 tff(10498,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[558, 10497, 3])).
% 1.63/1.88 tff(10499,plain,
% 1.63/1.88 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3570, 10498, 1391, 501])).
% 1.63/1.88 tff(10500,plain,
% 1.63/1.88 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1521, 10499, 319])).
% 1.63/1.88 tff(10501,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5554, 112, 10500, 10496, 10482])).
% 1.63/1.88 tff(10502,plain,((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (s(z) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10503,plain,
% 1.63/1.88 (~b(s(elem!1), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10502, 363, 501, 3, 77, 1391, 166, 344, 129, 408])).
% 1.63/1.88 tff(10504,plain,
% 1.63/1.88 (r(s(elem!1), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[498, 10503])).
% 1.63/1.88 tff(10505,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2692, 112, 408, 363, 10504])).
% 1.63/1.88 tff(10506,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10507,plain,
% 1.63/1.88 (~r(elem!1, z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10506, 129, 501, 3, 77, 10123, 409, 10440, 408])).
% 1.63/1.88 tff(10508,plain,
% 1.63/1.88 (b(elem!1, z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[403, 10507, 157])).
% 1.63/1.88 tff(10509,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10445, 224, 10123, 441, 427])).
% 1.63/1.88 tff(10510,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10509])).
% 1.63/1.88 tff(10511,plain,
% 1.63/1.88 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3397, 112, 10510, 10454])).
% 1.63/1.88 tff(10512,plain,
% 1.63/1.88 (b(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[358, 68, 10511, 353])).
% 1.63/1.88 tff(10513,plain,
% 1.63/1.88 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10462, 224, 501, 10123, 344])).
% 1.63/1.88 tff(10514,plain,
% 1.63/1.88 (~b(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10513, 10512])).
% 1.63/1.88 tff(10515,plain,
% 1.63/1.88 (r(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[593, 10514])).
% 1.63/1.88 tff(10516,plain,
% 1.63/1.88 (b(s(s(elem!1)), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[530, 526, 10122])).
% 1.63/1.88 tff(10517,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10445, 224, 10516, 1347, 683])).
% 1.63/1.88 tff(10518,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10517])).
% 1.63/1.88 tff(10519,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.63/1.88 tff(10520,plain,
% 1.63/1.88 (r(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[558, 3, 10519])).
% 1.63/1.88 tff(10521,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[999, 112, 10520, 10518, 993])).
% 1.63/1.88 tff(10522,plain,((elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10523,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10522, 10454, 3, 10122, 441, 427])).
% 1.63/1.88 tff(10524,plain,
% 1.63/1.88 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3570, 10523, 10123, 501])).
% 1.63/1.88 tff(10525,plain,
% 1.63/1.88 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1521, 10524, 319])).
% 1.63/1.88 tff(10526,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1513, 112, 10525, 10515, 467])).
% 1.63/1.88 tff(10527,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10528,plain,
% 1.63/1.88 (~r(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10527, 467, 501, 344, 3, 10122, 2655, 166, 408])).
% 1.63/1.88 tff(10529,plain,
% 1.63/1.88 (b(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[454, 10528, 129])).
% 1.63/1.88 tff(10530,plain,
% 1.63/1.88 (~b(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2904, 10529, 77, 344])).
% 1.63/1.88 tff(10531,plain,
% 1.63/1.88 (r(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1275, 68, 10530, 2655])).
% 1.63/1.88 tff(10532,plain,
% 1.63/1.88 (~b(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[461, 224, 405, 10529, 344])).
% 1.63/1.88 tff(10533,plain,
% 1.63/1.88 (r(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[194, 10532])).
% 1.63/1.88 tff(10534,plain,
% 1.63/1.88 (~r(s(z), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4231, 10533, 568])).
% 1.63/1.88 tff(10535,plain,
% 1.63/1.88 (b(s(z), s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[426, 68, 10534, 415])).
% 1.63/1.88 tff(10536,plain,
% 1.63/1.88 (~r(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[482, 112, 10533, 467])).
% 1.63/1.88 tff(10537,plain,
% 1.63/1.88 (b(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[440, 68, 166, 10536])).
% 1.63/1.88 tff(10538,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10445, 224, 10123, 10537, 10535])).
% 1.63/1.88 tff(10539,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[901, 10538])).
% 1.63/1.88 tff(10540,plain,
% 1.63/1.88 (~r(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[895, 10539, 10533])).
% 1.63/1.88 tff(10541,plain,
% 1.63/1.88 (b(s(s(elem!1)), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[593, 10540])).
% 1.63/1.88 tff(10542,plain,
% 1.63/1.88 (~b(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10513, 10541])).
% 1.63/1.88 tff(10543,plain,
% 1.63/1.88 (r(s(s(elem!1)), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[358, 68, 353, 10542])).
% 1.63/1.88 tff(10544,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3397, 112, 10543, 10539, 10531])).
% 1.63/1.88 tff(10545,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(z))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(10546,plain,
% 1.63/1.88 (~r(s(elem!1), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10545, 10508, 10440, 409, 10438, 501, 77, 129, 3, 10122, 408])).
% 1.63/1.88 tff(10547,plain,
% 1.63/1.88 (b(s(elem!1), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[498, 10546])).
% 1.63/1.88 tff(10548,plain,
% 1.63/1.88 (~r(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[10474, 10547, 77, 501, 10123, 10440, 353, 2655, 409, 408])).
% 1.63/1.88 tff(10549,plain,
% 1.63/1.88 (b(s(z), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[454, 10548, 129])).
% 1.63/1.88 tff(10550,plain,
% 1.63/1.88 (~b(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[461, 224, 10508, 10549, 10440])).
% 1.63/1.88 tff(10551,plain,
% 1.63/1.88 (r(s(z), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[194, 10550])).
% 1.63/1.88 tff(10552,plain,
% 1.63/1.88 (~b(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2904, 10549, 77, 10440])).
% 1.63/1.88 tff(10553,plain,
% 1.63/1.88 (r(elem!1, s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1275, 68, 10552, 2655])).
% 1.63/1.88 tff(10554,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10555,plain,
% 1.63/1.88 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(10556,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[10555])).
% 1.63/1.88 tff(10557,plain,
% 1.63/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[10556, 10554])).
% 1.63/1.88 tff(10558,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(10559,plain,
% 1.63/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10558, 10557])).
% 1.63/1.89 tff(10560,plain,
% 1.63/1.89 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10559, 224, 501, 10123, 10508, 10547])).
% 1.63/1.89 tff(10561,plain,
% 1.63/1.89 (r(elem!1, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[558, 10560, 3])).
% 1.63/1.89 tff(10562,plain,
% 1.63/1.89 (~r(s(s(elem!1)), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1001, 10561, 10553])).
% 1.63/1.89 tff(10563,plain,
% 1.63/1.89 (b(s(s(elem!1)), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[901, 10562])).
% 1.63/1.89 tff(10564,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10565,plain,
% 1.63/1.89 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10566,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10565])).
% 1.63/1.89 tff(10567,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10566, 10564])).
% 1.63/1.89 tff(10568,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10569,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10568, 10567])).
% 1.63/1.89 tff(10570,plain,
% 1.63/1.89 (~b(s(s(elem!1)), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10569, 224, 77, 10123, 10547, 10563])).
% 1.63/1.89 tff(10571,plain,
% 1.63/1.89 (r(s(s(elem!1)), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[593, 10570])).
% 1.63/1.89 tff(10572,plain,
% 1.63/1.89 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10146, 224, 501, 10123, 10549])).
% 1.63/1.89 tff(10573,plain,
% 1.63/1.89 (~b(s(s(elem!1)), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10572, 10563])).
% 1.63/1.89 tff(10574,plain,
% 1.63/1.89 (r(s(s(elem!1)), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[358, 68, 353, 10573])).
% 1.63/1.89 tff(10575,plain,
% 1.63/1.89 (~r(s(z), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2096, 112, 10574, 10571, 10551])).
% 1.63/1.89 tff(10576,plain,
% 1.63/1.89 (b(s(z), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[653, 10575])).
% 1.63/1.89 tff(10577,plain,
% 1.63/1.89 (~r(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4010, 10561, 408])).
% 1.63/1.89 tff(10578,plain,
% 1.63/1.89 (b(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1521, 10577, 319])).
% 1.63/1.89 tff(10579,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10580,plain,
% 1.63/1.89 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10581,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10580])).
% 1.63/1.89 tff(10582,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10581, 10579])).
% 1.63/1.89 tff(10583,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10584,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10583, 10582])).
% 1.63/1.89 tff(10585,plain,
% 1.63/1.89 (~b(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10584, 224, 501, 10578, 10576, 10549])).
% 1.63/1.89 tff(10586,plain,
% 1.63/1.89 (~r(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4231, 10551, 10438])).
% 1.63/1.89 tff(10587,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[426, 68, 10586, 10585, 561])).
% 1.63/1.89 tff(10588,plain,((s(z) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(10589,plain,
% 1.63/1.89 (~b(elem!1, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10588, 10121, 149, 3, 157, 10081, 10089])).
% 1.63/1.89 tff(10590,plain,
% 1.63/1.89 (r(elem!1, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[515, 10589, 327])).
% 1.63/1.89 tff(10591,plain,
% 1.63/1.89 (~r(elem!1, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1604, 10590, 10098])).
% 1.63/1.89 tff(10592,plain,
% 1.63/1.89 (b(elem!1, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1277, 10591, 88])).
% 1.63/1.89 tff(10593,plain,
% 1.63/1.89 (~r(s(z), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[449, 10089, 409, 10081, 10083])).
% 1.63/1.89 tff(10594,plain,
% 1.63/1.89 (b(s(z), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[454, 10593, 149])).
% 1.63/1.89 tff(10595,plain,
% 1.63/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3631, 293, 688])).
% 1.63/1.89 tff(10596,plain,
% 1.63/1.89 (b(elem!1, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[558, 10595, 3])).
% 1.63/1.89 tff(10597,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10598,plain,
% 1.63/1.89 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10599,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10598])).
% 1.63/1.89 tff(10600,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10599, 10597])).
% 1.63/1.89 tff(10601,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10602,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10601, 10600])).
% 1.63/1.89 tff(10603,plain,
% 1.63/1.89 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10602, 224, 3919, 684, 2896])).
% 1.63/1.89 tff(10604,plain,
% 1.63/1.89 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 10603])).
% 1.63/1.89 tff(10605,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10606,plain,
% 1.63/1.89 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10607,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10606])).
% 1.63/1.89 tff(10608,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10607, 10605])).
% 1.63/1.89 tff(10609,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10610,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10609, 10608])).
% 1.63/1.89 tff(10611,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10610, 112, 102, 5704, 7479, 10604])).
% 1.63/1.89 tff(10612,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(10613,plain,
% 1.63/1.89 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10612, 10596, 7240, 102, 390, 10594, 10592])).
% 1.63/1.89 tff(10614,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1317, 10613, 1287, 10113])).
% 1.63/1.89 tff(10615,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1345, 10614, 10112])).
% 1.63/1.89 tff(10616,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10617,plain,
% 1.63/1.89 (((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10618,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10617])).
% 1.63/1.89 tff(10619,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10618, 10616])).
% 1.63/1.89 tff(10620,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10621,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10620, 10619])).
% 1.63/1.89 tff(10622,plain,
% 1.63/1.89 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10621, 224, 10085, 10083, 10615])).
% 1.63/1.89 tff(10623,plain,
% 1.63/1.89 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1294, 10613, 10113])).
% 1.63/1.89 tff(10624,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10625,plain,
% 1.63/1.89 (((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10626,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[10625])).
% 1.63/1.89 tff(10627,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.63/1.89 inference(transitivity,[status(thm)],[10626, 10624])).
% 1.63/1.89 tff(10628,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(10629,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[10628, 10627])).
% 1.63/1.89 tff(10630,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10629, 112, 10623, 688])).
% 1.63/1.89 tff(10631,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1338, 10630, 10622])).
% 1.63/1.89 tff(10632,plain,((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(10633,plain,
% 1.63/1.89 (~r(z, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10632, 656, 1287, 102, 390, 83, 3, 157, 688, 7644])).
% 1.63/1.89 tff(10634,plain,
% 1.63/1.89 (b(z, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[752, 10633])).
% 1.63/1.89 tff(10635,plain,
% 1.63/1.89 (~r(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4010, 545, 408])).
% 1.63/1.89 tff(10636,plain,
% 1.63/1.89 (b(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1521, 10635, 523])).
% 1.63/1.89 tff(10637,plain,
% 1.63/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4124, 10636, 1180, 407])).
% 1.63/1.89 tff(10638,plain,
% 1.63/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[530, 10637, 1923])).
% 1.63/1.89 tff(10639,plain,
% 1.63/1.89 (~r(elem!1, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[553, 10638, 545])).
% 1.63/1.89 tff(10640,plain,
% 1.63/1.89 (b(elem!1, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[515, 10639, 2506])).
% 1.63/1.89 tff(10641,plain,
% 1.63/1.89 (~b(elem!1, z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[509, 10640, 500, 407])).
% 1.63/1.89 tff(10642,plain,
% 1.63/1.89 (r(elem!1, z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[403, 10641, 157])).
% 1.63/1.89 tff(10643,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[8268, 112, 545, 10638, 10642, 102])).
% 1.63/1.89 tff(10644,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (elem!1 = s(elem!1)) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(10645,plain,
% 1.63/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10644, 10634, 157, 10085, 10083, 327, 102, 319, 10081])).
% 1.63/1.89 tff(10646,plain,
% 1.63/1.89 (b(z, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10079, 10645, 2, 102, 170, 157, 3])).
% 1.63/1.89 tff(10647,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[983, 112, 102, 179, 656])).
% 1.63/1.89 tff(10648,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(10649,plain,
% 1.63/1.89 (~r(s(z), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10648, 656, 102])).
% 1.63/1.89 tff(10650,plain,
% 1.63/1.89 (b(s(z), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[194, 10649])).
% 1.63/1.89 tff(10651,plain,
% 1.63/1.89 (~b(s(elem!1), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6470, 10650, 10085, 10646])).
% 1.63/1.89 tff(10652,plain,
% 1.63/1.89 (r(s(elem!1), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1476, 10651, 409])).
% 1.63/1.89 tff(10653,plain,
% 1.63/1.89 (~b(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[10118, 224, 10650, 10085, 10083])).
% 1.63/1.89 tff(10654,plain,
% 1.63/1.89 (r(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[670, 10653, 561])).
% 1.63/1.89 tff(10655,plain,
% 1.63/1.89 (~r(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[664, 10654, 656])).
% 1.63/1.89 tff(10656,plain,
% 1.63/1.89 (b(s(s(elem!1)), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[530, 10655, 526])).
% 1.63/1.89 tff(10657,plain,
% 1.63/1.89 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4124, 10656, 10634, 10083])).
% 1.63/1.89 tff(10658,plain,
% 1.63/1.89 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1521, 10657, 319])).
% 1.63/1.89 tff(10659,plain,
% 1.63/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10660,plain,
% 1.63/1.89 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(10661,plain,
% 1.63/1.89 (((~![X0: $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(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(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10660])).
% 1.73/1.90 tff(10662,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10661, 10659])).
% 1.73/1.90 tff(10663,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(10664,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10663, 10662])).
% 1.73/1.90 tff(10665,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10664, 112, 10658, 656, 10654, 10652])).
% 1.73/1.90 tff(10666,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | b(s(elem!1), elem!1) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10667,plain,
% 1.73/1.90 (~r(s(z), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10666, 1287, 2, 170, 157, 3, 102, 390, 688])).
% 1.73/1.90 tff(10668,plain,
% 1.73/1.90 (b(s(z), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[653, 10667])).
% 1.73/1.90 tff(10669,plain,
% 1.73/1.90 (~r(s(s(elem!1)), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2346, 102, 688])).
% 1.73/1.90 tff(10670,plain,
% 1.73/1.90 (~b(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3687, 2597, 3, 328, 2252])).
% 1.73/1.90 tff(10671,plain,
% 1.73/1.90 (~r(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[449, 10080, 409, 408, 407])).
% 1.73/1.90 tff(10672,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[454, 10671, 10670, 91])).
% 1.73/1.90 tff(10673,plain,(r(elem!1, s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | b(s(z), s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10674,plain,
% 1.73/1.90 (r(elem!1, s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10673, 10081, 10083, 3, 10669, 10668, 2, 102, 170, 157])).
% 1.73/1.90 tff(10675,plain,
% 1.73/1.90 (~r(z, s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3631, 10674, 688])).
% 1.73/1.90 tff(10676,plain,
% 1.73/1.90 (~b(z, s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10644, 10674, 157, 10085, 10083, 327, 102, 319, 10081])).
% 1.73/1.90 tff(10677,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[752, 10676, 10675])).
% 1.73/1.90 tff(10678,plain,(b(s(elem!1), elem!1) | (elem!1 = z) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10679,plain,
% 1.73/1.90 (b(s(elem!1), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10678, 102, 157, 688, 3, 2, 170, 390])).
% 1.73/1.90 tff(10680,plain,
% 1.73/1.90 (~b(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3687, 2252, 3, 10669, 2597])).
% 1.73/1.90 tff(10681,plain,
% 1.73/1.90 (r(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[454, 10680, 91])).
% 1.73/1.90 tff(10682,plain,
% 1.73/1.90 (~r(s(s(s(z))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2374, 10681, 178])).
% 1.73/1.90 tff(10683,plain,
% 1.73/1.90 (b(s(s(s(z))), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7643, 178, 3, 2])).
% 1.73/1.90 tff(10684,plain,
% 1.73/1.90 (~r(s(z), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3332, 10681, 688])).
% 1.73/1.90 tff(10685,plain,
% 1.73/1.90 (b(s(z), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[194, 10684])).
% 1.73/1.90 tff(10686,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10094, 224, 77, 10685, 10683])).
% 1.73/1.90 tff(10687,plain,
% 1.73/1.90 (r(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[925, 10686])).
% 1.73/1.90 tff(10688,plain,
% 1.73/1.90 (~r(s(s(z)), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2468, 10681, 77, 688])).
% 1.73/1.90 tff(10689,plain,
% 1.73/1.90 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2541, 224, 1488, 4261, 390])).
% 1.73/1.90 tff(10690,plain,
% 1.73/1.90 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1521, 10689, 319])).
% 1.73/1.90 tff(10691,plain,
% 1.73/1.90 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5895, 112, 1798, 416])).
% 1.73/1.90 tff(10692,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4896, 68, 1364, 10691])).
% 1.73/1.90 tff(10693,plain,
% 1.73/1.90 (~r(z, s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[9084, 112, 1798, 688])).
% 1.73/1.90 tff(10694,plain,
% 1.73/1.90 (b(z, s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4412, 10693])).
% 1.73/1.90 tff(10695,plain,
% 1.73/1.90 (~r(s(s(s(s(elem!1)))), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10629, 112, 1798, 688])).
% 1.73/1.90 tff(10696,plain,
% 1.73/1.90 (b(s(s(s(s(elem!1)))), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1338, 10695])).
% 1.73/1.90 tff(10697,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4909, 224, 3656, 10696, 10694, 10692])).
% 1.73/1.90 tff(10698,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10699,plain,
% 1.73/1.90 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10698, 10681, 688])).
% 1.73/1.90 tff(10700,plain,
% 1.73/1.90 (s(s(z)) = elem!1),
% 1.73/1.90 inference(transitivity,[status(thm)],[32, 9066, 121])).
% 1.73/1.90 tff(10701,plain,
% 1.73/1.90 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10700, 9065])).
% 1.73/1.90 tff(10702,plain,
% 1.73/1.90 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10700])).
% 1.73/1.90 tff(10703,plain,
% 1.73/1.90 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.73/1.90 inference(symmetry,[status(thm)],[10702])).
% 1.73/1.90 tff(10704,plain,
% 1.73/1.90 (r(s(z), s(s(z)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[416, 10703])).
% 1.73/1.90 tff(10705,plain,
% 1.73/1.90 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6296, 10704, 178])).
% 1.73/1.90 tff(10706,plain,
% 1.73/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[249, 10705])).
% 1.73/1.90 tff(10707,plain,
% 1.73/1.90 (b(elem!1, s(elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10706, 10701])).
% 1.73/1.90 tff(10708,plain,
% 1.73/1.90 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10709,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10708])).
% 1.73/1.90 tff(10710,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10709, 1489])).
% 1.73/1.90 tff(10711,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(10712,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10711, 10710])).
% 1.73/1.90 tff(10713,plain,
% 1.73/1.90 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10712, 224, 10707, 1488, 390])).
% 1.73/1.90 tff(10714,plain,
% 1.73/1.90 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[9065])).
% 1.73/1.90 tff(10715,plain,
% 1.73/1.90 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10714, 1143])).
% 1.73/1.90 tff(10716,plain,
% 1.73/1.90 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10715])).
% 1.73/1.90 tff(10717,plain,
% 1.73/1.90 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1165, 10716])).
% 1.73/1.90 tff(10718,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.73/1.90 tff(10719,plain,
% 1.73/1.90 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[9074, 9065])).
% 1.73/1.90 tff(10720,plain,
% 1.73/1.90 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1294, 10719, 10718])).
% 1.73/1.90 tff(10721,plain,
% 1.73/1.90 (~r(s(s(elem!1)), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[7481, 10707, 2287, 682, 10720, 390, 10717, 1488])).
% 1.73/1.90 tff(10722,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[530, 10721, 10713, 2505])).
% 1.73/1.90 tff(10723,plain,((~(s(s(s(z))) = s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | r(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10724,plain,
% 1.73/1.90 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10723, 10681, 7240, 4261, 390, 1488, 178, 526, 10699])).
% 1.73/1.90 tff(10725,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10726,plain,
% 1.73/1.90 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10727,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10726])).
% 1.73/1.90 tff(10728,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10727, 10725])).
% 1.73/1.90 tff(10729,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(10730,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10729, 10728])).
% 1.73/1.90 tff(10731,plain,
% 1.73/1.90 (~r(z, s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10730, 112, 1700, 293])).
% 1.73/1.90 tff(10732,plain,
% 1.73/1.90 (b(z, s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[625, 10731])).
% 1.73/1.90 tff(10733,plain,
% 1.73/1.90 (~r(s(elem!1), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10321, 112, 1700, 293])).
% 1.73/1.90 tff(10734,plain,
% 1.73/1.90 (b(s(elem!1), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[498, 10733])).
% 1.73/1.90 tff(10735,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10105, 224, 10734, 10732, 7672])).
% 1.73/1.90 tff(10736,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.73/1.90 tff(10737,plain,
% 1.73/1.90 (r(s(s(s(z))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[816, 68, 10736, 10735])).
% 1.73/1.90 tff(10738,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10094, 224, 77, 1, 7672])).
% 1.73/1.90 tff(10739,plain,
% 1.73/1.90 (r(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[925, 10738])).
% 1.73/1.90 tff(10740,plain,
% 1.73/1.90 (~b(s(elem!1), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6470, 10734, 1, 77])).
% 1.73/1.90 tff(10741,plain,
% 1.73/1.90 (r(s(elem!1), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1476, 10740, 166])).
% 1.73/1.90 tff(10742,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[9022, 112, 10741, 10739, 10737])).
% 1.73/1.90 tff(10743,plain,((~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(elem!1)) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10744,plain,
% 1.73/1.90 (~r(z, s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10743, 10724, 10683, 409, 10685, 77, 10690])).
% 1.73/1.90 tff(10745,plain,
% 1.73/1.90 (b(z, s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[752, 10744])).
% 1.73/1.90 tff(10746,plain,
% 1.73/1.90 (s(s(s(z))) = elem!1),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3418, 2471])).
% 1.73/1.90 tff(10747,plain,
% 1.73/1.90 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.73/1.90 inference(monotonicity,[status(thm)],[341])).
% 1.73/1.90 tff(10748,plain,
% 1.73/1.90 (r(s(s(elem!1)), elem!1)),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[827, 10747])).
% 1.73/1.90 tff(10749,plain,
% 1.73/1.90 (r(elem!1, s(z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[3188, 5032])).
% 1.73/1.90 tff(10750,plain,
% 1.73/1.90 (~r(s(s(elem!1)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[3588, 10749, 10748])).
% 1.73/1.90 tff(10751,plain,
% 1.73/1.90 (b(s(s(elem!1)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[901, 10750])).
% 1.73/1.90 tff(10752,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10751, 10034])).
% 1.73/1.90 tff(10753,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4511, 341, 2252])).
% 1.73/1.90 tff(10754,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4505])).
% 1.73/1.90 tff(10755,plain,
% 1.73/1.90 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[10754])).
% 1.73/1.90 tff(10756,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1180, 10755])).
% 1.73/1.90 tff(10757,plain,
% 1.73/1.90 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4503, 10756, 10753, 77])).
% 1.73/1.90 tff(10758,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10757, 10752])).
% 1.73/1.90 tff(10759,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10760,plain,
% 1.73/1.90 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10759, 10746, 3188, 77, 1180, 2252])).
% 1.73/1.90 tff(10761,plain,
% 1.73/1.90 (b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[147, 10760, 2])).
% 1.73/1.90 tff(10762,plain,
% 1.73/1.90 (b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[9594, 10746, 2597])).
% 1.73/1.90 tff(10763,plain,
% 1.73/1.90 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[2471])).
% 1.73/1.90 tff(10764,plain,
% 1.73/1.90 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10763])).
% 1.73/1.90 tff(10765,plain,
% 1.73/1.90 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[2586, 10764])).
% 1.73/1.90 tff(10766,plain,
% 1.73/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[249, 10765])).
% 1.73/1.90 tff(10767,plain,
% 1.73/1.90 (~b(s(s(z)), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6362, 10766, 10762, 10761])).
% 1.73/1.90 tff(10768,plain,
% 1.73/1.90 (r(s(s(z)), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[265, 10767, 259])).
% 1.73/1.90 tff(10769,plain,
% 1.73/1.90 (~r(s(s(z)), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[276, 10768, 102])).
% 1.73/1.90 tff(10770,plain,
% 1.73/1.90 (b(s(s(z)), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[281, 10769])).
% 1.73/1.90 tff(10771,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4511, 10746, 2252])).
% 1.73/1.90 tff(10772,plain,
% 1.73/1.90 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[3026])).
% 1.73/1.90 tff(10773,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1180, 10772])).
% 1.73/1.90 tff(10774,plain,
% 1.73/1.90 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4503, 10773, 77, 10771])).
% 1.73/1.90 tff(10775,plain,
% 1.73/1.90 (~b(s(s(elem!1)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10038, 10774, 10746])).
% 1.73/1.90 tff(10776,plain,
% 1.73/1.90 (r(s(s(elem!1)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[901, 10775])).
% 1.73/1.90 tff(10777,plain,
% 1.73/1.90 (~r(s(s(z)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2993, 10776, 10768])).
% 1.73/1.90 tff(10778,plain,
% 1.73/1.90 (b(s(s(z)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2726, 10777])).
% 1.73/1.90 tff(10779,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2846, 10778, 10770, 77, 1])).
% 1.73/1.90 tff(10780,plain,((~(elem!1 = s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | r(s(s(z)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(10781,plain,
% 1.73/1.90 (~(elem!1 = s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10780, 10685, 77, 102, 1108, 10745, 10688, 2, 10687, 2252, 2597])).
% 1.73/1.90 tff(10782,plain,
% 1.73/1.90 (~(s(s(s(z))) = elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2487, 10781])).
% 1.73/1.90 tff(10783,plain,
% 1.73/1.90 (b(s(s(s(z))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[374, 10782, 10682])).
% 1.73/1.90 tff(10784,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2761, 224, 4261, 390, 10783])).
% 1.73/1.90 tff(10785,plain,
% 1.73/1.90 (r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[135, 68, 132, 10784])).
% 1.73/1.90 tff(10786,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(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), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10787,plain,
% 1.73/1.90 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10788,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10787])).
% 1.73/1.90 tff(10789,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10788, 10786])).
% 1.73/1.90 tff(10790,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(10791,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10790, 10789])).
% 1.73/1.90 tff(10792,plain,
% 1.73/1.90 (~r(s(s(s(z))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[10791, 112, 10690, 10785])).
% 1.73/1.90 tff(10793,plain,
% 1.73/1.90 (b(s(s(s(z))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[816, 68, 10724, 10792])).
% 1.73/1.90 tff(10794,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10795,plain,
% 1.73/1.90 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(10796,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[10795])).
% 1.73/1.90 tff(10797,plain,
% 1.73/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.73/1.90 inference(transitivity,[status(thm)],[10796, 10794])).
% 1.73/1.90 tff(10798,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(10799,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[10798, 10797])).
% 1.73/1.90 tff(10800,plain,
% 1.73/1.90 ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10799, 224])).
% 1.73/1.91 tff(10801,plain,
% 1.73/1.91 (~b(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10800, 405, 1180, 682, 1])).
% 1.73/1.91 tff(10802,plain,
% 1.73/1.91 (r(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1277, 10801, 88])).
% 1.73/1.91 tff(10803,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10804,plain,
% 1.73/1.91 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10805,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[10804])).
% 1.73/1.91 tff(10806,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[10805, 10803])).
% 1.73/1.91 tff(10807,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(10808,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[10807, 10806])).
% 1.73/1.91 tff(10809,plain,
% 1.73/1.91 ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10808, 224, 682, 1180, 7672])).
% 1.73/1.91 tff(10810,plain,
% 1.73/1.91 (~b(elem!1, s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10809, 405])).
% 1.73/1.91 tff(10811,plain,
% 1.73/1.91 (r(elem!1, s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[388, 10810, 680])).
% 1.73/1.91 tff(10812,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1028, 10811, 10802, 178])).
% 1.73/1.91 tff(10813,plain,((~b(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10814,plain,
% 1.73/1.91 (~b(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10813, 10781, 178, 83, 4261, 10745, 10683, 10685])).
% 1.73/1.91 tff(10815,plain,
% 1.73/1.91 (r(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[403, 10814, 157])).
% 1.73/1.91 tff(10816,plain,
% 1.73/1.91 (~r(z, s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2621, 10815, 102, 390, 688, 526, 303])).
% 1.73/1.91 tff(10817,plain,
% 1.73/1.91 (b(z, s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[625, 10816])).
% 1.73/1.91 tff(10818,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10819,plain,
% 1.73/1.91 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10820,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[10819])).
% 1.73/1.91 tff(10821,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[10820, 10818])).
% 1.73/1.91 tff(10822,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(10823,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[10822, 10821])).
% 1.73/1.91 tff(10824,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10823, 224, 1488, 10783, 10817, 10683, 10793])).
% 1.73/1.91 tff(10825,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | r(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10826,plain,
% 1.73/1.91 (~b(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10825, 10080, 102, 390, 688, 157, 176, 10679, 2, 2597, 3])).
% 1.73/1.91 tff(10827,plain,
% 1.73/1.91 (r(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[653, 10826])).
% 1.73/1.91 tff(10828,plain,
% 1.73/1.91 (~r(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10648, 10827, 102])).
% 1.73/1.91 tff(10829,plain,
% 1.73/1.91 (b(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[194, 10828])).
% 1.73/1.91 tff(10830,plain,
% 1.73/1.91 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2541, 224, 10679, 4261, 390])).
% 1.73/1.91 tff(10831,plain,
% 1.73/1.91 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1521, 10830, 319])).
% 1.73/1.91 tff(10832,plain,
% 1.73/1.91 (~r(s(elem!1), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2649, 112, 10831, 10827])).
% 1.73/1.91 tff(10833,plain,
% 1.73/1.91 (b(s(elem!1), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1476, 10832, 409])).
% 1.73/1.91 tff(10834,plain,
% 1.73/1.91 (~b(s(elem!1), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6470, 10833, 10829, 10080])).
% 1.73/1.91 tff(10835,plain,
% 1.73/1.91 (r(s(elem!1), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[498, 10834])).
% 1.73/1.91 tff(10836,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1513, 112, 10831, 102, 10835])).
% 1.73/1.91 tff(10837,plain,(r(elem!1, s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10838,plain,
% 1.73/1.91 (r(elem!1, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10837, 102, 390, 688, 157, 2, 3, 170])).
% 1.73/1.91 tff(10839,plain,
% 1.73/1.91 (~r(z, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3631, 10838, 688])).
% 1.73/1.91 tff(10840,plain,
% 1.73/1.91 (b(z, s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[752, 10839])).
% 1.73/1.91 tff(10841,plain,
% 1.73/1.91 (~b(z, s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10018, 4569, 3, 4538, 157, 102, 2, 170])).
% 1.73/1.91 tff(10842,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[100, 10841, 8990])).
% 1.73/1.91 tff(10843,plain,((~r(z, s(z))) | (elem!1 = s(s(elem!1))) | b(z, elem!1) | (elem!1 = z) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10844,plain,
% 1.73/1.91 (~r(z, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10843, 102, 4538, 157, 3, 2, 170])).
% 1.73/1.91 tff(10845,plain,
% 1.73/1.91 (b(z, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[5459, 10844])).
% 1.73/1.91 tff(10846,plain,
% 1.73/1.91 (~r(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10648, 179, 102])).
% 1.73/1.91 tff(10847,plain,
% 1.73/1.91 (b(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[653, 10846])).
% 1.73/1.91 tff(10848,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1203, 224, 77, 10847, 1546, 1180])).
% 1.73/1.91 tff(10849,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10850,plain,
% 1.73/1.91 (~r(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10849, 10845, 10840, 102])).
% 1.73/1.91 tff(10851,plain,
% 1.73/1.91 (b(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[194, 10850])).
% 1.73/1.91 tff(10852,plain,
% 1.73/1.91 (~r(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[9964, 112, 545, 656])).
% 1.73/1.91 tff(10853,plain,
% 1.73/1.91 (b(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1277, 10852, 88])).
% 1.73/1.91 tff(10854,plain,
% 1.73/1.91 (~r(s(z), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2573, 112, 545, 656])).
% 1.73/1.91 tff(10855,plain,
% 1.73/1.91 (b(s(z), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[454, 10854, 149])).
% 1.73/1.91 tff(10856,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[5674, 224, 10855, 10853, 390])).
% 1.73/1.91 tff(10857,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[901, 10856])).
% 1.73/1.91 tff(10858,plain,
% 1.73/1.91 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10859,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[10858])).
% 1.73/1.91 tff(10860,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[10859, 1461])).
% 1.73/1.91 tff(10861,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(10862,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[10861, 10860])).
% 1.73/1.91 tff(10863,plain,
% 1.73/1.91 (~b(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10862, 224, 77, 1, 10853])).
% 1.73/1.91 tff(10864,plain,
% 1.73/1.91 (r(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[403, 10863, 157])).
% 1.73/1.91 tff(10865,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10866,plain,
% 1.73/1.91 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10867,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[10866])).
% 1.73/1.91 tff(10868,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[10867, 10865])).
% 1.73/1.91 tff(10869,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(10870,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[10869, 10868])).
% 1.73/1.91 tff(10871,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10870, 112, 545, 10864, 102, 10857])).
% 1.73/1.91 tff(10872,plain,((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10873,plain,
% 1.73/1.91 (~r(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10872, 10838, 102, 157, 10845, 10851, 390, 83])).
% 1.73/1.91 tff(10874,plain,
% 1.73/1.91 (b(s(z), s(s(elem!1)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[653, 10873])).
% 1.73/1.91 tff(10875,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1203, 224, 77, 2252, 1241, 1180])).
% 1.73/1.91 tff(10876,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10877,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10876, 10845, 10874, 10840])).
% 1.73/1.91 tff(10878,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[901, 10877])).
% 1.73/1.91 tff(10879,plain,
% 1.73/1.91 (~r(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1001, 10878, 10838])).
% 1.73/1.91 tff(10880,plain,
% 1.73/1.91 (b(elem!1, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1277, 10879, 83])).
% 1.73/1.91 tff(10881,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1466, 224, 77, 405, 1, 2896])).
% 1.73/1.91 tff(10882,plain,((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10883,plain,
% 1.73/1.91 (~b(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10882, 10845, 10851, 10880])).
% 1.73/1.91 tff(10884,plain,
% 1.73/1.91 (r(elem!1, z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[403, 10883, 157])).
% 1.73/1.91 tff(10885,plain,
% 1.73/1.91 (~r(z, s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2621, 10884, 102, 390, 688, 526, 303])).
% 1.73/1.91 tff(10886,plain,
% 1.73/1.91 (b(z, s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[625, 10885])).
% 1.73/1.91 tff(10887,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10207, 224, 77, 1391, 2252, 1180, 407])).
% 1.73/1.91 tff(10888,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10889,plain,
% 1.73/1.91 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10888, 10886, 10874, 10840, 10845])).
% 1.73/1.91 tff(10890,plain,
% 1.73/1.91 (r(s(s(elem!1)), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[530, 10889, 526])).
% 1.73/1.91 tff(10891,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[8268, 112, 10838, 10890, 10884, 102])).
% 1.73/1.91 tff(10892,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | b(z, elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(10893,plain,
% 1.73/1.91 (~r(s(s(elem!1)), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[10892, 9906, 7067, 11, 4538, 3, 2, 170])).
% 1.73/1.91 tff(10894,plain,
% 1.73/1.91 (b(s(s(elem!1)), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[593, 10893])).
% 1.73/1.91 tff(10895,plain,
% 1.73/1.91 (b(elem!1, s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[8971, 4569, 170, 688, 4538])).
% 1.73/1.91 tff(10896,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10897,plain,
% 1.73/1.91 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(10898,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[10897])).
% 1.73/1.91 tff(10899,plain,
% 1.73/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[10898, 10896])).
% 1.73/1.92 tff(10900,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(10901,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[10900, 10899])).
% 1.73/1.92 tff(10902,plain,
% 1.73/1.92 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10901, 224, 1240, 390, 10895, 7672])).
% 1.73/1.92 tff(10903,plain,
% 1.73/1.92 (r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[147, 10902, 2])).
% 1.73/1.92 tff(10904,plain,
% 1.73/1.92 (~r(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4039, 10903, 176])).
% 1.73/1.92 tff(10905,plain,
% 1.73/1.92 (b(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[901, 10904])).
% 1.73/1.92 tff(10906,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5674, 224, 8987, 10905, 9000, 390])).
% 1.73/1.92 tff(10907,plain,((~r(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | b(s(z), s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10908,plain,
% 1.73/1.92 (~r(z, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10907, 9906, 2, 10894, 7644, 7067, 170, 4538])).
% 1.73/1.92 tff(10909,plain,
% 1.73/1.92 (b(z, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5459, 10908])).
% 1.73/1.92 tff(10910,plain,
% 1.73/1.92 (~r(s(s(elem!1)), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3500, 293, 688])).
% 1.73/1.92 tff(10911,plain,
% 1.73/1.92 (~r(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3332, 179, 688])).
% 1.73/1.92 tff(10912,plain,
% 1.73/1.92 (b(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[454, 10911, 129])).
% 1.73/1.92 tff(10913,plain,
% 1.73/1.92 (~r(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3061, 179, 688, 293])).
% 1.73/1.92 tff(10914,plain,
% 1.73/1.92 (b(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[653, 10913])).
% 1.73/1.92 tff(10915,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3687, 10914, 10912, 3, 10595, 10910])).
% 1.73/1.92 tff(10916,plain,((~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10917,plain,
% 1.73/1.92 (~r(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10916, 293, 91, 688, 3])).
% 1.73/1.92 tff(10918,plain,
% 1.73/1.92 (b(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[194, 10917])).
% 1.73/1.92 tff(10919,plain,
% 1.73/1.92 (~b(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10094, 224, 77, 10918, 7644])).
% 1.73/1.92 tff(10920,plain,
% 1.73/1.92 (r(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[925, 10919])).
% 1.73/1.92 tff(10921,plain,
% 1.73/1.92 (~b(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1249, 10918, 1240, 77])).
% 1.73/1.92 tff(10922,plain,
% 1.73/1.92 (r(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[901, 10921])).
% 1.73/1.92 tff(10923,plain,
% 1.73/1.92 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5351, 112, 10922, 10920])).
% 1.73/1.92 tff(10924,plain,
% 1.73/1.92 (b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[135, 68, 132, 10923])).
% 1.73/1.92 tff(10925,plain,
% 1.73/1.92 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4039, 10922, 176])).
% 1.73/1.92 tff(10926,plain,
% 1.73/1.92 (b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[147, 10925, 2])).
% 1.73/1.92 tff(10927,plain,
% 1.73/1.92 (~b(elem!1, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1008, 224, 10596, 10926, 10924])).
% 1.73/1.92 tff(10928,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7680, 224, 1240, 152, 6255, 7672])).
% 1.73/1.92 tff(10929,plain,((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10930,plain,
% 1.73/1.92 (~b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10929, 10926, 1240, 7644])).
% 1.73/1.92 tff(10931,plain,
% 1.73/1.92 (r(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[100, 10930])).
% 1.73/1.92 tff(10932,plain,
% 1.73/1.92 (~r(elem!1, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2420, 10931, 688])).
% 1.73/1.92 tff(10933,plain,
% 1.73/1.92 (elem!1 = s(s(s(z)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[388, 10932, 10927])).
% 1.73/1.92 tff(10934,plain,
% 1.73/1.92 (~b(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2477, 10933, 170])).
% 1.73/1.92 tff(10935,plain,
% 1.73/1.92 (r(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[454, 10934, 91])).
% 1.73/1.92 tff(10936,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10698, 10935, 688])).
% 1.73/1.92 tff(10937,plain,
% 1.73/1.92 (~r(s(elem!1), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2502, 10935, 166, 688, 77])).
% 1.73/1.92 tff(10938,plain,
% 1.73/1.92 (b(s(elem!1), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[939, 10937, 303])).
% 1.73/1.92 tff(10939,plain,
% 1.73/1.92 (~(s(s(s(z))) = s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10723, 10938, 7240, 10596, 390, 10935, 176, 526, 10936])).
% 1.73/1.92 tff(10940,plain,
% 1.73/1.92 (~r(s(elem!1), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10743, 10939, 7644, 166, 293, 77, 10918])).
% 1.73/1.92 tff(10941,plain,
% 1.73/1.92 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1521, 10940, 319])).
% 1.73/1.92 tff(10942,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2541, 224, 10938, 10596, 10941, 390])).
% 1.73/1.92 tff(10943,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(z, elem!1)) | b(s(z), s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10944,plain,
% 1.73/1.92 (~r(z, s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10943, 9906, 160, 10909, 7067, 170, 10894, 2, 3])).
% 1.73/1.92 tff(10945,plain,
% 1.73/1.92 (b(z, s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[752, 10944])).
% 1.73/1.92 tff(10946,plain,
% 1.73/1.92 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[7654, 224, 10894, 10945, 7644])).
% 1.73/1.92 tff(10947,plain,
% 1.73/1.92 (r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[135, 68, 132, 10946])).
% 1.73/1.92 tff(10948,plain,
% 1.73/1.92 (~b(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4051, 1, 1240, 1180])).
% 1.73/1.92 tff(10949,plain,
% 1.73/1.92 (r(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[653, 10948])).
% 1.73/1.92 tff(10950,plain,
% 1.73/1.92 (~r(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[9107, 10949, 6847])).
% 1.73/1.92 tff(10951,plain,
% 1.73/1.92 (b(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[925, 10950])).
% 1.73/1.92 tff(10952,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[769, 224, 77, 1, 7672, 10951])).
% 1.73/1.92 tff(10953,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10954,plain,
% 1.73/1.92 (~b(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10953, 10909, 7644, 10947, 10894, 10945])).
% 1.73/1.92 tff(10955,plain,
% 1.73/1.92 (r(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[194, 10954])).
% 1.73/1.92 tff(10956,plain,
% 1.73/1.92 (~r(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[9119, 10955, 176])).
% 1.73/1.92 tff(10957,plain,
% 1.73/1.92 (b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[100, 10956])).
% 1.73/1.92 tff(10958,plain,
% 1.73/1.92 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10929, 10957, 10894, 7644])).
% 1.73/1.92 tff(10959,plain,
% 1.73/1.92 (r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[147, 10958, 2])).
% 1.73/1.92 tff(10960,plain,
% 1.73/1.92 (~r(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[835, 10959, 176])).
% 1.73/1.92 tff(10961,plain,
% 1.73/1.92 (b(s(z), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[653, 10960])).
% 1.73/1.92 tff(10962,plain,
% 1.73/1.92 (~r(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4039, 10959, 176])).
% 1.73/1.92 tff(10963,plain,
% 1.73/1.92 (b(s(s(elem!1)), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[901, 10962])).
% 1.73/1.92 tff(10964,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10876, 10963, 10961, 10909, 10945])).
% 1.73/1.92 tff(10965,plain,((z = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10966,plain,
% 1.73/1.92 (z = elem!1),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10965, 170, 2, 3, 4538])).
% 1.73/1.92 tff(10967,plain,
% 1.73/1.92 (s(z) = s(elem!1)),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10966])).
% 1.73/1.92 tff(10968,plain,
% 1.73/1.92 (s(s(z)) = s(s(elem!1))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10967])).
% 1.73/1.92 tff(10969,plain,
% 1.73/1.92 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10968])).
% 1.73/1.92 tff(10970,plain,
% 1.73/1.92 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.73/1.92 inference(symmetry,[status(thm)],[10969])).
% 1.73/1.92 tff(10971,plain,
% 1.73/1.92 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10967])).
% 1.73/1.92 tff(10972,plain,
% 1.73/1.92 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10966])).
% 1.73/1.92 tff(10973,plain,
% 1.73/1.92 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.73/1.92 inference(transitivity,[status(thm)],[10972, 10971])).
% 1.73/1.92 tff(10974,plain,
% 1.73/1.92 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4613, 4559])).
% 1.73/1.92 tff(10975,plain,
% 1.73/1.92 (~r(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5470, 9147, 178])).
% 1.73/1.92 tff(10976,plain,
% 1.73/1.92 (b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[100, 10975])).
% 1.73/1.92 tff(10977,plain,
% 1.73/1.92 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[10976, 10974])).
% 1.73/1.92 tff(10978,plain,
% 1.73/1.92 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.73/1.92 inference(monotonicity,[status(thm)],[1620])).
% 1.73/1.92 tff(10979,plain,
% 1.73/1.92 (b(s(s(s(z))), elem!1)),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[10683, 4600])).
% 1.73/1.92 tff(10980,plain,
% 1.73/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[10979, 10978])).
% 1.73/1.92 tff(10981,plain,
% 1.73/1.92 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[1619])).
% 1.73/1.92 tff(10982,plain,
% 1.73/1.92 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/1.92 inference(symmetry,[status(thm)],[10981])).
% 1.73/1.92 tff(10983,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.73/1.92 tff(10984,plain,
% 1.73/1.92 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.73/1.92 inference(symmetry,[status(thm)],[10983])).
% 1.73/1.92 tff(10985,plain,
% 1.73/1.92 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[1620, 10984])).
% 1.73/1.92 tff(10986,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1165, 10985])).
% 1.73/1.92 tff(10987,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(10988,plain,
% 1.73/1.92 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[10987, 335])).
% 1.73/1.92 tff(10989,plain,
% 1.73/1.92 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4562, 4564])).
% 1.73/1.92 tff(10990,plain,
% 1.73/1.92 (r(elem!1, s(elem!1))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[9147, 10989])).
% 1.73/1.92 tff(10991,plain,
% 1.73/1.92 (~r(s(s(elem!1)), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[539, 1181, 10990])).
% 1.73/1.92 tff(10992,plain,
% 1.73/1.92 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[530, 10991, 1923])).
% 1.73/1.92 tff(10993,plain,
% 1.73/1.92 (b(elem!1, s(s(s(z))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[10976, 4613])).
% 1.73/1.92 tff(10994,plain,
% 1.73/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[787, 4544])).
% 1.73/1.92 tff(10995,plain,
% 1.73/1.92 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[1617])).
% 1.73/1.92 tff(10996,plain,
% 1.73/1.92 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.73/1.92 inference(transitivity,[status(thm)],[10995, 519])).
% 1.73/1.92 tff(10997,plain,
% 1.73/1.92 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.73/1.92 inference(transitivity,[status(thm)],[10996, 520])).
% 1.73/1.92 tff(10998,plain,
% 1.73/1.92 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[10997])).
% 1.73/1.92 tff(10999,plain,
% 1.73/1.92 (~(s(elem!1) = s(s(elem!1)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[648, 10998])).
% 1.73/1.92 tff(11000,plain,
% 1.73/1.92 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1521, 4103, 10999])).
% 1.73/1.92 tff(11001,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11002,plain,
% 1.73/1.92 (((~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))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11003,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[11002])).
% 1.73/1.92 tff(11004,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[11003, 11001])).
% 1.73/1.92 tff(11005,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(11006,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[11005, 11004])).
% 1.73/1.92 tff(11007,plain,
% 1.73/1.92 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[11006, 112, 408, 1740])).
% 1.73/1.92 tff(11008,plain,
% 1.73/1.92 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1857, 68, 7466, 11007])).
% 1.73/1.92 tff(11009,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11010,plain,
% 1.73/1.92 (((~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11011,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[11010])).
% 1.73/1.92 tff(11012,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[11011, 11009])).
% 1.73/1.92 tff(11013,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(11014,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[11013, 11012])).
% 1.73/1.92 tff(11015,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[11014, 224, 1391, 1390, 11008, 1764])).
% 1.73/1.92 tff(11016,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(11017,plain,
% 1.73/1.92 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[11016, 11000, 1391, 1717, 1854, 1181, 408])).
% 1.73/1.92 tff(11018,plain,
% 1.73/1.92 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1777, 11017, 1615])).
% 1.73/1.92 tff(11019,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11020,plain,
% 1.73/1.92 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11021,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[11020])).
% 1.73/1.92 tff(11022,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.92 inference(transitivity,[status(thm)],[11021, 11019])).
% 1.73/1.92 tff(11023,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(11024,plain,
% 1.73/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[11023, 11022])).
% 1.73/1.92 tff(11025,plain,
% 1.73/1.92 ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[11024, 224, 11018])).
% 1.73/1.92 tff(11026,plain,
% 1.73/1.92 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[11025, 4724, 10994])).
% 1.73/1.92 tff(11027,plain,
% 1.73/1.92 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 11026])).
% 1.73/1.92 tff(11028,plain,
% 1.73/1.92 (r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[7883, 1948])).
% 1.73/1.92 tff(11029,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11030,plain,
% 1.73/1.92 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(11031,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[11030])).
% 1.73/1.92 tff(11032,plain,
% 1.73/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[11031, 11029])).
% 1.73/1.93 tff(11033,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11034,plain,
% 1.73/1.93 ((~![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(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11033, 11032])).
% 1.73/1.93 tff(11035,plain,
% 1.73/1.93 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11034, 112, 408, 11028, 11027])).
% 1.73/1.93 tff(11036,plain,
% 1.73/1.93 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1857, 68, 1854, 11035])).
% 1.73/1.93 tff(11037,plain,
% 1.73/1.93 (r(elem!1, s(z))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4569, 4562])).
% 1.73/1.93 tff(11038,plain,
% 1.73/1.93 (r(elem!1, s(elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11037, 4564])).
% 1.73/1.93 tff(11039,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4702, 11000, 1181, 1391, 11038, 335])).
% 1.73/1.93 tff(11040,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11039, 3933])).
% 1.73/1.93 tff(11041,plain,
% 1.73/1.93 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1884, 11040])).
% 1.73/1.93 tff(11042,plain,
% 1.73/1.93 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11041, 1786])).
% 1.73/1.93 tff(11043,plain,
% 1.73/1.93 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11044,plain,
% 1.73/1.93 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11045,plain,
% 1.73/1.93 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11044])).
% 1.73/1.93 tff(11046,plain,
% 1.73/1.93 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[11045, 11043])).
% 1.73/1.93 tff(11047,plain,
% 1.73/1.93 ((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11048,plain,
% 1.73/1.93 ((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11047, 11046])).
% 1.73/1.93 tff(11049,plain,
% 1.73/1.93 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11048, 112, 11042, 11027])).
% 1.73/1.93 tff(11050,plain,
% 1.73/1.93 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 11049])).
% 1.73/1.93 tff(11051,plain,
% 1.73/1.93 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4743, 112, 11042])).
% 1.73/1.93 tff(11052,plain,
% 1.73/1.93 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11051, 11028])).
% 1.73/1.93 tff(11053,plain,
% 1.73/1.93 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1869, 11052, 1683])).
% 1.73/1.93 tff(11054,plain,
% 1.73/1.93 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4596, 11000, 4569, 1391, 1181, 335])).
% 1.73/1.93 tff(11055,plain,
% 1.73/1.93 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1294, 11054, 1733])).
% 1.73/1.93 tff(11056,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11057,plain,
% 1.73/1.93 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11058,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11057])).
% 1.73/1.93 tff(11059,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[11058, 11056])).
% 1.73/1.93 tff(11060,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11061,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11060, 11059])).
% 1.73/1.93 tff(11062,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11061, 224, 11055, 11053, 11018, 11050, 11036])).
% 1.73/1.93 tff(11063,plain,((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(11064,plain,
% 1.73/1.93 (~r(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11063, 10992, 335, 4718, 787, 10993, 1181, 9147])).
% 1.73/1.93 tff(11065,plain,
% 1.73/1.93 (b(s(elem!1), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[939, 11064, 324])).
% 1.73/1.93 tff(11066,plain,
% 1.73/1.93 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[787, 10978])).
% 1.73/1.93 tff(11067,plain,
% 1.73/1.93 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[7989, 11065, 4538, 10990, 1181, 10992])).
% 1.73/1.93 tff(11068,plain,
% 1.73/1.93 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1521, 11067, 523])).
% 1.73/1.93 tff(11069,plain,
% 1.73/1.93 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.73/1.93 inference(commutativity,[status(thm)],[])).
% 1.73/1.93 tff(11070,plain,
% 1.73/1.93 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[11069])).
% 1.73/1.93 tff(11071,plain,
% 1.73/1.93 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11070])).
% 1.73/1.93 tff(11072,plain,
% 1.73/1.93 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[1854, 11071])).
% 1.73/1.93 tff(11073,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.73/1.93 tff(11074,plain,
% 1.73/1.93 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11024, 224, 7305, 11073, 7170])).
% 1.73/1.93 tff(11075,plain,
% 1.73/1.93 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 11074])).
% 1.73/1.93 tff(11076,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11077,plain,
% 1.73/1.93 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11078,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11077])).
% 1.73/1.93 tff(11079,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[11078, 11076])).
% 1.73/1.93 tff(11080,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11081,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11080, 11079])).
% 1.73/1.93 tff(11082,plain,
% 1.73/1.93 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11081, 112, 11075])).
% 1.73/1.93 tff(11083,plain,
% 1.73/1.93 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11082, 11028])).
% 1.73/1.93 tff(11084,plain,
% 1.73/1.93 (((~![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)))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11085,plain,
% 1.73/1.93 ((~![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)))))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11086,plain,
% 1.73/1.93 ((~![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))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11085, 11084])).
% 1.73/1.93 tff(11087,plain,
% 1.73/1.93 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11086, 68, 11083])).
% 1.73/1.93 tff(11088,plain,
% 1.73/1.93 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11087, 11072])).
% 1.73/1.93 tff(11089,assumption,(b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.73/1.93 tff(11090,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.73/1.93 tff(11091,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11092,plain,
% 1.73/1.93 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11093,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11092])).
% 1.73/1.93 tff(11094,plain,
% 1.73/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[11093, 11091])).
% 1.73/1.93 tff(11095,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(11096,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[11095, 11094])).
% 1.73/1.93 tff(11097,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11096, 224, 1488, 7305, 11090, 11089])).
% 1.73/1.93 tff(11098,plain,((~b(elem!1, s(s(s(s(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), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(11099,plain,
% 1.73/1.93 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11098, 7305, 1488, 11088])).
% 1.73/1.93 tff(11100,plain,
% 1.73/1.93 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2014, 68, 11099])).
% 1.73/1.93 tff(11101,plain,
% 1.73/1.93 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[11100, 1616])).
% 1.73/1.93 tff(11102,plain,
% 1.73/1.93 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.73/1.93 inference(commutativity,[status(thm)],[])).
% 1.73/1.93 tff(11103,plain,
% 1.73/1.93 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[11102])).
% 1.73/1.93 tff(11104,plain,
% 1.73/1.93 ((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[11103])).
% 1.73/1.93 tff(11105,plain,
% 1.73/1.93 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[1717, 11104])).
% 1.73/1.93 tff(11106,plain,
% 1.73/1.93 (((~![X0: $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(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(11107,plain,
% 1.73/1.93 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11108,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11107])).
% 1.73/1.94 tff(11109,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(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), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11108, 11106])).
% 1.73/1.94 tff(11110,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(11111,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11110, 11109])).
% 1.73/1.94 tff(11112,plain,
% 1.73/1.94 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11111, 112, 1700, 11075])).
% 1.73/1.94 tff(11113,plain,
% 1.73/1.94 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11112, 11028])).
% 1.73/1.94 tff(11114,plain,
% 1.73/1.94 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1857, 68, 1854, 11113])).
% 1.73/1.94 tff(11115,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11116,plain,
% 1.73/1.94 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(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(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11117,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11116])).
% 1.73/1.94 tff(11118,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11117, 11115])).
% 1.73/1.94 tff(11119,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(11120,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11119, 11118])).
% 1.73/1.94 tff(11121,plain,
% 1.73/1.94 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11120, 224, 1391, 11114, 11088])).
% 1.73/1.94 tff(11122,plain,
% 1.73/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), 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(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11123,plain,
% 1.73/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(11124,plain,
% 1.73/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11123, 11122])).
% 1.73/1.94 tff(11125,plain,
% 1.73/1.94 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11124, 68, 11121])).
% 1.73/1.94 tff(11126,plain,
% 1.73/1.94 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11125, 11105])).
% 1.73/1.94 tff(11127,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11128,plain,
% 1.73/1.94 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11129,plain,
% 1.73/1.94 (((~![X0: $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(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11128])).
% 1.73/1.94 tff(11130,plain,
% 1.73/1.94 (((~![X0: $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(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11129, 11127])).
% 1.73/1.94 tff(11131,plain,
% 1.73/1.94 ((~![X0: $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(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(11132,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11131, 11130])).
% 1.73/1.94 tff(11133,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11132, 112, 1181, 11126, 11101])).
% 1.73/1.94 tff(11134,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(11135,plain,
% 1.73/1.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11134, 11068, 11066, 10977, 10992, 4718, 335, 11065, 1181])).
% 1.73/1.94 tff(11136,plain,
% 1.73/1.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1777, 11135, 1615])).
% 1.73/1.94 tff(11137,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7489, 112, 1798, 1740])).
% 1.73/1.94 tff(11138,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2047, 68, 2044, 11137])).
% 1.73/1.94 tff(11139,plain,
% 1.73/1.94 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 1759])).
% 1.73/1.94 tff(11140,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11141,plain,
% 1.73/1.94 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(11142,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11141])).
% 1.73/1.94 tff(11143,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11142, 11140])).
% 1.73/1.94 tff(11144,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(11145,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11144, 11143])).
% 1.73/1.94 tff(11146,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11145, 224, 1391, 4594, 4568, 11139, 11138])).
% 1.73/1.94 tff(11147,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(11148,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11147, 11136, 335, 9147, 1181, 10992])).
% 1.73/1.94 tff(11149,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1294, 11148, 1733])).
% 1.73/1.94 tff(11150,plain,
% 1.73/1.94 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1617, 1619])).
% 1.73/1.94 tff(11151,plain,
% 1.73/1.94 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[5187, 11150])).
% 1.73/1.94 tff(11152,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1515, 11151])).
% 1.73/1.94 tff(11153,plain,((~b(s(z), s(s(z)))) | b(s(elem!1), s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(11154,plain,
% 1.73/1.94 (~b(s(z), s(s(z)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11153, 11067, 335])).
% 1.73/1.94 tff(11155,plain,
% 1.73/1.94 (r(s(z), s(s(z)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1071, 11154])).
% 1.73/1.94 tff(11156,plain,
% 1.73/1.94 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6296, 11155, 178])).
% 1.73/1.94 tff(11157,plain,
% 1.73/1.94 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[249, 11156])).
% 1.73/1.94 tff(11158,plain,
% 1.73/1.94 (~b(s(s(z)), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2412, 11157, 787, 10993])).
% 1.73/1.94 tff(11159,plain,
% 1.73/1.94 (r(elem!1, s(z))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[9147, 4562])).
% 1.73/1.94 tff(11160,plain,
% 1.73/1.94 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[335])).
% 1.73/1.94 tff(11161,plain,
% 1.73/1.94 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11160, 75])).
% 1.73/1.94 tff(11162,plain,
% 1.73/1.94 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.73/1.94 inference(transitivity,[status(thm)],[11161, 76])).
% 1.73/1.94 tff(11163,plain,
% 1.73/1.94 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11162])).
% 1.73/1.94 tff(11164,plain,
% 1.73/1.94 (~(s(s(elem!1)) = elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[566, 11163])).
% 1.73/1.94 tff(11165,plain,
% 1.73/1.94 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1619])).
% 1.73/1.94 tff(11166,plain,
% 1.73/1.94 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11165])).
% 1.73/1.94 tff(11167,plain,
% 1.73/1.94 (~b(s(s(elem!1)), elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[5829, 11166])).
% 1.73/1.94 tff(11168,plain,
% 1.73/1.94 (r(s(s(elem!1)), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[360, 11167, 11164])).
% 1.73/1.94 tff(11169,plain,
% 1.73/1.94 (~r(z, s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4621, 3188, 9147])).
% 1.73/1.94 tff(11170,plain,
% 1.73/1.94 (b(z, s(s(s(z))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[100, 11169])).
% 1.73/1.94 tff(11171,plain,
% 1.73/1.94 (b(elem!1, s(s(s(z))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11170, 4613])).
% 1.73/1.94 tff(11172,plain,
% 1.73/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11171, 4559])).
% 1.73/1.94 tff(11173,plain,
% 1.73/1.94 (~r(s(s(s(z))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4608, 3188, 9147])).
% 1.73/1.94 tff(11174,plain,
% 1.73/1.94 (b(s(s(s(z))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[72, 11173])).
% 1.73/1.94 tff(11175,plain,
% 1.73/1.94 (b(s(s(s(z))), elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11174, 4600])).
% 1.73/1.94 tff(11176,plain,
% 1.73/1.94 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11175, 4544])).
% 1.73/1.94 tff(11177,plain,
% 1.73/1.94 (r(elem!1, s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11159, 4564])).
% 1.73/1.94 tff(11178,plain,
% 1.73/1.94 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1633])).
% 1.73/1.94 tff(11179,plain,
% 1.73/1.94 ((~b(z, s(z))) <=> (~b(elem!1, s(z)))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[1634])).
% 1.73/1.94 tff(11180,plain,
% 1.73/1.94 (~b(elem!1, s(z))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[9138, 11179])).
% 1.73/1.94 tff(11181,plain,
% 1.73/1.94 (~b(elem!1, s(elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[11180, 11178])).
% 1.73/1.94 tff(11182,plain,
% 1.73/1.94 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11161])).
% 1.73/1.94 tff(11183,plain,
% 1.73/1.94 (~(elem!1 = s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[566, 11182])).
% 1.73/1.94 tff(11184,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[541, 11167, 11183, 11181])).
% 1.73/1.94 tff(11185,plain,
% 1.73/1.94 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.73/1.94 inference(monotonicity,[status(thm)],[335])).
% 1.73/1.94 tff(11186,plain,
% 1.73/1.94 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.73/1.94 inference(transitivity,[status(thm)],[11185, 320])).
% 1.73/1.94 tff(11187,plain,
% 1.73/1.94 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.73/1.94 inference(transitivity,[status(thm)],[11186, 321])).
% 1.73/1.94 tff(11188,plain,
% 1.73/1.94 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[11187])).
% 1.73/1.94 tff(11189,plain,
% 1.73/1.94 (~(s(elem!1) = elem!1)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[494, 11188])).
% 1.73/1.94 tff(11190,plain,
% 1.73/1.94 (~r(s(elem!1), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11063, 4718, 335, 11171, 11175, 11184, 11168, 9147])).
% 1.73/1.94 tff(11191,plain,
% 1.73/1.94 (b(s(elem!1), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[939, 11190, 11189])).
% 1.73/1.94 tff(11192,plain,
% 1.73/1.94 (~b(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[7989, 11191, 11184, 11168, 11177, 4538])).
% 1.73/1.94 tff(11193,plain,
% 1.73/1.94 (r(s(elem!1), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1521, 11192, 10999])).
% 1.73/1.94 tff(11194,plain,
% 1.73/1.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11134, 11168, 11191, 11184, 11193, 4718, 335, 11176, 11172])).
% 1.73/1.94 tff(11195,plain,
% 1.73/1.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1777, 11194, 1615])).
% 1.73/1.94 tff(11196,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[11147, 11184, 9147, 11195, 11168, 335])).
% 1.73/1.94 tff(11197,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1294, 11196, 1733])).
% 1.73/1.94 tff(11198,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4634, 11197, 9147, 3188, 335])).
% 1.73/1.94 tff(11199,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11198, 3933])).
% 1.73/1.95 tff(11200,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1884, 11199])).
% 1.73/1.95 tff(11201,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4829, 11200, 3188, 335])).
% 1.73/1.95 tff(11202,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1345, 11201, 1832])).
% 1.73/1.95 tff(11203,plain,
% 1.73/1.95 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4746, 11202, 178, 335, 11191, 11197, 11159])).
% 1.73/1.95 tff(11204,plain,
% 1.73/1.95 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1869, 11203, 1683])).
% 1.73/1.95 tff(11205,plain,
% 1.73/1.95 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[1694, 7373])).
% 1.73/1.95 tff(11206,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11207,plain,
% 1.73/1.95 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11208,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[11207])).
% 1.73/1.95 tff(11209,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11208, 11206])).
% 1.73/1.95 tff(11210,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(11211,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11210, 11209])).
% 1.73/1.95 tff(11212,plain,
% 1.73/1.95 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11211, 224, 11184, 11202, 11204])).
% 1.73/1.95 tff(11213,plain,
% 1.73/1.95 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1422, 68, 11212])).
% 1.73/1.95 tff(11214,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11213, 11205])).
% 1.73/1.95 tff(11215,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[8075, 11168, 11214])).
% 1.73/1.95 tff(11216,plain,
% 1.73/1.95 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1439, 11215, 1782])).
% 1.73/1.95 tff(11217,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1864, 224, 11191, 11197, 11216, 11204])).
% 1.73/1.95 tff(11218,plain,((~(z = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | b(z, elem!1) | b(s(s(z)), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11219,plain,
% 1.73/1.95 (~r(s(s(s(z))), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11218, 11158, 335, 4538, 9138, 178])).
% 1.73/1.95 tff(11220,plain,
% 1.73/1.95 (b(s(s(s(z))), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[925, 11219])).
% 1.73/1.95 tff(11221,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11220, 1624])).
% 1.73/1.95 tff(11222,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11223,plain,
% 1.73/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11224,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[11223])).
% 1.73/1.95 tff(11225,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11224, 11222])).
% 1.73/1.95 tff(11226,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(11227,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11226, 11225])).
% 1.73/1.95 tff(11228,plain,
% 1.73/1.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11227, 224, 11065, 10992, 11221, 11066])).
% 1.73/1.95 tff(11229,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7968, 11228, 335, 10992, 10993, 11065, 1181, 11149])).
% 1.73/1.95 tff(11230,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4631, 224, 11149, 11066, 10977])).
% 1.73/1.95 tff(11231,plain,
% 1.73/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11232,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(11233,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11232, 11231])).
% 1.73/1.95 tff(11234,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11233, 68, 11230, 11229, 10988])).
% 1.73/1.95 tff(11235,plain,((~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | b(z, elem!1) | b(z, s(z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11236,plain,
% 1.73/1.95 (~r(s(s(elem!1)), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11235, 9138, 4538, 335, 178, 10979, 319, 303])).
% 1.73/1.95 tff(11237,plain,
% 1.73/1.95 (~r(s(s(elem!1)), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[333, 11236, 1668])).
% 1.73/1.95 tff(11238,plain,
% 1.73/1.95 (b(s(s(elem!1)), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[593, 11237])).
% 1.73/1.95 tff(11239,plain,
% 1.73/1.95 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[10929, 11238, 10976, 10683])).
% 1.73/1.95 tff(11240,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[147, 11239, 2])).
% 1.73/1.95 tff(11241,plain,
% 1.73/1.95 (r(s(s(z)), s(s(s(z))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11240, 10982])).
% 1.73/1.95 tff(11242,plain,
% 1.73/1.95 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.73/1.95 inference(symmetry,[status(thm)],[11150])).
% 1.73/1.95 tff(11243,plain,
% 1.73/1.95 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[1617])).
% 1.73/1.95 tff(11244,plain,
% 1.73/1.95 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11243, 11242])).
% 1.73/1.95 tff(11245,plain,
% 1.73/1.95 (~r(s(z), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[835, 11240, 178])).
% 1.73/1.95 tff(11246,plain,
% 1.73/1.95 (b(s(z), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[653, 11245])).
% 1.73/1.95 tff(11247,plain,
% 1.73/1.95 (b(s(z), s(s(z)))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11246, 11244])).
% 1.73/1.95 tff(11248,plain,
% 1.73/1.95 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[1619, 1617])).
% 1.73/1.95 tff(11249,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.73/1.95 inference(symmetry,[status(thm)],[11248])).
% 1.73/1.95 tff(11250,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[1617])).
% 1.73/1.95 tff(11251,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11250, 11249])).
% 1.73/1.95 tff(11252,plain,
% 1.73/1.95 (~r(s(s(elem!1)), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4039, 11240, 178])).
% 1.73/1.95 tff(11253,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[901, 11252])).
% 1.73/1.95 tff(11254,plain,
% 1.73/1.95 (b(s(s(z)), s(z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11253, 11251])).
% 1.73/1.95 tff(11255,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.95 tff(11256,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11233, 68, 11255, 10988])).
% 1.73/1.95 tff(11257,plain,
% 1.73/1.95 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[1687, 1620])).
% 1.73/1.95 tff(11258,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[11257])).
% 1.73/1.95 tff(11259,plain,
% 1.73/1.95 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[11258])).
% 1.73/1.95 tff(11260,plain,
% 1.73/1.95 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11255, 11259])).
% 1.73/1.95 tff(11261,plain,
% 1.73/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3252, 11260])).
% 1.73/1.95 tff(11262,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3259, 112, 196, 3318, 6075])).
% 1.73/1.95 tff(11263,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11264,plain,
% 1.73/1.95 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11263, 11261, 196])).
% 1.73/1.95 tff(11265,plain,
% 1.73/1.95 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6185, 11264])).
% 1.73/1.95 tff(11266,plain,
% 1.73/1.95 (~b(s(s(s(s(z)))), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[5196, 11265, 2844, 5187])).
% 1.73/1.95 tff(11267,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7550, 11266, 335])).
% 1.73/1.95 tff(11268,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1345, 11267, 1832])).
% 1.73/1.95 tff(11269,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4855, 112, 11268, 11256, 7353])).
% 1.73/1.95 tff(11270,plain,(b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11271,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11270, 11254, 335, 4719, 11247, 11241])).
% 1.73/1.95 tff(11272,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4700, 224, 11271, 10980, 10977])).
% 1.73/1.95 tff(11273,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1294, 11272, 1733])).
% 1.73/1.95 tff(11274,plain,
% 1.73/1.95 (r(s(s(s(s(z)))), z)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11273, 4574])).
% 1.73/1.95 tff(11275,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4592, 11274, 1668, 9147])).
% 1.73/1.95 tff(11276,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1345, 11275, 1832])).
% 1.73/1.95 tff(11277,plain,
% 1.73/1.95 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11246, 11243])).
% 1.73/1.95 tff(11278,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11253, 11250])).
% 1.73/1.95 tff(11279,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1397, 224, 11278, 11277, 11276])).
% 1.73/1.95 tff(11280,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1401, 68, 11279, 7240])).
% 1.73/1.95 tff(11281,plain,
% 1.73/1.95 (s(elem!1) = s(z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3984, 1668])).
% 1.73/1.95 tff(11282,plain,
% 1.73/1.95 (s(z) = s(elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3988, 11281])).
% 1.73/1.95 tff(11283,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11240, 4639])).
% 1.73/1.95 tff(11284,plain,
% 1.73/1.95 (b(s(s(elem!1)), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[360, 11236, 353])).
% 1.73/1.95 tff(11285,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11286,plain,
% 1.73/1.95 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11287,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[11286])).
% 1.73/1.95 tff(11288,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11287, 11285])).
% 1.73/1.95 tff(11289,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(11290,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11289, 11288])).
% 1.73/1.95 tff(11291,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11290, 112, 408, 11268, 11256, 7353])).
% 1.73/1.95 tff(11292,plain,(b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11293,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11292, 10081, 7353, 335, 2844, 5187, 196])).
% 1.73/1.95 tff(11294,plain,
% 1.73/1.95 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4700, 224, 11293, 11073, 7170])).
% 1.73/1.95 tff(11295,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1294, 11294, 1733])).
% 1.73/1.95 tff(11296,plain,
% 1.73/1.95 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[10270, 11295, 10081])).
% 1.73/1.95 tff(11297,plain,
% 1.73/1.95 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1869, 11296, 1683])).
% 1.73/1.95 tff(11298,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1317, 11294, 1733, 1287])).
% 1.73/1.95 tff(11299,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1345, 11298, 1832])).
% 1.73/1.95 tff(11300,plain,
% 1.73/1.95 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[7497, 112, 1798, 1740])).
% 1.73/1.95 tff(11301,plain,
% 1.73/1.95 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1838, 68, 2041, 11300])).
% 1.73/1.95 tff(11302,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11303,plain,
% 1.73/1.95 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(11304,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[11303])).
% 1.73/1.95 tff(11305,plain,
% 1.73/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[11304, 11302])).
% 1.73/1.95 tff(11306,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(11307,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[11306, 11305])).
% 1.73/1.95 tff(11308,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11307, 224, 1409, 10224, 11008, 11301])).
% 1.73/1.95 tff(11309,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(11310,plain,
% 1.73/1.95 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11309, 11299, 11297, 1835, 1854, 11295, 10081])).
% 1.73/1.95 tff(11311,plain,
% 1.73/1.95 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1777, 11310, 1615])).
% 1.73/1.95 tff(11312,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.95 tff(11313,plain,
% 1.73/1.95 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11211, 224, 1391, 11299, 11297])).
% 1.73/1.95 tff(11314,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1422, 68, 7374, 11313])).
% 1.73/1.95 tff(11315,plain,
% 1.73/1.95 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[1620])).
% 1.73/1.96 tff(11316,plain,
% 1.73/1.96 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[1619])).
% 1.73/1.96 tff(11317,plain,
% 1.73/1.96 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(symmetry,[status(thm)],[11316])).
% 1.73/1.96 tff(11318,plain,
% 1.73/1.96 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11314, 11317])).
% 1.73/1.96 tff(11319,plain,
% 1.73/1.96 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5413, 11318, 196])).
% 1.73/1.96 tff(11320,plain,
% 1.73/1.96 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5426, 11319])).
% 1.73/1.96 tff(11321,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11320, 11315])).
% 1.73/1.96 tff(11322,plain,
% 1.73/1.96 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[7418, 224, 11293, 7170, 11321])).
% 1.73/1.96 tff(11323,plain,
% 1.73/1.96 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1439, 11322, 1782])).
% 1.73/1.96 tff(11324,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11325,plain,
% 1.73/1.96 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11326,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11325])).
% 1.73/1.96 tff(11327,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11326, 11324])).
% 1.73/1.96 tff(11328,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11329,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11328, 11327])).
% 1.73/1.96 tff(11330,plain,
% 1.73/1.96 (~r(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11329, 112, 11323, 11314, 11312])).
% 1.73/1.96 tff(11331,plain,
% 1.73/1.96 (b(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[558, 11330, 3])).
% 1.73/1.96 tff(11332,plain,
% 1.73/1.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[7462, 224, 11331, 390, 11311])).
% 1.73/1.96 tff(11333,plain,
% 1.73/1.96 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 11332])).
% 1.73/1.96 tff(11334,plain,
% 1.73/1.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11024, 224, 11311, 11073, 7170])).
% 1.73/1.96 tff(11335,plain,
% 1.73/1.96 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 11334])).
% 1.73/1.96 tff(11336,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11337,plain,
% 1.73/1.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11338,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11337])).
% 1.73/1.96 tff(11339,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11338, 11336])).
% 1.73/1.96 tff(11340,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11341,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11340, 11339])).
% 1.73/1.96 tff(11342,plain,
% 1.73/1.96 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11341, 224, 11331, 390, 11073])).
% 1.73/1.96 tff(11343,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3905, 11342, 7255])).
% 1.73/1.96 tff(11344,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11345,plain,
% 1.73/1.96 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11346,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11345])).
% 1.73/1.96 tff(11347,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11346, 11344])).
% 1.73/1.96 tff(11348,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11349,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11348, 11347])).
% 1.73/1.96 tff(11350,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11349, 112, 11343, 11335, 11333])).
% 1.73/1.96 tff(11351,plain,(b(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(11352,plain,
% 1.73/1.96 (b(s(elem!1), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11351, 10977, 10980, 11284, 3, 11283, 335, 11241, 11278, 4719, 11254, 11247])).
% 1.73/1.96 tff(11353,plain,
% 1.73/1.96 (b(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4001, 11352, 11282])).
% 1.73/1.96 tff(11354,plain,
% 1.73/1.96 (~b(z, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4051, 11353, 11238, 11246])).
% 1.73/1.96 tff(11355,plain,
% 1.73/1.96 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.73/1.96 inference(symmetry,[status(thm)],[4706])).
% 1.73/1.96 tff(11356,plain,
% 1.73/1.96 (b(z, s(s(elem!1)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[682, 11355])).
% 1.73/1.96 tff(11357,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[750, 11356])).
% 1.73/1.96 tff(11358,plain,((~b(elem!1, s(s(elem!1)))) | b(z, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(11359,plain,
% 1.73/1.96 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11358, 11354, 335])).
% 1.73/1.96 tff(11360,plain,
% 1.73/1.96 (r(elem!1, s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[558, 11359, 3])).
% 1.73/1.96 tff(11361,plain,
% 1.73/1.96 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11362,plain,
% 1.73/1.96 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11363,plain,
% 1.73/1.96 (((~![X0: $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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11362])).
% 1.73/1.96 tff(11364,plain,
% 1.73/1.96 (((~![X0: $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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11363, 11361])).
% 1.73/1.96 tff(11365,plain,
% 1.73/1.96 ((~![X0: $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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11366,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11365, 11364])).
% 1.73/1.96 tff(11367,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11366, 112, 10990, 11360, 11273, 11280])).
% 1.73/1.96 tff(11368,plain,(b(z, s(z)) | (~(z = elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(11369,plain,
% 1.73/1.96 (b(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11368, 10966, 3, 176, 2, 4538])).
% 1.73/1.96 tff(11370,plain,
% 1.73/1.96 (b(elem!1, s(elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11369, 10973])).
% 1.73/1.96 tff(11371,plain,
% 1.73/1.96 (~b(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[7095, 354, 335])).
% 1.73/1.96 tff(11372,plain,
% 1.73/1.96 (r(s(s(elem!1)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[593, 11371])).
% 1.73/1.96 tff(11373,plain,
% 1.73/1.96 (b(s(elem!1), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[10650, 1928])).
% 1.73/1.96 tff(11374,plain,
% 1.73/1.96 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[835, 656, 178])).
% 1.73/1.96 tff(11375,plain,
% 1.73/1.96 (b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[147, 11374, 2])).
% 1.73/1.96 tff(11376,plain,
% 1.73/1.96 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11375, 7328])).
% 1.73/1.96 tff(11377,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11378,plain,
% 1.73/1.96 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11379,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11378])).
% 1.73/1.96 tff(11380,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11379, 11377])).
% 1.73/1.96 tff(11381,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11382,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11381, 11380])).
% 1.73/1.96 tff(11383,plain,
% 1.73/1.96 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[11382, 224, 501, 1488, 11073])).
% 1.73/1.96 tff(11384,plain,
% 1.73/1.96 (~b(s(s(s(z))), s(z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11383, 1626])).
% 1.73/1.96 tff(11385,plain,
% 1.73/1.96 (r(s(s(s(z))), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[925, 11384])).
% 1.73/1.96 tff(11386,plain,
% 1.73/1.96 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1345, 7314, 1832])).
% 1.73/1.96 tff(11387,plain,
% 1.73/1.96 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4829, 11386, 335, 11385])).
% 1.73/1.96 tff(11388,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1884, 11387])).
% 1.73/1.96 tff(11389,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11388, 1699])).
% 1.73/1.96 tff(11390,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11391,plain,
% 1.73/1.96 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(11392,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[11391])).
% 1.73/1.96 tff(11393,plain,
% 1.73/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[11392, 11390])).
% 1.73/1.96 tff(11394,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(11395,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[11394, 11393])).
% 1.73/1.97 tff(11396,plain,
% 1.73/1.97 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11395, 224, 3919, 11073, 1737])).
% 1.73/1.97 tff(11397,plain,
% 1.73/1.97 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11396, 11389])).
% 1.73/1.97 tff(11398,plain,
% 1.73/1.97 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1401, 68, 11397, 2287])).
% 1.73/1.97 tff(11399,plain,
% 1.73/1.97 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11398, 7254])).
% 1.73/1.97 tff(11400,plain,
% 1.73/1.97 (r(s(s(s(s(z)))), s(z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11386, 7275])).
% 1.73/1.97 tff(11401,plain,
% 1.73/1.97 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[7280, 11400, 656])).
% 1.73/1.97 tff(11402,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11401, 11399])).
% 1.73/1.97 tff(11403,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(11404,plain,
% 1.73/1.97 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11403, 11376, 7240, 10980, 335, 656, 501, 11373])).
% 1.73/1.97 tff(11405,plain,
% 1.73/1.97 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1294, 11404, 1733])).
% 1.73/1.97 tff(11406,plain,
% 1.73/1.97 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[1620, 1617])).
% 1.73/1.97 tff(11407,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11382, 224, 501, 11373, 10980])).
% 1.73/1.97 tff(11408,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11407, 1626])).
% 1.73/1.97 tff(11409,plain,
% 1.73/1.97 (r(s(s(s(z))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[925, 11408])).
% 1.73/1.97 tff(11410,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11409, 11406])).
% 1.73/1.97 tff(11411,plain,
% 1.73/1.97 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5903, 112, 11405, 1181])).
% 1.73/1.97 tff(11412,plain,
% 1.73/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1422, 68, 11411, 7374])).
% 1.73/1.97 tff(11413,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[3188, 11406])).
% 1.73/1.97 tff(11414,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11415,plain,
% 1.73/1.97 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11416,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11415])).
% 1.73/1.97 tff(11417,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[11416, 11414])).
% 1.73/1.97 tff(11418,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(11419,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11418, 11417])).
% 1.73/1.97 tff(11420,plain,
% 1.73/1.97 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11419, 112, 1289, 11413])).
% 1.73/1.97 tff(11421,plain,
% 1.73/1.97 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11420, 7381])).
% 1.73/1.97 tff(11422,plain,
% 1.73/1.97 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5426, 11421])).
% 1.73/1.97 tff(11423,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11422, 11315])).
% 1.73/1.97 tff(11424,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.97 tff(11425,plain,
% 1.73/1.97 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4829, 1289, 335, 3188])).
% 1.73/1.97 tff(11426,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1884, 11425])).
% 1.73/1.97 tff(11427,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11426, 1699])).
% 1.73/1.97 tff(11428,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[7409, 224, 11427, 1737, 11424, 11423])).
% 1.73/1.97 tff(11429,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(11430,plain,
% 1.73/1.97 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11429, 11376, 11412, 335, 11409])).
% 1.73/1.97 tff(11431,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1345, 11430, 1832])).
% 1.73/1.97 tff(11432,plain,
% 1.73/1.97 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[9107, 11409, 656])).
% 1.73/1.97 tff(11433,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[1621])).
% 1.73/1.97 tff(11434,plain,
% 1.73/1.97 (r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[3888, 11433])).
% 1.73/1.97 tff(11435,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.73/1.97 tff(11436,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11435, 11434])).
% 1.73/1.97 tff(11437,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(z))), s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(11438,plain,
% 1.73/1.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11437, 11432, 335])).
% 1.73/1.97 tff(11439,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3905, 11438, 7255])).
% 1.73/1.97 tff(11440,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4920, 11404, 1733, 1181])).
% 1.73/1.97 tff(11441,plain,
% 1.73/1.97 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11442,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11441])).
% 1.73/1.97 tff(11443,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[11442, 1887])).
% 1.73/1.97 tff(11444,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(11445,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11444, 11443])).
% 1.73/1.97 tff(11446,plain,
% 1.73/1.97 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11445, 224, 11440, 11439, 11376])).
% 1.73/1.97 tff(11447,plain,
% 1.73/1.97 (~r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2029, 11439, 1181, 11376, 335, 11405])).
% 1.73/1.97 tff(11448,plain,
% 1.73/1.97 (b(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[388, 11447, 4561])).
% 1.73/1.97 tff(11449,plain,
% 1.73/1.97 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11448, 4559])).
% 1.73/1.97 tff(11450,plain,
% 1.73/1.97 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[7135, 224, 11439, 11449, 11376])).
% 1.73/1.97 tff(11451,plain,
% 1.73/1.97 (r(elem!1, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[558, 11450, 3])).
% 1.73/1.97 tff(11452,plain,
% 1.73/1.97 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[1611, 1609])).
% 1.73/1.97 tff(11453,plain,
% 1.73/1.97 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11452])).
% 1.73/1.97 tff(11454,plain,
% 1.73/1.97 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[1614, 11453])).
% 1.73/1.97 tff(11455,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.73/1.97 tff(11456,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.73/1.97 tff(11457,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1857, 68, 7466, 11455, 11456])).
% 1.73/1.97 tff(11458,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,[]))).
% 1.73/1.97 tff(11459,plain,
% 1.73/1.97 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11458, 11455, 7466])).
% 1.73/1.97 tff(11460,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.97 tff(11461,plain,
% 1.73/1.97 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11233, 68, 11255, 11460])).
% 1.73/1.97 tff(11462,plain,
% 1.73/1.97 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4743, 112, 11461, 7353])).
% 1.73/1.97 tff(11463,plain,
% 1.73/1.97 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1869, 11462, 1829])).
% 1.73/1.97 tff(11464,plain,
% 1.73/1.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11307, 224, 1409, 11463, 11459])).
% 1.73/1.97 tff(11465,plain,
% 1.73/1.97 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1838, 68, 2041, 11464])).
% 1.73/1.97 tff(11466,plain,
% 1.73/1.97 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(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(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11467,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(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(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11466])).
% 1.73/1.97 tff(11468,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(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(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[11467, 1840])).
% 1.73/1.97 tff(11469,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(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(elem!1))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(11470,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11469, 11468])).
% 1.73/1.97 tff(11471,plain,
% 1.73/1.97 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11470, 224, 501, 1488, 11459])).
% 1.73/1.97 tff(11472,plain,
% 1.73/1.97 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1777, 11471, 7140])).
% 1.73/1.97 tff(11473,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[7497, 112, 1798, 11472, 11465])).
% 1.73/1.97 tff(11474,plain,(r(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(11475,plain,
% 1.73/1.97 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11474, 11255, 1835, 1615, 1409, 501, 1488, 1854, 1683, 7353, 1798, 10988])).
% 1.73/1.97 tff(11476,plain,
% 1.73/1.97 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11255, 3933])).
% 1.73/1.97 tff(11477,plain,
% 1.73/1.97 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1884, 11476])).
% 1.73/1.97 tff(11478,plain,
% 1.73/1.97 (~r(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1806, 11477, 1798])).
% 1.73/1.97 tff(11479,plain,
% 1.73/1.97 (b(elem!1, s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[388, 11478, 4561])).
% 1.73/1.97 tff(11480,plain,
% 1.73/1.97 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11479, 4559])).
% 1.73/1.97 tff(11481,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[7179, 11480, 7144, 545, 1717, 11475, 1737, 1736, 11454])).
% 1.73/1.97 tff(11482,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3905, 11481, 7255])).
% 1.73/1.97 tff(11483,plain,
% 1.73/1.97 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4743, 112, 11256, 7353])).
% 1.73/1.97 tff(11484,plain,
% 1.73/1.97 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1869, 11483, 1683])).
% 1.73/1.97 tff(11485,plain,
% 1.73/1.97 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11486,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11485])).
% 1.73/1.97 tff(11487,plain,
% 1.73/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[11486, 11206])).
% 1.73/1.97 tff(11488,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(11489,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11488, 11487])).
% 1.73/1.97 tff(11490,plain,
% 1.73/1.97 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11489, 224, 1409, 11484, 11424])).
% 1.73/1.97 tff(11491,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(elem!1))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[530, 11490, 2505])).
% 1.73/1.97 tff(11492,plain,
% 1.73/1.97 (((~![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(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11493,plain,
% 1.73/1.97 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(11494,plain,
% 1.73/1.97 (((~![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(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[11493])).
% 1.73/1.97 tff(11495,plain,
% 1.73/1.97 (((~![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(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[11494, 11492])).
% 1.73/1.97 tff(11496,plain,
% 1.73/1.97 ((~![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(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(11497,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[11496, 11495])).
% 1.73/1.97 tff(11498,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[11497, 112, 11491, 11482, 7144])).
% 1.73/1.97 tff(11499,plain,(b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11500,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11499, 11451, 11446, 526, 11431, 11412, 11410, 11376, 4719, 335, 11405, 501, 11373])).
% 1.73/1.98 tff(11501,plain,((~r(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11502,plain,
% 1.73/1.98 (~r(s(z), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11501, 3340, 501, 3, 335, 2, 11372, 178])).
% 1.73/1.98 tff(11503,plain,
% 1.73/1.98 (b(s(z), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[653, 11502])).
% 1.73/1.98 tff(11504,plain,
% 1.73/1.98 (b(s(elem!1), s(s(elem!1)))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11503, 11243])).
% 1.73/1.98 tff(11505,plain,
% 1.73/1.98 (~r(z, s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[9119, 1648, 178])).
% 1.73/1.98 tff(11506,plain,
% 1.73/1.98 (b(z, s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[100, 11505])).
% 1.73/1.98 tff(11507,plain,
% 1.73/1.98 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11506, 10974])).
% 1.73/1.98 tff(11508,plain,
% 1.73/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[530, 4113, 2505])).
% 1.73/1.98 tff(11509,plain,
% 1.73/1.98 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11016, 11508, 1717, 1854, 1181, 1390, 408])).
% 1.73/1.98 tff(11510,plain,
% 1.73/1.98 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1777, 11509, 1615])).
% 1.73/1.98 tff(11511,plain,
% 1.73/1.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11024, 224, 11510, 11073, 11507])).
% 1.73/1.98 tff(11512,plain,
% 1.73/1.98 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 11511])).
% 1.73/1.98 tff(11513,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5914, 1644, 1181, 1733])).
% 1.73/1.98 tff(11514,plain,
% 1.73/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4631, 224, 11513, 11073, 11507])).
% 1.73/1.98 tff(11515,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11233, 68, 11514, 10988])).
% 1.73/1.98 tff(11516,plain,
% 1.73/1.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11048, 112, 11515, 11512])).
% 1.73/1.98 tff(11517,plain,
% 1.73/1.98 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 11516])).
% 1.73/1.98 tff(11518,plain,
% 1.73/1.98 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11034, 112, 408, 4719, 11512])).
% 1.73/1.98 tff(11519,plain,
% 1.73/1.98 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11458, 11518, 1854])).
% 1.73/1.98 tff(11520,plain,
% 1.73/1.98 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4743, 112, 11515, 4719])).
% 1.73/1.98 tff(11521,plain,
% 1.73/1.98 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1869, 11520, 1683])).
% 1.73/1.98 tff(11522,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11061, 224, 11513, 11521, 11510, 11519, 11517])).
% 1.73/1.98 tff(11523,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11524,plain,
% 1.73/1.98 (~r(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11523, 3340, 335, 10980, 11504, 526, 178])).
% 1.73/1.98 tff(11525,plain,
% 1.73/1.98 (b(s(elem!1), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[939, 11524, 303])).
% 1.73/1.98 tff(11526,plain,
% 1.73/1.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11382, 224, 501, 11525, 10980])).
% 1.73/1.98 tff(11527,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(z))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11526, 1626])).
% 1.73/1.98 tff(11528,plain,
% 1.73/1.98 (r(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[925, 11527])).
% 1.73/1.98 tff(11529,plain,
% 1.73/1.98 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4829, 1787, 335, 3188])).
% 1.73/1.98 tff(11530,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1345, 11529, 1832])).
% 1.73/1.98 tff(11531,plain,
% 1.73/1.98 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4382, 224, 501, 1488, 11530])).
% 1.73/1.98 tff(11532,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1294, 11531, 1733])).
% 1.73/1.98 tff(11533,plain,
% 1.73/1.98 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5903, 112, 11532, 1181])).
% 1.73/1.98 tff(11534,plain,
% 1.73/1.98 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1422, 68, 11533, 1386])).
% 1.73/1.98 tff(11535,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4920, 11531, 1733, 1181])).
% 1.73/1.98 tff(11536,plain,
% 1.73/1.98 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4743, 112, 1788, 7353])).
% 1.73/1.98 tff(11537,plain,
% 1.73/1.98 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1869, 11536, 1683])).
% 1.73/1.98 tff(11538,plain,
% 1.73/1.98 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11539,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11538])).
% 1.73/1.98 tff(11540,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[11539, 10425])).
% 1.73/1.98 tff(11541,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(11542,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11541, 11540])).
% 1.73/1.98 tff(11543,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11542, 224, 1390, 11537, 11535, 11534])).
% 1.73/1.98 tff(11544,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11545,plain,
% 1.73/1.98 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11544, 11504, 7374, 3340, 4719, 501, 11525, 335, 11528])).
% 1.73/1.98 tff(11546,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1884, 11545])).
% 1.73/1.98 tff(11547,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[4753, 1699])).
% 1.73/1.98 tff(11548,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11255, 11547])).
% 1.73/1.98 tff(11549,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11550,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11549, 11546, 335])).
% 1.73/1.98 tff(11551,plain,
% 1.73/1.98 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[7328])).
% 1.73/1.98 tff(11552,plain,
% 1.73/1.98 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11551])).
% 1.73/1.98 tff(11553,plain,
% 1.73/1.98 (b(s(s(s(z))), elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[7672, 4600])).
% 1.73/1.98 tff(11554,plain,
% 1.73/1.98 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11553, 10978])).
% 1.73/1.98 tff(11555,plain,
% 1.73/1.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11382, 224, 501, 1488, 11554])).
% 1.73/1.98 tff(11556,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(z))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11555, 1626])).
% 1.73/1.98 tff(11557,plain,
% 1.73/1.98 (r(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[925, 11556])).
% 1.73/1.98 tff(11558,plain,
% 1.73/1.98 (r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11557, 11406])).
% 1.73/1.98 tff(11559,plain,
% 1.73/1.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11419, 112, 1289, 11558])).
% 1.73/1.98 tff(11560,plain,
% 1.73/1.98 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11559, 7381])).
% 1.73/1.98 tff(11561,plain,
% 1.73/1.98 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5426, 11560])).
% 1.73/1.98 tff(11562,plain,
% 1.73/1.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11561, 11315])).
% 1.73/1.98 tff(11563,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.98 tff(11564,plain,
% 1.73/1.98 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[4613])).
% 1.73/1.98 tff(11565,plain,
% 1.73/1.98 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[4558, 11564])).
% 1.73/1.98 tff(11566,plain,
% 1.73/1.98 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(z)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11565])).
% 1.73/1.98 tff(11567,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4631, 224, 3919, 4599, 11073, 7170])).
% 1.73/1.98 tff(11568,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11569,plain,
% 1.73/1.98 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11568, 3919, 4599, 11554])).
% 1.73/1.98 tff(11570,plain,
% 1.73/1.98 (~b(z, s(s(s(z))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11569, 11566])).
% 1.73/1.98 tff(11571,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[147, 9145, 6484])).
% 1.73/1.98 tff(11572,plain,
% 1.73/1.98 (((~![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)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11573,plain,
% 1.73/1.98 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11574,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11573])).
% 1.73/1.98 tff(11575,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[11574, 11572])).
% 1.73/1.98 tff(11576,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(11577,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11576, 11575])).
% 1.73/1.98 tff(11578,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11577, 112, 9146, 11571, 689])).
% 1.73/1.98 tff(11579,plain,(b(s(s(elem!1)), z) | (~r(z, s(s(s(z))))) | b(s(s(elem!1)), s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11580,plain,
% 1.73/1.98 (b(s(s(elem!1)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11579, 101, 6484, 7672])).
% 1.73/1.98 tff(11581,plain,
% 1.73/1.98 (r(s(s(elem!1)), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[147, 2, 6484])).
% 1.73/1.98 tff(11582,plain,
% 1.73/1.98 (~r(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3074, 11581, 101])).
% 1.73/1.98 tff(11583,plain,
% 1.73/1.98 (b(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[752, 11582])).
% 1.73/1.98 tff(11584,plain,
% 1.73/1.98 (~b(s(z), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4051, 11583, 11580, 2252])).
% 1.73/1.98 tff(11585,plain,
% 1.73/1.98 (r(s(z), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[194, 11584])).
% 1.73/1.98 tff(11586,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7654, 224, 11580, 11583, 7672])).
% 1.73/1.98 tff(11587,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[135, 68, 132, 11586])).
% 1.73/1.98 tff(11588,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.73/1.98 tff(11589,plain,
% 1.73/1.98 (s(s(z)) = s(s(s(z)))),
% 1.73/1.98 inference(symmetry,[status(thm)],[11588])).
% 1.73/1.98 tff(11590,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[55, 11589])).
% 1.73/1.98 tff(11591,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11592,plain,
% 1.73/1.98 (b(z, s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[752, 749])).
% 1.73/1.98 tff(11593,plain,
% 1.73/1.98 (~r(s(z), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[9119, 179, 689])).
% 1.73/1.98 tff(11594,plain,
% 1.73/1.98 (b(s(z), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[175, 11593])).
% 1.73/1.98 tff(11595,plain,
% 1.73/1.98 (~r(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4621, 4569, 689])).
% 1.73/1.98 tff(11596,plain,
% 1.73/1.98 (b(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[925, 11595])).
% 1.73/1.98 tff(11597,plain,
% 1.73/1.98 (~r(s(s(z)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3472, 11596, 689, 179, 11594])).
% 1.73/1.98 tff(11598,plain,
% 1.73/1.98 (b(s(s(z)), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[281, 11597])).
% 1.73/1.98 tff(11599,plain,
% 1.73/1.98 (~b(s(s(z)), s(s(elem!1)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5939, 11598, 11592, 1240])).
% 1.73/1.98 tff(11600,plain,
% 1.73/1.98 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[4580])).
% 1.73/1.98 tff(11601,plain,
% 1.73/1.98 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[11600])).
% 1.73/1.98 tff(11602,plain,
% 1.73/1.98 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7576])).
% 1.73/1.98 tff(11603,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/1.98 inference(monotonicity,[status(thm)],[1669])).
% 1.73/1.98 tff(11604,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.73/1.98 inference(symmetry,[status(thm)],[11603])).
% 1.73/1.98 tff(11605,plain,
% 1.73/1.98 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = z)),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7])).
% 1.73/1.98 tff(11606,plain,
% 1.73/1.98 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.73/1.98 inference(symmetry,[status(thm)],[11605])).
% 1.73/1.98 tff(11607,plain,
% 1.73/1.98 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11606])).
% 1.73/1.98 tff(11608,plain,
% 1.73/1.98 (~(s(s(s(s(z)))) = elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[2330, 11607])).
% 1.73/1.98 tff(11609,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7])).
% 1.73/1.98 tff(11610,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.73/1.98 inference(symmetry,[status(thm)],[11609])).
% 1.73/1.98 tff(11611,plain,
% 1.73/1.98 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11610])).
% 1.73/1.98 tff(11612,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[4580])).
% 1.73/1.98 tff(11613,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[11612])).
% 1.73/1.98 tff(11614,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[4579])).
% 1.73/1.98 tff(11615,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[11614])).
% 1.73/1.98 tff(11616,plain,
% 1.73/1.98 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11615])).
% 1.73/1.98 tff(11617,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[4579, 3982])).
% 1.73/1.98 tff(11618,plain,
% 1.73/1.98 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1831, 7557])).
% 1.73/1.98 tff(11619,plain,
% 1.73/1.98 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4592, 2276, 4569, 7])).
% 1.73/1.98 tff(11620,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1345, 11619, 11618])).
% 1.73/1.98 tff(11621,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), s(z))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11620, 11617])).
% 1.73/1.98 tff(11622,plain,
% 1.73/1.98 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1577, 224, 1090, 5754, 11621])).
% 1.73/1.98 tff(11623,plain,
% 1.73/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11622, 11616])).
% 1.73/1.98 tff(11624,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1884, 11623])).
% 1.73/1.98 tff(11625,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11624, 11613])).
% 1.73/1.98 tff(11626,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11627,plain,
% 1.73/1.98 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11628,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11627])).
% 1.73/1.98 tff(11629,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[11628, 11626])).
% 1.73/1.98 tff(11630,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(11631,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11630, 11629])).
% 1.73/1.98 tff(11632,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11631, 112, 4569, 689, 2276, 11625])).
% 1.73/1.98 tff(11633,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~(elem!1 = z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(11634,plain,
% 1.73/1.98 (~r(s(s(s(s(z)))), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11633, 7, 4569, 689, 1090])).
% 1.73/1.98 tff(11635,plain,
% 1.73/1.98 (~r(s(s(s(s(z)))), elem!1)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11634, 11611])).
% 1.73/1.98 tff(11636,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3183, 11635, 11608])).
% 1.73/1.98 tff(11637,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), z)),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[11636, 11604])).
% 1.73/1.98 tff(11638,plain,
% 1.73/1.98 (z = elem!1),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[10, 7])).
% 1.73/1.98 tff(11639,plain,
% 1.73/1.98 (~r(z, s(s(z)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7250, 11638, 749])).
% 1.73/1.98 tff(11640,plain,
% 1.73/1.98 (b(z, s(s(z)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1088, 11639])).
% 1.73/1.98 tff(11641,plain,
% 1.73/1.98 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[3298, 224, 11640, 1118])).
% 1.73/1.98 tff(11642,plain,
% 1.73/1.98 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[11641, 11637])).
% 1.73/1.98 tff(11643,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6185, 11642])).
% 1.73/1.98 tff(11644,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[4577])).
% 1.73/1.98 tff(11645,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(z)))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[6847, 11644])).
% 1.73/1.98 tff(11646,plain,
% 1.73/1.98 (((~![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))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11647,plain,
% 1.73/1.98 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(11648,plain,
% 1.73/1.98 (((~![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))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[11647])).
% 1.73/1.99 tff(11649,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11648, 11646])).
% 1.73/1.99 tff(11650,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11651,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11650, 11649])).
% 1.73/1.99 tff(11652,plain,
% 1.73/1.99 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11651, 112, 11645, 11643])).
% 1.73/1.99 tff(11653,plain,
% 1.73/1.99 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3252, 11652])).
% 1.73/1.99 tff(11654,plain,
% 1.73/1.99 (~b(s(s(s(s(z)))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1579, 11653, 1090, 11596])).
% 1.73/1.99 tff(11655,plain,
% 1.73/1.99 (r(s(s(s(s(z)))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3168, 11654])).
% 1.73/1.99 tff(11656,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11657,plain,
% 1.73/1.99 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11658,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11657])).
% 1.73/1.99 tff(11659,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11658, 11656])).
% 1.73/1.99 tff(11660,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11661,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11660, 11659])).
% 1.73/1.99 tff(11662,plain,
% 1.73/1.99 (~r(z, s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11661, 112, 4569, 11655])).
% 1.73/1.99 tff(11663,plain,
% 1.73/1.99 (~r(z, s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11662, 11602])).
% 1.73/1.99 tff(11664,plain,
% 1.73/1.99 (b(z, s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4412, 11663])).
% 1.73/1.99 tff(11665,plain,
% 1.73/1.99 (b(z, s(s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11664, 11601])).
% 1.73/1.99 tff(11666,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[4579])).
% 1.73/1.99 tff(11667,plain,
% 1.73/1.99 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[4580])).
% 1.73/1.99 tff(11668,plain,
% 1.73/1.99 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11667])).
% 1.73/1.99 tff(11669,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))), s(s(z)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11670,plain,
% 1.73/1.99 (((~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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11671,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11670])).
% 1.73/1.99 tff(11672,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11671, 11669])).
% 1.73/1.99 tff(11673,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11674,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11673, 11672])).
% 1.73/1.99 tff(11675,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11674, 112, 11645, 11643])).
% 1.73/1.99 tff(11676,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11675, 11668])).
% 1.73/1.99 tff(11677,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5426, 11676])).
% 1.73/1.99 tff(11678,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11677, 11666])).
% 1.73/1.99 tff(11679,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11680,plain,
% 1.73/1.99 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11681,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11680])).
% 1.73/1.99 tff(11682,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11681, 11679])).
% 1.73/1.99 tff(11683,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11684,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11683, 11682])).
% 1.73/1.99 tff(11685,plain,
% 1.73/1.99 (~b(z, s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11684, 224, 7672, 11678, 11637])).
% 1.73/1.99 tff(11686,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11685, 11665])).
% 1.73/1.99 tff(11687,plain,((~(elem!1 = z)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | r(z, s(s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(11688,plain,
% 1.73/1.99 (~(elem!1 = z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11687, 4569, 7672, 11594, 11598, 6847, 749, 689])).
% 1.73/1.99 tff(11689,plain,
% 1.73/1.99 (~(s(elem!1) = s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[159, 11688])).
% 1.73/1.99 tff(11690,plain,
% 1.73/1.99 (~(s(s(z)) = s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[168, 11689])).
% 1.73/1.99 tff(11691,plain,
% 1.73/1.99 (r(s(s(z)), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[265, 11690, 11599])).
% 1.73/1.99 tff(11692,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6051, 112, 11691, 6847])).
% 1.73/1.99 tff(11693,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3535, 68, 11692, 11591])).
% 1.73/1.99 tff(11694,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(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(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11695,plain,
% 1.73/1.99 (((~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(s(z))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11696,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z))))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11695])).
% 1.73/1.99 tff(11697,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11696, 11694])).
% 1.73/1.99 tff(11698,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11699,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11698, 11697])).
% 1.73/1.99 tff(11700,plain,
% 1.73/1.99 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11699, 112, 11691, 6847])).
% 1.73/1.99 tff(11701,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[249, 11700])).
% 1.73/1.99 tff(11702,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11703,plain,
% 1.73/1.99 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11704,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11703])).
% 1.73/1.99 tff(11705,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[11704, 11702])).
% 1.73/1.99 tff(11706,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(11707,plain,
% 1.73/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[11706, 11705])).
% 1.73/1.99 tff(11708,plain,
% 1.73/1.99 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11707, 224, 11594, 7672, 11598])).
% 1.73/1.99 tff(11709,plain,
% 1.73/1.99 (~b(s(s(z)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11708, 11701])).
% 1.73/1.99 tff(11710,plain,
% 1.73/1.99 (r(s(s(z)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2726, 11709])).
% 1.73/1.99 tff(11711,plain,
% 1.73/1.99 (~r(z, s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6072, 112, 4569, 11710])).
% 1.73/1.99 tff(11712,plain,
% 1.73/1.99 (b(z, s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1088, 11711])).
% 1.73/1.99 tff(11713,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[9633, 224, 7672, 11712, 11598, 11693])).
% 1.73/1.99 tff(11714,plain,((~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | r(z, s(s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(11715,plain,
% 1.73/1.99 (~r(z, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[11714, 11587, 7672, 11582, 101, 11580, 11585])).
% 1.73/1.99 tff(11716,plain,
% 1.73/1.99 (b(z, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5459, 11715])).
% 1.73/1.99 tff(11717,plain,
% 1.73/1.99 (~b(s(z), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4051, 3358, 1240, 2252])).
% 1.73/1.99 tff(11718,plain,
% 1.73/1.99 (r(s(z), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[194, 11717])).
% 1.73/1.99 tff(11719,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.73/1.99 tff(11720,plain,
% 1.73/1.99 (b(elem!1, z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[403, 157, 11719])).
% 1.73/1.99 tff(11721,plain,
% 1.73/1.99 (~r(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[9119, 11718, 689])).
% 1.73/1.99 tff(11722,plain,
% 1.73/1.99 (b(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[175, 11721])).
% 1.73/1.99 tff(11723,plain,
% 1.73/1.99 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[613, 11720, 3358, 1240])).
% 1.73/1.99 tff(11724,plain,
% 1.73/1.99 (r(elem!1, s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[558, 11723, 3])).
% 1.73/1.99 tff(11725,plain,
% 1.73/1.99 (~r(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1205, 4061, 77, 1180])).
% 1.73/1.99 tff(11726,plain,
% 1.73/1.99 (~r(s(s(s(z))), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5988, 4061, 1090, 2, 2252])).
% 1.73/1.99 tff(11727,plain,
% 1.73/1.99 (r(elem!1, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2951, 11726, 1090, 362, 354, 11725])).
% 1.73/1.99 tff(11728,plain,
% 1.73/1.99 (~r(z, elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2420, 11727, 689])).
% 1.73/1.99 tff(11729,plain,
% 1.73/1.99 (b(z, elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[289, 11728, 4])).
% 1.73/1.99 tff(11730,plain,
% 1.73/1.99 (b(s(z), elem!1)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[454, 11725, 91])).
% 1.73/1.99 tff(11731,plain,
% 1.73/1.99 (~b(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2904, 11729, 77, 11730])).
% 1.73/1.99 tff(11732,plain,
% 1.73/1.99 (r(elem!1, s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1277, 11731, 83])).
% 1.73/1.99 tff(11733,plain,
% 1.73/1.99 (~r(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1001, 11732, 545])).
% 1.73/1.99 tff(11734,plain,
% 1.73/1.99 (b(s(s(elem!1)), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[901, 11733])).
% 1.73/1.99 tff(11735,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11736,plain,
% 1.73/1.99 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(11737,plain,
% 1.73/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[11736])).
% 1.73/1.99 tff(11738,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[11737, 11735])).
% 1.73/2.00 tff(11739,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(11740,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11739, 11738])).
% 1.73/2.00 tff(11741,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11740, 224, 77, 11730, 11734, 1180, 11729])).
% 1.73/2.00 tff(11742,plain,(b(s(s(elem!1)), elem!1) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (z = elem!1) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11743,plain,
% 1.73/2.00 (b(s(s(elem!1)), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11742, 11724, 689, 2252, 77, 11722, 3358, 362, 2, 511, 353])).
% 1.73/2.00 tff(11744,plain,
% 1.73/2.00 (~b(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3407, 11743, 11720, 1240])).
% 1.73/2.00 tff(11745,plain,
% 1.73/2.00 (r(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[289, 11744, 511])).
% 1.73/2.00 tff(11746,plain,
% 1.73/2.00 (~r(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3332, 11745, 11718])).
% 1.73/2.00 tff(11747,plain,
% 1.73/2.00 (~r(elem!1, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3368, 11720, 689, 3, 1240, 827])).
% 1.73/2.00 tff(11748,plain,
% 1.73/2.00 (~r(s(s(s(z))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[698, 11745, 689])).
% 1.73/2.00 tff(11749,plain,
% 1.73/2.00 (~b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4200, 11748, 11722, 362, 11747])).
% 1.73/2.00 tff(11750,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[454, 11749, 11746, 91])).
% 1.73/2.00 tff(11751,plain,((elem!1 = z) | (s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11752,plain,
% 1.73/2.00 (r(elem!1, z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11751, 362, 689, 1240, 2252, 77, 2, 3, 827, 157])).
% 1.73/2.00 tff(11753,plain,
% 1.73/2.00 (~r(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2841, 11752, 11718])).
% 1.73/2.00 tff(11754,plain,
% 1.73/2.00 (b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[454, 11753, 91])).
% 1.73/2.00 tff(11755,plain,
% 1.73/2.00 (~r(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1259, 11752, 11718])).
% 1.73/2.00 tff(11756,plain,
% 1.73/2.00 (b(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1277, 11755, 83])).
% 1.73/2.00 tff(11757,plain,
% 1.73/2.00 (~b(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2904, 11756, 77, 11754])).
% 1.73/2.00 tff(11758,plain,
% 1.73/2.00 (r(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[289, 11757, 511])).
% 1.73/2.00 tff(11759,plain,
% 1.73/2.00 (~r(s(s(s(z))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[698, 11758, 689])).
% 1.73/2.00 tff(11760,plain,
% 1.73/2.00 (~r(elem!1, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2420, 11758, 689])).
% 1.73/2.00 tff(11761,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4200, 11760, 11759, 11722, 362, 11754])).
% 1.73/2.00 tff(11762,plain,((s(s(s(z))) = elem!1) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11763,plain,
% 1.73/2.00 (s(s(s(z))) = elem!1),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11762, 157, 77, 1240, 2252, 2, 3, 827, 101])).
% 1.73/2.00 tff(11764,plain,
% 1.73/2.00 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11763])).
% 1.73/2.00 tff(11765,plain,
% 1.73/2.00 (~r(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3074, 827, 101])).
% 1.73/2.00 tff(11766,plain,
% 1.73/2.00 (b(z, s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[752, 11765])).
% 1.73/2.00 tff(11767,plain,
% 1.73/2.00 (~b(s(z), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4051, 11766, 1240, 2252])).
% 1.73/2.00 tff(11768,plain,
% 1.73/2.00 (r(s(z), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[194, 11767])).
% 1.73/2.00 tff(11769,plain,
% 1.73/2.00 (~r(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[9119, 11768, 101])).
% 1.73/2.00 tff(11770,plain,
% 1.73/2.00 (b(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[175, 11769])).
% 1.73/2.00 tff(11771,plain,
% 1.73/2.00 (~(s(s(s(z))) = elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[10759, 3188, 3358, 77, 827, 2252])).
% 1.73/2.00 tff(11772,plain,
% 1.73/2.00 (s(s(z)) = s(s(elem!1))),
% 1.73/2.00 inference(symmetry,[status(thm)],[4577])).
% 1.73/2.00 tff(11773,plain,
% 1.73/2.00 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11772])).
% 1.73/2.00 tff(11774,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11773])).
% 1.73/2.00 tff(11775,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[3982])).
% 1.73/2.00 tff(11776,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.73/2.00 inference(transitivity,[status(thm)],[11775, 11774])).
% 1.73/2.00 tff(11777,plain,
% 1.73/2.00 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[3982])).
% 1.73/2.00 tff(11778,plain,
% 1.73/2.00 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11777])).
% 1.73/2.00 tff(11779,plain,
% 1.73/2.00 (b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[2252, 11778])).
% 1.73/2.00 tff(11780,plain,
% 1.73/2.00 (b(z, s(elem!1)) <=> b(z, s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[3982])).
% 1.73/2.00 tff(11781,plain,
% 1.73/2.00 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11780])).
% 1.73/2.00 tff(11782,plain,
% 1.73/2.00 (b(z, s(elem!1))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[77, 11781])).
% 1.73/2.00 tff(11783,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4124, 11782, 1180, 11779])).
% 1.73/2.00 tff(11784,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[530, 11783, 2505])).
% 1.73/2.00 tff(11785,plain,
% 1.73/2.00 (r(s(s(z)), s(z))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11784, 11776])).
% 1.73/2.00 tff(11786,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[4577])).
% 1.73/2.00 tff(11787,plain,
% 1.73/2.00 (r(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[827, 11786])).
% 1.73/2.00 tff(11788,plain,
% 1.73/2.00 (~r(s(s(z)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3196, 11787, 3188])).
% 1.73/2.00 tff(11789,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11788, 11785])).
% 1.73/2.00 tff(11790,plain,((~(elem!1 = z)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11791,plain,
% 1.73/2.00 (~(elem!1 = z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11790, 3188, 526, 3358, 827, 77, 2252])).
% 1.73/2.00 tff(11792,plain,
% 1.73/2.00 (r(elem!1, z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11751, 11791, 689, 1240, 2252, 77, 2, 3, 827, 11771])).
% 1.73/2.00 tff(11793,plain,
% 1.73/2.00 (~r(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2841, 11792, 11718])).
% 1.73/2.00 tff(11794,plain,
% 1.73/2.00 (b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[454, 11793, 91])).
% 1.73/2.00 tff(11795,plain,
% 1.73/2.00 (~(z = elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[338, 11791])).
% 1.73/2.00 tff(11796,plain,
% 1.73/2.00 (~r(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1259, 11792, 11718])).
% 1.73/2.00 tff(11797,plain,
% 1.73/2.00 (b(elem!1, s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1277, 11796, 83])).
% 1.73/2.00 tff(11798,plain,
% 1.73/2.00 (~b(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2904, 11797, 77, 11794])).
% 1.73/2.00 tff(11799,plain,
% 1.73/2.00 (r(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[289, 11798, 11795])).
% 1.73/2.00 tff(11800,plain,
% 1.73/2.00 (~r(s(s(s(z))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[698, 11799, 689])).
% 1.73/2.00 tff(11801,plain,
% 1.73/2.00 (~r(elem!1, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2420, 11799, 689])).
% 1.73/2.00 tff(11802,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4200, 11801, 11800, 11722, 11771, 11794])).
% 1.73/2.00 tff(11803,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11804,plain,
% 1.73/2.00 (~r(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11803, 77, 101, 1240, 2252, 2, 3, 827])).
% 1.73/2.00 tff(11805,plain,
% 1.73/2.00 (b(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[925, 11804])).
% 1.73/2.00 tff(11806,plain,
% 1.73/2.00 (~r(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3472, 11805, 101, 11768, 11770])).
% 1.73/2.00 tff(11807,plain,
% 1.73/2.00 (b(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[281, 11806])).
% 1.73/2.00 tff(11808,plain,
% 1.73/2.00 (~b(s(s(z)), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5939, 11807, 11766, 1240])).
% 1.73/2.00 tff(11809,plain,
% 1.73/2.00 (r(s(s(z)), s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[265, 1108, 11808])).
% 1.73/2.00 tff(11810,plain,
% 1.73/2.00 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4511, 11763, 2252])).
% 1.73/2.00 tff(11811,plain,
% 1.73/2.00 (s(s(s(s(z)))) = s(elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11763])).
% 1.73/2.00 tff(11812,plain,
% 1.73/2.00 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11811])).
% 1.73/2.00 tff(11813,plain,
% 1.73/2.00 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11812])).
% 1.73/2.00 tff(11814,plain,
% 1.73/2.00 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11813])).
% 1.73/2.00 tff(11815,plain,
% 1.73/2.00 (b(z, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11766, 11814])).
% 1.73/2.00 tff(11816,plain,
% 1.73/2.00 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4503, 11815, 11810, 77])).
% 1.73/2.00 tff(11817,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[10038, 11816, 11763])).
% 1.73/2.00 tff(11818,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[901, 11817])).
% 1.73/2.00 tff(11819,plain,
% 1.73/2.00 (~r(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5439, 11818, 827, 11809])).
% 1.73/2.00 tff(11820,plain,
% 1.73/2.00 (b(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[249, 11819])).
% 1.73/2.00 tff(11821,plain,
% 1.73/2.00 (b(s(s(z)), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11820, 11764])).
% 1.73/2.00 tff(11822,plain,
% 1.73/2.00 (~b(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[347, 11763, 74])).
% 1.73/2.00 tff(11823,plain,
% 1.73/2.00 (r(z, elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[289, 11822, 511])).
% 1.73/2.00 tff(11824,plain,
% 1.73/2.00 (~r(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3332, 11823, 11768])).
% 1.73/2.00 tff(11825,plain,
% 1.73/2.00 (b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[454, 11824, 91])).
% 1.73/2.00 tff(11826,plain,
% 1.73/2.00 (~r(s(s(z)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2993, 11818, 11809])).
% 1.73/2.00 tff(11827,plain,
% 1.73/2.00 (b(s(s(z)), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2726, 11826])).
% 1.73/2.00 tff(11828,plain,
% 1.73/2.00 (~b(s(s(z)), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5045, 11827, 77, 11825, 11807])).
% 1.73/2.00 tff(11829,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11828, 11821])).
% 1.73/2.00 tff(11830,plain,((elem!1 = z) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | b(z, s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11831,plain,
% 1.73/2.00 (elem!1 = z),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11830, 11716, 11581, 2252, 74, 11580, 2, 3])).
% 1.73/2.00 tff(11832,plain,
% 1.73/2.00 (z = elem!1),
% 1.73/2.00 inference(symmetry,[status(thm)],[11831])).
% 1.73/2.00 tff(11833,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11832])).
% 1.73/2.00 tff(11834,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.73/2.00 inference(symmetry,[status(thm)],[11833])).
% 1.73/2.00 tff(11835,plain,
% 1.73/2.00 (s(elem!1) = s(z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11831])).
% 1.73/2.00 tff(11836,plain,
% 1.73/2.00 (s(s(elem!1)) = s(s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11835])).
% 1.73/2.00 tff(11837,plain,
% 1.73/2.00 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11836])).
% 1.73/2.00 tff(11838,plain,
% 1.73/2.00 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11837])).
% 1.73/2.00 tff(11839,plain,
% 1.73/2.00 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11838])).
% 1.73/2.00 tff(11840,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11839, 11831])).
% 1.73/2.00 tff(11841,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(symmetry,[status(thm)],[11840])).
% 1.73/2.00 tff(11842,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11831])).
% 1.73/2.00 tff(11843,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(transitivity,[status(thm)],[11842, 11841])).
% 1.73/2.00 tff(11844,plain,
% 1.73/2.00 (s(elem!1) = s(z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3984, 11831])).
% 1.73/2.00 tff(11845,plain,
% 1.73/2.00 (s(z) = s(elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3988, 11844])).
% 1.73/2.00 tff(11846,plain,
% 1.73/2.00 (~b(s(elem!1), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4001, 11845, 11584])).
% 1.73/2.00 tff(11847,plain,
% 1.73/2.00 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11831])).
% 1.73/2.00 tff(11848,plain,
% 1.73/2.00 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.73/2.00 inference(symmetry,[status(thm)],[11847])).
% 1.73/2.00 tff(11849,plain,
% 1.73/2.00 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11848])).
% 1.73/2.00 tff(11850,plain,
% 1.73/2.00 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[1334, 11849])).
% 1.73/2.00 tff(11851,plain,
% 1.73/2.00 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1682, 11831])).
% 1.73/2.00 tff(11852,plain,
% 1.73/2.00 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1831, 11851])).
% 1.73/2.00 tff(11853,plain,
% 1.73/2.00 (z = elem!1),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[10, 11831])).
% 1.73/2.00 tff(11854,plain,
% 1.73/2.00 (~r(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11803, 11716, 101, 11580, 2252, 2, 3, 11581])).
% 1.73/2.00 tff(11855,plain,
% 1.73/2.00 (b(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[925, 11854])).
% 1.73/2.00 tff(11856,plain,
% 1.73/2.00 (~r(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[9119, 11585, 101])).
% 1.73/2.00 tff(11857,plain,
% 1.73/2.00 (b(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[175, 11856])).
% 1.73/2.00 tff(11858,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11836])).
% 1.73/2.00 tff(11859,plain,
% 1.73/2.00 (r(s(s(z)), s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11581, 11858])).
% 1.73/2.00 tff(11860,plain,
% 1.73/2.00 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11831])).
% 1.73/2.00 tff(11861,plain,
% 1.73/2.00 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11860])).
% 1.73/2.00 tff(11862,plain,
% 1.73/2.00 (r(elem!1, s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[101, 11861])).
% 1.73/2.00 tff(11863,plain,
% 1.73/2.00 (~r(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3472, 11855, 101, 11585, 11857])).
% 1.73/2.00 tff(11864,plain,
% 1.73/2.00 (b(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[281, 11863])).
% 1.73/2.00 tff(11865,plain,
% 1.73/2.00 (~r(z, s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7250, 11853, 11582])).
% 1.73/2.00 tff(11866,plain,
% 1.73/2.00 (b(z, s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1088, 11865])).
% 1.73/2.00 tff(11867,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[4580, 7])).
% 1.73/2.00 tff(11868,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(symmetry,[status(thm)],[11867])).
% 1.73/2.00 tff(11869,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7])).
% 1.73/2.00 tff(11870,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(transitivity,[status(thm)],[11869, 11868])).
% 1.73/2.00 tff(11871,plain,
% 1.73/2.00 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7])).
% 1.73/2.00 tff(11872,plain,
% 1.73/2.00 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.73/2.00 inference(symmetry,[status(thm)],[11871])).
% 1.73/2.00 tff(11873,plain,
% 1.73/2.00 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11872])).
% 1.73/2.00 tff(11874,plain,
% 1.73/2.00 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[1334, 11873])).
% 1.73/2.00 tff(11875,plain,
% 1.73/2.00 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[3318, 11612])).
% 1.73/2.00 tff(11876,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1806, 11875, 1020])).
% 1.73/2.00 tff(11877,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1294, 11876, 11874])).
% 1.73/2.00 tff(11878,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11877, 11870])).
% 1.73/2.00 tff(11879,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), z)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11878, 11604])).
% 1.73/2.00 tff(11880,plain,
% 1.73/2.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11263, 3318, 196])).
% 1.73/2.00 tff(11881,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6185, 11880])).
% 1.73/2.00 tff(11882,plain,
% 1.73/2.00 (~b(s(s(s(s(z)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6090, 224, 2191, 1118, 11881])).
% 1.73/2.00 tff(11883,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11882, 11879])).
% 1.73/2.00 tff(11884,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11885,plain,
% 1.73/2.00 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11884, 11831, 11866, 11864, 11862, 11859])).
% 1.73/2.00 tff(11886,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3252, 11885])).
% 1.73/2.00 tff(11887,plain,
% 1.73/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1579, 11886, 11857, 11855])).
% 1.73/2.00 tff(11888,plain,
% 1.73/2.00 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7550, 11887, 11853])).
% 1.73/2.00 tff(11889,plain,
% 1.73/2.00 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1345, 11888, 11852])).
% 1.73/2.00 tff(11890,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1317, 11889, 11850, 11846])).
% 1.73/2.00 tff(11891,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), elem!1)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11890, 11843])).
% 1.73/2.00 tff(11892,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), z)),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11891, 11834])).
% 1.73/2.00 tff(11893,plain,
% 1.73/2.00 (s(s(z)) = s(s(elem!1))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11836])).
% 1.73/2.00 tff(11894,plain,
% 1.73/2.00 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11893])).
% 1.73/2.00 tff(11895,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11894])).
% 1.73/2.00 tff(11896,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11835])).
% 1.73/2.00 tff(11897,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.73/2.00 inference(transitivity,[status(thm)],[11896, 11895])).
% 1.73/2.00 tff(11898,plain,
% 1.73/2.00 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11835])).
% 1.73/2.00 tff(11899,plain,
% 1.73/2.00 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11898])).
% 1.73/2.00 tff(11900,plain,
% 1.73/2.00 (b(s(elem!1), s(s(elem!1)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[2252, 11899])).
% 1.73/2.00 tff(11901,plain,
% 1.73/2.00 (b(z, s(elem!1)) <=> b(z, s(z))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11835])).
% 1.73/2.00 tff(11902,plain,
% 1.73/2.00 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11901])).
% 1.73/2.00 tff(11903,plain,
% 1.73/2.00 (b(z, s(elem!1))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11716, 11902])).
% 1.73/2.00 tff(11904,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4124, 11903, 11583, 11900])).
% 1.73/2.00 tff(11905,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[530, 11904, 526])).
% 1.73/2.00 tff(11906,plain,
% 1.73/2.00 (r(s(s(z)), s(z))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11905, 11897])).
% 1.73/2.00 tff(11907,plain,
% 1.73/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3168, 11887])).
% 1.73/2.00 tff(11908,plain,
% 1.73/2.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[9293, 112, 11859, 11907, 11906])).
% 1.73/2.00 tff(11909,plain,
% 1.73/2.00 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6185, 11908])).
% 1.73/2.00 tff(11910,plain,
% 1.73/2.00 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3298, 224, 11866, 11864])).
% 1.73/2.00 tff(11911,plain,
% 1.73/2.00 (~b(s(s(s(s(z)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11910, 11909])).
% 1.73/2.00 tff(11912,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11911, 11892])).
% 1.73/2.00 tff(11913,plain,((s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(elem!1)))) | b(z, s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | b(s(s(elem!1)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11914,plain,
% 1.73/2.00 (b(s(s(elem!1)), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11913, 11570, 2, 3, 7672, 2252])).
% 1.73/2.00 tff(11915,plain,
% 1.73/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11914, 7328])).
% 1.73/2.00 tff(11916,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7409, 224, 4599, 11915, 11563])).
% 1.73/2.00 tff(11917,plain,
% 1.73/2.00 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1422, 68, 7374, 11916])).
% 1.73/2.00 tff(11918,plain,
% 1.73/2.00 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[8075, 11917, 1181])).
% 1.73/2.00 tff(11919,plain,
% 1.73/2.00 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1439, 11918, 1782])).
% 1.73/2.00 tff(11920,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(11921,plain,
% 1.73/2.00 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(11922,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[11921])).
% 1.73/2.00 tff(11923,plain,
% 1.73/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[11922, 11920])).
% 1.73/2.00 tff(11924,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(11925,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11924, 11923])).
% 1.73/2.00 tff(11926,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11925, 224, 3919, 11919, 11554, 11563])).
% 1.73/2.00 tff(11927,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11928,plain,
% 1.73/2.00 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11927, 11562, 1181, 4599, 335, 2, 3, 7672, 2252])).
% 1.73/2.00 tff(11929,plain,
% 1.73/2.00 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1294, 11928, 1733])).
% 1.73/2.00 tff(11930,plain,
% 1.73/2.00 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5903, 112, 11929, 1181])).
% 1.73/2.00 tff(11931,plain,
% 1.73/2.00 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1422, 68, 11930, 7374])).
% 1.73/2.00 tff(11932,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11429, 11931, 1289, 335, 11557])).
% 1.73/2.00 tff(11933,plain,
% 1.73/2.00 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11932, 11552])).
% 1.73/2.00 tff(11934,plain,
% 1.73/2.00 (b(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11913, 11933, 2, 3, 7672, 2252])).
% 1.73/2.00 tff(11935,plain,
% 1.73/2.00 (b(elem!1, s(s(s(elem!1))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[11934, 10974])).
% 1.73/2.00 tff(11936,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.73/2.00 tff(11937,plain,
% 1.73/2.00 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.73/2.00 inference(symmetry,[status(thm)],[11936])).
% 1.73/2.00 tff(11938,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1760, 11937])).
% 1.73/2.00 tff(11939,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(11940,plain,
% 1.73/2.00 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[11939, 1717])).
% 1.73/2.00 tff(11941,plain,
% 1.73/2.00 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(11942,plain,
% 1.73/2.00 (((~r(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(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(11943,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[11942])).
% 1.73/2.01 tff(11944,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[11943, 11941])).
% 1.73/2.01 tff(11945,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(11946,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[11945, 11944])).
% 1.73/2.01 tff(11947,plain,
% 1.73/2.01 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11946, 112, 1181, 1740])).
% 1.73/2.01 tff(11948,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.73/2.01 tff(11949,plain,
% 1.73/2.01 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11124, 68, 11948, 11947])).
% 1.73/2.01 tff(11950,plain,
% 1.73/2.01 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2043, 2041])).
% 1.73/2.01 tff(11951,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2047, 68, 11950, 11137])).
% 1.73/2.01 tff(11952,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(11953,plain,
% 1.73/2.01 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(11954,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[11953])).
% 1.73/2.01 tff(11955,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[11954, 11952])).
% 1.73/2.01 tff(11956,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(11957,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[11956, 11955])).
% 1.73/2.01 tff(11958,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11957, 224, 11424, 11951, 11949, 11301])).
% 1.73/2.01 tff(11959,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(11960,plain,
% 1.73/2.01 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11959, 11931, 1835, 11940, 11929, 1181])).
% 1.73/2.01 tff(11961,plain,
% 1.73/2.01 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1777, 11960, 1615])).
% 1.73/2.01 tff(11962,plain,
% 1.73/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11024, 224, 11961, 11554, 11935])).
% 1.73/2.01 tff(11963,plain,
% 1.73/2.01 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 11962])).
% 1.73/2.01 tff(11964,assumption,(b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.73/2.01 tff(11965,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1845, 224, 501, 1488, 7305, 11964])).
% 1.73/2.01 tff(11966,plain,((~b(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(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(11967,plain,
% 1.73/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11966, 11961, 1488, 501])).
% 1.73/2.01 tff(11968,plain,
% 1.73/2.01 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[11458, 11967, 1854])).
% 1.73/2.01 tff(11969,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4920, 11928, 1733, 1181])).
% 1.73/2.01 tff(11970,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(11971,plain,
% 1.84/2.01 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(11972,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[11971])).
% 1.84/2.01 tff(11973,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[11972, 11970])).
% 1.84/2.01 tff(11974,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.01 inference(quant_inst,[status(thm)],[])).
% 1.84/2.01 tff(11975,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[11974, 11973])).
% 1.84/2.01 tff(11976,plain,
% 1.84/2.01 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11975, 224, 11969, 11931, 11562])).
% 1.84/2.01 tff(11977,plain,
% 1.84/2.01 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[3905, 11976, 7255])).
% 1.84/2.01 tff(11978,plain,
% 1.84/2.01 (((~![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(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(11979,plain,
% 1.84/2.01 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(11980,plain,
% 1.84/2.01 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[11979])).
% 1.84/2.01 tff(11981,plain,
% 1.84/2.01 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[11980, 11978])).
% 1.84/2.01 tff(11982,plain,
% 1.84/2.01 ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.01 inference(quant_inst,[status(thm)],[])).
% 1.84/2.01 tff(11983,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[11982, 11981])).
% 1.84/2.01 tff(11984,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11983, 112, 11977, 11558, 11968, 11963])).
% 1.84/2.01 tff(11985,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(11986,plain,
% 1.84/2.01 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11985, 11525, 501, 3340, 335, 2, 3, 10683, 11503, 11550])).
% 1.84/2.01 tff(11987,plain,
% 1.84/2.01 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[1345, 11986, 1832])).
% 1.84/2.01 tff(11988,plain,
% 1.84/2.01 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[7550, 11987, 335])).
% 1.84/2.01 tff(11989,plain,
% 1.84/2.01 (b(s(z), s(s(z)))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[11503, 11244])).
% 1.84/2.01 tff(11990,plain,
% 1.84/2.01 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[1619])).
% 1.84/2.01 tff(11991,plain,
% 1.84/2.01 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.01 inference(symmetry,[status(thm)],[11990])).
% 1.84/2.01 tff(11992,plain,
% 1.84/2.01 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.01 inference(transitivity,[status(thm)],[7254, 11991])).
% 1.84/2.01 tff(11993,plain,
% 1.84/2.01 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[11992])).
% 1.84/2.01 tff(11994,plain,
% 1.84/2.01 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[4382, 224, 501, 11525, 11987])).
% 1.84/2.01 tff(11995,plain,
% 1.84/2.01 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[1294, 11994, 1733])).
% 1.84/2.01 tff(11996,plain,
% 1.84/2.01 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2022, 112, 11995, 3340])).
% 1.84/2.01 tff(11997,plain,
% 1.84/2.01 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[11996, 11993])).
% 1.84/2.01 tff(11998,plain,
% 1.84/2.01 (b(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[6185, 11997])).
% 1.84/2.01 tff(11999,plain,
% 1.84/2.01 (~b(s(s(z)), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[5196, 11998, 11989, 11988])).
% 1.84/2.01 tff(12000,plain,
% 1.84/2.01 (r(s(s(z)), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2726, 11999])).
% 1.84/2.01 tff(12001,plain,
% 1.84/2.01 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[3196, 12000, 11528])).
% 1.84/2.01 tff(12002,plain,
% 1.84/2.01 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[249, 12001])).
% 1.84/2.01 tff(12003,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12002, 7330])).
% 1.84/2.01 tff(12004,plain,
% 1.84/2.01 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[4920, 11994, 1733, 3340])).
% 1.84/2.01 tff(12005,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(12006,plain,
% 1.84/2.01 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(12007,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12006])).
% 1.84/2.01 tff(12008,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[12007, 12005])).
% 1.84/2.01 tff(12009,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.84/2.01 inference(quant_inst,[status(thm)],[])).
% 1.84/2.01 tff(12010,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12009, 12008])).
% 1.84/2.01 tff(12011,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[12010, 224, 11504, 11987, 12004, 11550, 12003])).
% 1.84/2.01 tff(12012,plain,(b(s(s(elem!1)), elem!1) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(12013,plain,
% 1.84/2.01 (b(s(s(elem!1)), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[12012, 10966, 11370, 2, 3, 176])).
% 1.84/2.01 tff(12014,plain,
% 1.84/2.01 (b(s(s(z)), elem!1)),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12013, 10970])).
% 1.84/2.01 tff(12015,plain,
% 1.84/2.01 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10968, 10967])).
% 1.84/2.01 tff(12016,plain,
% 1.84/2.01 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.84/2.01 inference(symmetry,[status(thm)],[12015])).
% 1.84/2.01 tff(12017,plain,
% 1.84/2.01 (r(s(z), z)),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[10081, 1647])).
% 1.84/2.01 tff(12018,plain,
% 1.84/2.01 (~r(z, s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[9119, 12017, 178])).
% 1.84/2.01 tff(12019,plain,
% 1.84/2.01 (b(z, s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[100, 12018])).
% 1.84/2.01 tff(12020,plain,
% 1.84/2.01 (b(s(s(elem!1)), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[12012, 335, 7440, 2, 3, 178])).
% 1.84/2.01 tff(12021,plain,
% 1.84/2.01 (~r(s(s(elem!1)), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[4039, 827, 178])).
% 1.84/2.01 tff(12022,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[901, 12021])).
% 1.84/2.01 tff(12023,plain,
% 1.84/2.01 (b(s(s(z)), s(z))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12022, 11251])).
% 1.84/2.01 tff(12024,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12022, 11250])).
% 1.84/2.01 tff(12025,plain,
% 1.84/2.01 (r(s(s(z)), s(s(s(z))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[827, 10982])).
% 1.84/2.01 tff(12026,plain,
% 1.84/2.01 (b(elem!1, s(s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12019, 10974])).
% 1.84/2.01 tff(12027,plain,
% 1.84/2.01 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[827, 4639])).
% 1.84/2.01 tff(12028,plain,
% 1.84/2.01 (~b(z, s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[10876, 12022, 77, 9731])).
% 1.84/2.01 tff(12029,plain,
% 1.84/2.01 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11358, 12028, 335])).
% 1.84/2.01 tff(12030,plain,
% 1.84/2.01 (r(elem!1, s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[558, 12029, 3])).
% 1.84/2.01 tff(12031,plain,
% 1.84/2.01 (~r(s(elem!1), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[4010, 12030, 10081])).
% 1.84/2.01 tff(12032,plain,
% 1.84/2.01 (b(s(elem!1), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[1521, 12031, 319])).
% 1.84/2.01 tff(12033,plain,
% 1.84/2.01 (b(s(z), s(s(z)))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12032, 11242])).
% 1.84/2.01 tff(12034,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11351, 12033, 12027, 390, 1287, 3, 12026, 335, 12025, 12024, 4719, 12023, 11073])).
% 1.84/2.01 tff(12035,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | b(s(elem!1), elem!1) | (elem!1 = s(s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(12036,plain,
% 1.84/2.01 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[12035, 1287, 12020, 3, 335, 10980, 77, 178])).
% 1.84/2.01 tff(12037,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[147, 12036, 2])).
% 1.84/2.01 tff(12038,plain,
% 1.84/2.01 (~b(s(s(elem!1)), z)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[10929, 12037, 12019, 10683])).
% 1.84/2.01 tff(12039,plain,
% 1.84/2.01 (r(s(s(elem!1)), z)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[593, 12038])).
% 1.84/2.01 tff(12040,plain,
% 1.84/2.01 (r(s(s(elem!1)), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[333, 12039, 1668])).
% 1.84/2.01 tff(12041,plain,
% 1.84/2.01 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11523, 12040, 335, 10980, 10081, 526, 178])).
% 1.84/2.01 tff(12042,plain,
% 1.84/2.01 (~r(s(elem!1), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[6557, 12040, 10081])).
% 1.84/2.01 tff(12043,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[1521, 12042, 12041, 319])).
% 1.84/2.01 tff(12044,plain,(b(s(elem!1), elem!1) | (~(z = elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(12045,plain,
% 1.84/2.01 (b(s(elem!1), elem!1)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[12044, 10966, 176, 2, 3, 11369])).
% 1.84/2.01 tff(12046,plain,
% 1.84/2.01 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[1496, 12045, 11370, 12013])).
% 1.84/2.01 tff(12047,plain,
% 1.84/2.01 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[530, 12046, 526])).
% 1.84/2.01 tff(12048,plain,
% 1.84/2.01 (r(s(s(z)), s(z))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12047, 12016])).
% 1.84/2.01 tff(12049,plain,
% 1.84/2.01 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[6257, 12048, 176])).
% 1.84/2.01 tff(12050,plain,
% 1.84/2.01 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[249, 12049])).
% 1.84/2.01 tff(12051,plain,
% 1.84/2.01 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10966])).
% 1.84/2.01 tff(12052,plain,
% 1.84/2.01 (b(s(s(s(z))), elem!1)),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[7644, 12051])).
% 1.84/2.01 tff(12053,plain,
% 1.84/2.01 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10966])).
% 1.84/2.01 tff(12054,plain,
% 1.84/2.01 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[12053, 283])).
% 1.84/2.01 tff(12055,plain,
% 1.84/2.01 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12054])).
% 1.84/2.01 tff(12056,plain,
% 1.84/2.01 (~(elem!1 = s(s(s(z))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[58, 12055])).
% 1.84/2.01 tff(12057,plain,
% 1.84/2.01 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10968])).
% 1.84/2.01 tff(12058,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12057])).
% 1.84/2.01 tff(12059,plain,
% 1.84/2.01 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10968])).
% 1.84/2.01 tff(12060,plain,
% 1.84/2.01 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[12059, 12058])).
% 1.84/2.01 tff(12061,plain,
% 1.84/2.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12050, 12060])).
% 1.84/2.01 tff(12062,plain,
% 1.84/2.01 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.84/2.01 inference(symmetry,[status(thm)],[12057])).
% 1.84/2.01 tff(12063,plain,
% 1.84/2.01 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12062])).
% 1.84/2.01 tff(12064,plain,
% 1.84/2.01 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.84/2.01 inference(symmetry,[status(thm)],[12063])).
% 1.84/2.01 tff(12065,plain,
% 1.84/2.01 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[10967])).
% 1.84/2.01 tff(12066,plain,
% 1.84/2.01 (r(s(elem!1), s(s(s(z))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[176, 12065])).
% 1.84/2.01 tff(12067,plain,
% 1.84/2.01 (r(s(elem!1), s(s(s(elem!1))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12066, 12064])).
% 1.84/2.01 tff(12068,plain,
% 1.84/2.01 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12057])).
% 1.84/2.01 tff(12069,plain,
% 1.84/2.01 (b(s(s(s(elem!1))), elem!1)),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12052, 12068])).
% 1.84/2.01 tff(12070,plain,
% 1.84/2.01 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[3878, 10966])).
% 1.84/2.01 tff(12071,plain,
% 1.84/2.01 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12057, 10967])).
% 1.84/2.01 tff(12072,plain,
% 1.84/2.01 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12057, 10967])).
% 1.84/2.01 tff(12073,plain,
% 1.84/2.01 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.84/2.01 inference(symmetry,[status(thm)],[12072])).
% 1.84/2.01 tff(12074,plain,
% 1.84/2.01 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[12073])).
% 1.84/2.01 tff(12075,plain,
% 1.84/2.01 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11382, 224, 11370, 12045, 12069])).
% 1.84/2.01 tff(12076,plain,
% 1.84/2.01 (~b(s(s(s(z))), s(z))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12075, 12074])).
% 1.84/2.01 tff(12077,plain,
% 1.84/2.01 (r(s(s(s(z))), s(z))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[925, 12076])).
% 1.84/2.01 tff(12078,plain,
% 1.84/2.01 (r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[12077, 12071])).
% 1.84/2.01 tff(12079,plain,
% 1.84/2.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[11497, 112, 12047, 12078])).
% 1.84/2.01 tff(12080,plain,
% 1.84/2.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[3905, 12079, 12070])).
% 1.84/2.01 tff(12081,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[11341, 224, 682, 390, 1698, 11073])).
% 1.84/2.02 tff(12082,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(12083,plain,
% 1.84/2.02 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12082, 12013, 12080, 12069])).
% 1.84/2.02 tff(12084,plain,
% 1.84/2.02 (r(elem!1, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[558, 12083, 3])).
% 1.84/2.02 tff(12085,plain,
% 1.84/2.02 (~r(elem!1, s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[7369, 12084, 12067, 12013, 11370, 12045, 12047, 12061, 10966])).
% 1.84/2.02 tff(12086,plain,
% 1.84/2.02 (b(elem!1, s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[388, 12085, 12056])).
% 1.84/2.02 tff(12087,plain,
% 1.84/2.02 (~b(s(s(z)), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2412, 12086, 12052, 12050])).
% 1.84/2.02 tff(12088,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12087, 12014])).
% 1.84/2.02 tff(12089,plain,(b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(12090,plain,
% 1.84/2.02 (b(s(z), s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12089, 4538, 2, 3])).
% 1.84/2.02 tff(12091,plain,
% 1.84/2.02 (~b(z, s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[9179, 1, 1090, 7672])).
% 1.84/2.02 tff(12092,plain,
% 1.84/2.02 (b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[11913, 12091, 2, 3, 7672, 2252])).
% 1.84/2.02 tff(12093,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12094,plain,
% 1.84/2.02 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12095,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12094])).
% 1.84/2.02 tff(12096,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12095, 12093])).
% 1.84/2.02 tff(12097,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(12098,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12097, 12096])).
% 1.84/2.02 tff(12099,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12098, 224, 1, 2252, 1090, 12092, 7672])).
% 1.84/2.02 tff(12100,plain,((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(12101,plain,
% 1.84/2.02 (~b(s(z), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12100, 2252, 1090, 7672, 2, 3])).
% 1.84/2.02 tff(12102,plain,
% 1.84/2.02 (r(s(z), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[194, 12101])).
% 1.84/2.02 tff(12103,plain,
% 1.84/2.02 (~r(z, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[10916, 12102, 91, 688, 3])).
% 1.84/2.02 tff(12104,plain,
% 1.84/2.02 (b(z, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[752, 12103])).
% 1.84/2.02 tff(12105,plain,
% 1.84/2.02 (~r(z, s(z))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[5480, 416, 688])).
% 1.84/2.02 tff(12106,plain,
% 1.84/2.02 (~b(z, s(z))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2502, 416, 166, 688, 408])).
% 1.84/2.02 tff(12107,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[5459, 12106, 12105])).
% 1.84/2.02 tff(12108,plain,((~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(12109,plain,
% 1.84/2.02 (~r(s(z), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12108, 10081, 688, 409])).
% 1.84/2.02 tff(12110,plain,
% 1.84/2.02 (b(s(z), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[454, 12109, 149])).
% 1.84/2.02 tff(12111,plain,
% 1.84/2.02 (~(s(s(s(z))) = s(elem!1))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[9074, 2767])).
% 1.84/2.02 tff(12112,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.84/2.02 tff(12113,plain,
% 1.84/2.02 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[816, 68, 12112])).
% 1.84/2.02 tff(12114,plain,
% 1.84/2.02 (r(s(s(s(z))), s(elem!1))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12113, 12111])).
% 1.84/2.02 tff(12115,plain,
% 1.84/2.02 (((~![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(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(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12116,plain,
% 1.84/2.02 (((~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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12117,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12116])).
% 1.84/2.02 tff(12118,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12117, 12115])).
% 1.84/2.02 tff(12119,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(12120,plain,
% 1.84/2.02 ((~![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(s(z))), s(elem!1)))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12119, 12118])).
% 1.84/2.02 tff(12121,plain,
% 1.84/2.02 (~r(elem!1, s(s(s(z))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12120, 112, 543, 12114])).
% 1.84/2.02 tff(12122,plain,
% 1.84/2.02 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2767])).
% 1.84/2.02 tff(12123,plain,
% 1.84/2.02 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(z))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12122, 283])).
% 1.84/2.02 tff(12124,plain,
% 1.84/2.02 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.84/2.02 inference(transitivity,[status(thm)],[12123, 284])).
% 1.84/2.02 tff(12125,plain,
% 1.84/2.02 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12124])).
% 1.84/2.02 tff(12126,plain,
% 1.84/2.02 (~(s(s(s(z))) = elem!1)),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[1165, 12125])).
% 1.84/2.02 tff(12127,plain,
% 1.84/2.02 (((~![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(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(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12128,plain,
% 1.84/2.02 (((~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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12129,plain,
% 1.84/2.02 (((~![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))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12128])).
% 1.84/2.02 tff(12130,plain,
% 1.84/2.02 (((~![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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12129, 12127])).
% 1.84/2.02 tff(12131,plain,
% 1.84/2.02 ((~![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)))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(12132,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 1.84/2.02 tff(12133,plain,
% 1.84/2.02 (~r(s(s(s(z))), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12132, 112, 543, 12114])).
% 1.84/2.02 tff(12134,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[4200, 12133, 12126, 1090, 684, 12121])).
% 1.84/2.02 tff(12135,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(12136,plain,
% 1.84/2.02 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12135, 543, 12110, 1090, 10106])).
% 1.84/2.02 tff(12137,plain,
% 1.84/2.02 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[10270, 1798, 408])).
% 1.84/2.02 tff(12138,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12139,plain,
% 1.84/2.02 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12140,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12139])).
% 1.84/2.02 tff(12141,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12140, 12138])).
% 1.84/2.02 tff(12142,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(12143,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12142, 12141])).
% 1.84/2.02 tff(12144,plain,
% 1.84/2.02 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12143, 224, 724, 10696, 10694])).
% 1.84/2.02 tff(12145,plain,
% 1.84/2.02 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1869, 12144, 12137])).
% 1.84/2.02 tff(12146,plain,
% 1.84/2.02 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12145])).
% 1.84/2.02 tff(12147,plain,
% 1.84/2.02 (elem!1 = s(s(s(elem!1)))),
% 1.84/2.02 inference(transitivity,[status(thm)],[155, 12146, 989])).
% 1.84/2.02 tff(12148,plain,
% 1.84/2.02 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12147])).
% 1.84/2.02 tff(12149,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[12148])).
% 1.84/2.02 tff(12150,plain,
% 1.84/2.02 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12149])).
% 1.84/2.02 tff(12151,plain,
% 1.84/2.02 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.84/2.02 inference(symmetry,[status(thm)],[12145])).
% 1.84/2.02 tff(12152,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12151])).
% 1.84/2.02 tff(12153,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[12152])).
% 1.84/2.02 tff(12154,plain,
% 1.84/2.02 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.84/2.02 inference(symmetry,[status(thm)],[12146])).
% 1.84/2.02 tff(12155,plain,
% 1.84/2.02 (s(s(s(elem!1))) = elem!1),
% 1.84/2.02 inference(transitivity,[status(thm)],[1153, 12154, 121])).
% 1.84/2.02 tff(12156,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12155, 12145])).
% 1.84/2.02 tff(12157,plain,
% 1.84/2.02 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.02 inference(symmetry,[status(thm)],[12156])).
% 1.84/2.02 tff(12158,plain,
% 1.84/2.02 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12145])).
% 1.84/2.02 tff(12159,plain,
% 1.84/2.02 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[543, 12158])).
% 1.84/2.02 tff(12160,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12159, 12157])).
% 1.84/2.02 tff(12161,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12160, 12153])).
% 1.84/2.02 tff(12162,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12163,plain,
% 1.84/2.02 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12164,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12163])).
% 1.84/2.02 tff(12165,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[12164, 12162])).
% 1.84/2.02 tff(12166,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(12167,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[12166, 12165])).
% 1.84/2.02 tff(12168,plain,
% 1.84/2.02 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[12167, 224, 10696, 10694, 7672])).
% 1.84/2.02 tff(12169,plain,
% 1.84/2.02 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[5426, 12168])).
% 1.84/2.02 tff(12170,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, 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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(12171,plain,
% 1.84/2.02 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12172,plain,
% 1.84/2.03 (((~![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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12171])).
% 1.84/2.03 tff(12173,plain,
% 1.84/2.03 (((~![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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12172, 12170])).
% 1.84/2.03 tff(12174,plain,
% 1.84/2.03 ((~![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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(12175,plain,
% 1.84/2.03 ((~![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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12174, 12173])).
% 1.84/2.03 tff(12176,plain,
% 1.84/2.03 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12175, 112, 12169])).
% 1.84/2.03 tff(12177,plain,
% 1.84/2.03 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12176, 12161])).
% 1.84/2.03 tff(12178,plain,
% 1.84/2.03 (~r(elem!1, s(s(s(z))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12177, 12150])).
% 1.84/2.03 tff(12179,plain,
% 1.84/2.03 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12147])).
% 1.84/2.03 tff(12180,plain,
% 1.84/2.03 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 1.84/2.03 inference(symmetry,[status(thm)],[12179])).
% 1.84/2.03 tff(12181,plain,
% 1.84/2.03 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12180])).
% 1.84/2.03 tff(12182,plain,
% 1.84/2.03 (((~![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(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12183,plain,
% 1.84/2.03 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12184,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!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(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12183])).
% 1.84/2.03 tff(12185,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!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(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12184, 12182])).
% 1.84/2.03 tff(12186,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(12187,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12186, 12185])).
% 1.84/2.03 tff(12188,plain,
% 1.84/2.03 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12187, 112, 12169])).
% 1.84/2.03 tff(12189,plain,
% 1.84/2.03 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12188, 12161])).
% 1.84/2.03 tff(12190,plain,
% 1.84/2.03 (~r(s(s(s(z))), elem!1)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12189, 12181])).
% 1.84/2.03 tff(12191,plain,
% 1.84/2.03 (s(s(s(z))) = elem!1),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4200, 12190, 1090, 684, 12178])).
% 1.84/2.03 tff(12192,plain,
% 1.84/2.03 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12191, 155, 12146, 989])).
% 1.84/2.03 tff(12193,plain,
% 1.84/2.03 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12192])).
% 1.84/2.03 tff(12194,plain,
% 1.84/2.03 (s(s(z)) = s(s(elem!1))),
% 1.84/2.03 inference(transitivity,[status(thm)],[32, 12193, 1156])).
% 1.84/2.03 tff(12195,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[259, 12194])).
% 1.84/2.03 tff(12196,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12197,plain,
% 1.84/2.03 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12196, 543, 1090, 12110, 1108, 7672, 688, 10081])).
% 1.84/2.03 tff(12198,plain,
% 1.84/2.03 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1294, 12197, 12136])).
% 1.84/2.03 tff(12199,plain,
% 1.84/2.03 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4126, 10081, 688, 319])).
% 1.84/2.03 tff(12200,plain,
% 1.84/2.03 (b(s(s(elem!1)), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[360, 12199, 353])).
% 1.84/2.03 tff(12201,plain,
% 1.84/2.03 (b(z, s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[625, 2500])).
% 1.84/2.03 tff(12202,plain,
% 1.84/2.03 (~r(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[3631, 545, 688])).
% 1.84/2.03 tff(12203,plain,
% 1.84/2.03 (b(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[752, 12202])).
% 1.84/2.03 tff(12204,plain,
% 1.84/2.03 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[553, 545, 543])).
% 1.84/2.03 tff(12205,plain,
% 1.84/2.03 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[530, 12204, 1923])).
% 1.84/2.03 tff(12206,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4124, 12205, 12203, 12201, 10636])).
% 1.84/2.03 tff(12207,plain,((~r(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12208,plain,
% 1.84/2.03 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12207, 543, 10081, 319, 688])).
% 1.84/2.03 tff(12209,plain,
% 1.84/2.03 (b(elem!1, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[558, 12208, 3])).
% 1.84/2.03 tff(12210,plain,
% 1.84/2.03 (~b(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[3687, 12208, 3, 12199, 12110])).
% 1.84/2.03 tff(12211,plain,
% 1.84/2.03 (r(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[653, 12210])).
% 1.84/2.03 tff(12212,plain,
% 1.84/2.03 (~r(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6325, 4569, 656])).
% 1.84/2.03 tff(12213,plain,
% 1.84/2.03 (b(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[752, 12212])).
% 1.84/2.03 tff(12214,plain,
% 1.84/2.03 (b(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1277, 8368, 88])).
% 1.84/2.03 tff(12215,plain,
% 1.84/2.03 (~r(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10612, 3919, 2287, 390, 682, 684, 2896])).
% 1.84/2.03 tff(12216,plain,
% 1.84/2.03 (b(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[593, 12215])).
% 1.84/2.03 tff(12217,plain,
% 1.84/2.03 (~b(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[613, 12216, 682, 1180])).
% 1.84/2.03 tff(12218,plain,
% 1.84/2.03 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4320, 12216, 407, 500])).
% 1.84/2.03 tff(12219,plain,
% 1.84/2.03 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[530, 12218, 2505])).
% 1.84/2.03 tff(12220,plain,
% 1.84/2.03 (~(s(z) = s(elem!1))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[409, 465])).
% 1.84/2.03 tff(12221,plain,
% 1.84/2.03 (~r(z, s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[604, 9756, 543])).
% 1.84/2.03 tff(12222,plain,
% 1.84/2.03 (b(z, s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[625, 12221])).
% 1.84/2.03 tff(12223,plain,
% 1.84/2.03 (~b(s(z), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10118, 224, 1, 500, 12222])).
% 1.84/2.03 tff(12224,plain,
% 1.84/2.03 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[426, 68, 12223])).
% 1.84/2.03 tff(12225,plain,
% 1.84/2.03 (r(s(z), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12224, 12220])).
% 1.84/2.03 tff(12226,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), 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(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12227,plain,
% 1.84/2.03 (((~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), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12228,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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), elem!1)) | (~r(s(z), s(elem!1)))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12227])).
% 1.84/2.03 tff(12229,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12228, 12226])).
% 1.84/2.03 tff(12230,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(12231,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12230, 12229])).
% 1.84/2.03 tff(12232,plain,
% 1.84/2.03 (~r(s(z), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12231, 112, 543, 12225])).
% 1.84/2.03 tff(12233,plain,
% 1.84/2.03 (~r(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[662, 112, 544, 12225])).
% 1.84/2.03 tff(12234,plain,
% 1.84/2.03 (b(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[653, 12233])).
% 1.84/2.03 tff(12235,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12236,plain,
% 1.84/2.03 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12237,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12236])).
% 1.84/2.03 tff(12238,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12237, 12235])).
% 1.84/2.03 tff(12239,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(12240,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12239, 12238])).
% 1.84/2.03 tff(12241,plain,
% 1.84/2.03 ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12240, 224, 682, 1240, 1])).
% 1.84/2.03 tff(12242,plain,
% 1.84/2.03 (~b(s(z), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12241, 12234])).
% 1.84/2.03 tff(12243,plain,
% 1.84/2.03 (s(z) = elem!1),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[454, 12242, 12232])).
% 1.84/2.03 tff(12244,plain,
% 1.84/2.03 (b(s(z), z) <=> b(elem!1, z)),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12243])).
% 1.84/2.03 tff(12245,plain,
% 1.84/2.03 (b(elem!1, z) <=> b(s(z), z)),
% 1.84/2.03 inference(symmetry,[status(thm)],[12244])).
% 1.84/2.03 tff(12246,plain,
% 1.84/2.03 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12245])).
% 1.84/2.03 tff(12247,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[3633, 12246])).
% 1.84/2.03 tff(12248,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1, 12247])).
% 1.84/2.03 tff(12249,plain,(b(elem!1, z) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12250,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12249, 12219, 157, 543, 12216, 12217, 500, 682])).
% 1.84/2.03 tff(12251,plain,
% 1.84/2.03 (r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[194, 12250])).
% 1.84/2.03 tff(12252,plain,
% 1.84/2.03 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6020, 112, 12251, 656, 7479])).
% 1.84/2.03 tff(12253,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 10603, 12252])).
% 1.84/2.03 tff(12254,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12255,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12254, 12214, 12213, 684, 656, 2287, 682, 390, 157, 543, 500, 2505, 3919, 407])).
% 1.84/2.03 tff(12256,plain,((~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (elem!1 = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12257,plain,
% 1.84/2.03 (~r(z, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12256, 12211, 12110, 7240, 12209, 12200, 157, 543, 10085, 526, 12198, 10083, 88, 688])).
% 1.84/2.03 tff(12258,plain,
% 1.84/2.03 (b(z, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[5459, 12257])).
% 1.84/2.03 tff(12259,plain,
% 1.84/2.03 (~r(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10632, 293, 12211, 1287, 12200, 88, 3, 157, 688, 7672])).
% 1.84/2.03 tff(12260,plain,
% 1.84/2.03 (b(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[593, 12259])).
% 1.84/2.03 tff(12261,plain,
% 1.84/2.03 (~r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10916, 293, 149, 688, 3])).
% 1.84/2.03 tff(12262,plain,
% 1.84/2.03 (b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[194, 12261])).
% 1.84/2.03 tff(12263,plain,
% 1.84/2.03 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4320, 12260, 10083, 10085])).
% 1.84/2.03 tff(12264,plain,
% 1.84/2.03 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[530, 12263, 526])).
% 1.84/2.03 tff(12265,plain,
% 1.84/2.03 (b(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12249, 12264, 157, 543, 12260, 12262, 10085, 12209])).
% 1.84/2.03 tff(12266,plain,
% 1.84/2.03 (~b(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6470, 12262, 10085, 77])).
% 1.84/2.03 tff(12267,plain,
% 1.84/2.03 (r(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1476, 12266, 409])).
% 1.84/2.03 tff(12268,plain,
% 1.84/2.03 (~r(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1604, 12267, 543])).
% 1.84/2.03 tff(12269,plain,
% 1.84/2.03 (b(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1277, 12268, 88])).
% 1.84/2.03 tff(12270,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12271,plain,
% 1.84/2.03 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(12272,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[12271])).
% 1.84/2.03 tff(12273,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.03 inference(transitivity,[status(thm)],[12272, 12270])).
% 1.84/2.03 tff(12274,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(12275,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[12274, 12273])).
% 1.84/2.03 tff(12276,plain,
% 1.84/2.03 ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12275, 224])).
% 1.84/2.03 tff(12277,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12276, 12269, 12265, 12260, 12209, 77])).
% 1.84/2.03 tff(12278,plain,((~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (elem!1 = s(z)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | b(s(elem!1), elem!1) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12279,plain,
% 1.84/2.03 (~r(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12278, 12258, 88, 157, 543, 1287, 3, 688, 7672])).
% 1.84/2.03 tff(12280,plain,
% 1.84/2.03 (b(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[752, 12279])).
% 1.84/2.03 tff(12281,plain,
% 1.84/2.03 (~b(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12254, 12280, 12110, 12211, 7240, 12209, 12200, 157, 543, 10085, 526, 12198, 10083])).
% 1.84/2.03 tff(12282,plain,
% 1.84/2.03 (r(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1277, 12281, 88])).
% 1.84/2.03 tff(12283,plain,
% 1.84/2.03 (~r(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1604, 12282, 543])).
% 1.84/2.03 tff(12284,plain,
% 1.84/2.03 (b(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1476, 12283, 409])).
% 1.84/2.03 tff(12285,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6470, 12284, 10085, 12258])).
% 1.84/2.03 tff(12286,plain,
% 1.84/2.03 (r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[194, 12285])).
% 1.84/2.03 tff(12287,plain,
% 1.84/2.03 (~r(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10648, 12286, 12211])).
% 1.84/2.03 tff(12288,plain,
% 1.84/2.03 (b(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[593, 12287])).
% 1.84/2.03 tff(12289,plain,
% 1.84/2.03 (~r(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1259, 12286, 12282])).
% 1.84/2.03 tff(12290,plain,
% 1.84/2.03 (b(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[403, 12289, 157])).
% 1.84/2.03 tff(12291,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[613, 12290, 12288, 12209, 12280])).
% 1.84/2.03 tff(12292,plain,((~r(elem!1, s(elem!1))) | (elem!1 = z) | (elem!1 = s(z)) | b(s(elem!1), elem!1) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12293,plain,
% 1.84/2.03 (~r(elem!1, s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12292, 1287, 88, 157, 3, 688, 7672, 1090])).
% 1.84/2.03 tff(12294,plain,
% 1.84/2.03 (b(elem!1, s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[515, 12293, 327])).
% 1.84/2.03 tff(12295,plain,
% 1.84/2.03 (~b(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[509, 12294, 10085, 10083])).
% 1.84/2.03 tff(12296,plain,
% 1.84/2.03 ((~b(elem!1, z)) <=> (~b(s(s(s(z))), z))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[2434])).
% 1.84/2.03 tff(12297,plain,
% 1.84/2.03 (~b(s(s(s(z))), z)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[3633, 12296])).
% 1.84/2.03 tff(12298,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[7672, 12297])).
% 1.84/2.03 tff(12299,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12300,plain,
% 1.84/2.03 (~(s(s(s(z))) = elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12299, 12295, 7672])).
% 1.84/2.03 tff(12301,plain,
% 1.84/2.03 (~r(s(s(s(z))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[698, 689, 688])).
% 1.84/2.03 tff(12302,plain,
% 1.84/2.03 (~r(elem!1, s(s(s(z))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2420, 689, 688])).
% 1.84/2.03 tff(12303,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4200, 12302, 12301, 1090, 684, 362])).
% 1.84/2.03 tff(12304,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12305,plain,
% 1.84/2.03 (~r(z, s(s(s(z))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12304, 12110, 1090, 12300, 688])).
% 1.84/2.03 tff(12306,plain,
% 1.84/2.03 (b(z, s(s(s(z))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[100, 12305])).
% 1.84/2.03 tff(12307,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[9179, 12306, 1090, 7672])).
% 1.84/2.03 tff(12308,plain,
% 1.84/2.03 (r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[194, 12307])).
% 1.84/2.03 tff(12309,plain,
% 1.84/2.03 (~r(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10916, 12308, 149, 688, 3])).
% 1.84/2.03 tff(12310,plain,
% 1.84/2.03 (b(z, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[752, 12309])).
% 1.84/2.03 tff(12311,plain,
% 1.84/2.03 (r(elem!1, z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[403, 12295, 157])).
% 1.84/2.03 tff(12312,plain,
% 1.84/2.03 (~b(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4279, 12203, 408, 523, 363, 545])).
% 1.84/2.03 tff(12313,plain,
% 1.84/2.03 (~r(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10644, 12203, 157, 408, 724, 2506, 545, 523, 12201])).
% 1.84/2.03 tff(12314,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[593, 12313, 12312])).
% 1.84/2.03 tff(12315,plain,((~r(elem!1, s(s(elem!1)))) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12316,plain,
% 1.84/2.03 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12315, 10081, 157, 327, 319, 12311, 688])).
% 1.84/2.03 tff(12317,plain,
% 1.84/2.03 (~b(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[3687, 12316, 3, 12199, 12110])).
% 1.84/2.03 tff(12318,plain,
% 1.84/2.03 (r(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[653, 12317])).
% 1.84/2.03 tff(12319,plain,
% 1.84/2.03 (~r(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10648, 12308, 12318])).
% 1.84/2.03 tff(12320,plain,
% 1.84/2.03 (b(s(s(elem!1)), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[593, 12319])).
% 1.84/2.03 tff(12321,plain,
% 1.84/2.03 (~r(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1259, 12308, 12311])).
% 1.84/2.03 tff(12322,plain,
% 1.84/2.03 (b(elem!1, s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1277, 12321, 88])).
% 1.84/2.03 tff(12323,plain,
% 1.84/2.03 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4320, 1240, 407, 500])).
% 1.84/2.03 tff(12324,plain,
% 1.84/2.03 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[530, 12323, 1923])).
% 1.84/2.03 tff(12325,plain,
% 1.84/2.03 (~r(s(z), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[664, 12324, 656])).
% 1.84/2.03 tff(12326,plain,
% 1.84/2.03 (b(s(z), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[670, 12325, 415])).
% 1.84/2.03 tff(12327,plain,
% 1.84/2.03 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4154, 1240, 500, 1180])).
% 1.84/2.03 tff(12328,plain,
% 1.84/2.03 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1521, 12327, 523])).
% 1.84/2.03 tff(12329,plain,
% 1.84/2.03 (~r(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2649, 112, 12328, 656])).
% 1.84/2.03 tff(12330,plain,
% 1.84/2.03 (b(s(elem!1), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1476, 12329, 166])).
% 1.84/2.03 tff(12331,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[10452, 224, 501, 2896, 12330, 12326])).
% 1.84/2.03 tff(12332,plain,((~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(12333,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[12332, 12322, 12320, 12294, 409, 12318, 319, 10085, 12310, 10083])).
% 1.84/2.04 tff(12334,plain,(b(s(elem!1), elem!1) | (elem!1 = s(z)) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12335,plain,
% 1.84/2.04 (b(s(elem!1), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12334, 688, 83, 3, 1090, 7672, 157])).
% 1.84/2.04 tff(12336,plain,
% 1.84/2.04 (~r(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3332, 12102, 688])).
% 1.84/2.04 tff(12337,plain,
% 1.84/2.04 (b(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[454, 12336, 91])).
% 1.84/2.04 tff(12338,plain,
% 1.84/2.04 (~r(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4231, 568, 179])).
% 1.84/2.04 tff(12339,plain,
% 1.84/2.04 (b(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[670, 12338, 666])).
% 1.84/2.04 tff(12340,plain,
% 1.84/2.04 (~b(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4221, 12339, 1488, 684])).
% 1.84/2.04 tff(12341,plain,
% 1.84/2.04 (r(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[515, 12340, 2506])).
% 1.84/2.04 tff(12342,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4866, 112, 12341, 688, 568])).
% 1.84/2.04 tff(12343,plain,((~r(z, s(elem!1))) | (~r(z, elem!1)) | (elem!1 = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12344,plain,
% 1.84/2.04 (~r(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12343, 12337, 327, 12335, 688, 561, 12102])).
% 1.84/2.04 tff(12345,plain,
% 1.84/2.04 (b(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[625, 12344])).
% 1.84/2.04 tff(12346,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12347,plain,
% 1.84/2.04 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12348,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12347])).
% 1.84/2.04 tff(12349,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[12348, 12346])).
% 1.84/2.04 tff(12350,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(12351,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12350, 12349])).
% 1.84/2.04 tff(12352,plain,
% 1.84/2.04 (~r(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12351, 112, 179, 467])).
% 1.84/2.04 tff(12353,plain,
% 1.84/2.04 (b(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[670, 12352, 561])).
% 1.84/2.04 tff(12354,plain,
% 1.84/2.04 (~b(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4221, 12353, 1488, 684])).
% 1.84/2.04 tff(12355,plain,
% 1.84/2.04 (r(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[515, 12354, 327])).
% 1.84/2.04 tff(12356,plain,
% 1.84/2.04 (~r(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4310, 12355, 467])).
% 1.84/2.04 tff(12357,plain,
% 1.84/2.04 (b(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[403, 12356, 157])).
% 1.84/2.04 tff(12358,plain,
% 1.84/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1556, 102, 166, 467, 179])).
% 1.84/2.04 tff(12359,plain,
% 1.84/2.04 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1521, 12358, 523])).
% 1.84/2.04 tff(12360,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1513, 112, 12359, 102, 467])).
% 1.84/2.04 tff(12361,plain,((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12362,plain,
% 1.84/2.04 (~r(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12361, 467, 319, 409, 179])).
% 1.84/2.04 tff(12363,plain,
% 1.84/2.04 (b(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[593, 12362])).
% 1.84/2.04 tff(12364,plain,
% 1.84/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[613, 12363, 12357, 1180])).
% 1.84/2.04 tff(12365,plain,
% 1.84/2.04 (r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[558, 12364, 3])).
% 1.84/2.04 tff(12366,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[553, 12365, 12355])).
% 1.84/2.04 tff(12367,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[530, 12366, 526])).
% 1.84/2.04 tff(12368,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6004, 224, 1488, 12367, 2252, 684, 12353])).
% 1.84/2.04 tff(12369,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12370,plain,
% 1.84/2.04 (~r(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12369, 2252, 12335, 12337, 3, 12104, 12102, 157])).
% 1.84/2.04 tff(12371,plain,
% 1.84/2.04 (b(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[498, 12370])).
% 1.84/2.04 tff(12372,plain,
% 1.84/2.04 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[553, 7686, 949])).
% 1.84/2.04 tff(12373,plain,
% 1.84/2.04 (b(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[541, 517, 3, 406])).
% 1.84/2.04 tff(12374,plain,
% 1.84/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3685, 12373, 2252, 684])).
% 1.84/2.04 tff(12375,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[558, 12374, 12372, 3])).
% 1.84/2.04 tff(12376,plain,(b(elem!1, s(elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12377,plain,
% 1.84/2.04 (b(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12376, 406, 2252, 12337, 3])).
% 1.84/2.04 tff(12378,plain,
% 1.84/2.04 (~b(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[509, 12377, 12371, 12345])).
% 1.84/2.04 tff(12379,plain,
% 1.84/2.04 (r(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[403, 12378, 157])).
% 1.84/2.04 tff(12380,plain,
% 1.84/2.04 (~r(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1259, 12379, 12102])).
% 1.84/2.04 tff(12381,plain,
% 1.84/2.04 (b(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1277, 12380, 83])).
% 1.84/2.04 tff(12382,plain,
% 1.84/2.04 (~b(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4221, 12377, 12335, 12337])).
% 1.84/2.04 tff(12383,plain,
% 1.84/2.04 (r(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[670, 12382, 561])).
% 1.84/2.04 tff(12384,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[9052, 112, 949, 12383])).
% 1.84/2.04 tff(12385,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[901, 12384])).
% 1.84/2.04 tff(12386,plain,
% 1.84/2.04 (~b(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5584, 224, 12337, 12385, 12381])).
% 1.84/2.04 tff(12387,plain,
% 1.84/2.04 (~(s(s(s(z))) = elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12299, 12378, 7672])).
% 1.84/2.04 tff(12388,plain,
% 1.84/2.04 (r(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[360, 12386, 353])).
% 1.84/2.04 tff(12389,plain,
% 1.84/2.04 (~r(s(s(s(z))), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5988, 12388, 2, 1090, 2252])).
% 1.84/2.04 tff(12390,plain,
% 1.84/2.04 (~r(elem!1, s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[7684, 12388, 7672, 2, 688])).
% 1.84/2.04 tff(12391,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2951, 12390, 12389, 1090, 12387, 12386, 12336])).
% 1.84/2.04 tff(12392,plain,(b(s(s(elem!1)), s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, elem!1)) | (~b(s(z), s(s(elem!1)))) | (elem!1 = z) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12393,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12392, 2252, 7672, 2, 688, 1090, 157, 3])).
% 1.84/2.04 tff(12394,plain,
% 1.84/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4124, 12393, 12345, 12104])).
% 1.84/2.04 tff(12395,plain,
% 1.84/2.04 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1521, 12394, 319])).
% 1.84/2.04 tff(12396,plain,
% 1.84/2.04 (~b(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4320, 12393, 12345, 12371])).
% 1.84/2.04 tff(12397,plain,
% 1.84/2.04 (r(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[593, 12396])).
% 1.84/2.04 tff(12398,plain,
% 1.84/2.04 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2346, 12397, 688])).
% 1.84/2.04 tff(12399,plain,
% 1.84/2.04 (r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3687, 12398, 3, 2252, 12337])).
% 1.84/2.04 tff(12400,plain,
% 1.84/2.04 (b(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[360, 12398, 353])).
% 1.84/2.04 tff(12401,plain,
% 1.84/2.04 (~b(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1496, 12400, 12335, 12393])).
% 1.84/2.04 tff(12402,plain,
% 1.84/2.04 (r(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[515, 12401, 327])).
% 1.84/2.04 tff(12403,plain,
% 1.84/2.04 (((~![X0: $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(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12404,plain,
% 1.84/2.04 (((~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(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12405,plain,
% 1.84/2.04 (((~![X0: $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(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12404])).
% 1.84/2.04 tff(12406,plain,
% 1.84/2.04 (((~![X0: $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(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[12405, 12403])).
% 1.84/2.04 tff(12407,plain,
% 1.84/2.04 ((~![X0: $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))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(12408,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12407, 12406])).
% 1.84/2.04 tff(12409,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12408, 112, 12402, 12399, 12395])).
% 1.84/2.04 tff(12410,plain,((~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12411,plain,
% 1.84/2.04 (~b(s(z), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12410, 688, 3, 7672, 2, 1090, 157])).
% 1.84/2.04 tff(12412,plain,
% 1.84/2.04 (r(s(z), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[653, 12411])).
% 1.84/2.04 tff(12413,plain,
% 1.84/2.04 (b(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5459, 12105])).
% 1.84/2.04 tff(12414,plain,
% 1.84/2.04 (~b(s(s(s(z))), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10094, 224, 12413, 3656, 7672])).
% 1.84/2.04 tff(12415,plain,
% 1.84/2.04 (r(s(s(s(z))), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[925, 12414])).
% 1.84/2.04 tff(12416,plain,
% 1.84/2.04 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6496, 416, 12412])).
% 1.84/2.04 tff(12417,plain,
% 1.84/2.04 (b(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[360, 12416, 353])).
% 1.84/2.04 tff(12418,plain,
% 1.84/2.04 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10872, 102, 157, 656, 77, 1, 390, 88])).
% 1.84/2.04 tff(12419,plain,
% 1.84/2.04 (b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[558, 12418, 3])).
% 1.84/2.04 tff(12420,plain,
% 1.84/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2541, 224, 1488, 12419, 390])).
% 1.84/2.04 tff(12421,plain,
% 1.84/2.04 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1521, 12420, 319])).
% 1.84/2.04 tff(12422,plain,
% 1.84/2.04 (~r(s(elem!1), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2649, 112, 12421, 656])).
% 1.84/2.04 tff(12423,plain,
% 1.84/2.04 (b(s(elem!1), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1476, 12422, 409])).
% 1.84/2.04 tff(12424,plain,
% 1.84/2.04 (~b(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6470, 12423, 77, 1])).
% 1.84/2.04 tff(12425,plain,
% 1.84/2.04 (r(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[498, 12424])).
% 1.84/2.04 tff(12426,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1513, 112, 12421, 102, 12425])).
% 1.84/2.04 tff(12427,plain,((~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12428,plain,
% 1.84/2.04 (~r(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12427, 12413, 3656, 12412, 12335, 12417, 3, 157, 83])).
% 1.84/2.04 tff(12429,plain,
% 1.84/2.04 (b(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[593, 12428])).
% 1.84/2.04 tff(12430,plain,
% 1.84/2.04 (~b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1249, 12429, 12413, 3656])).
% 1.84/2.04 tff(12431,plain,
% 1.84/2.04 (r(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[901, 12430])).
% 1.84/2.04 tff(12432,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5342, 112, 12431, 12415])).
% 1.84/2.04 tff(12433,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[147, 12432, 2])).
% 1.84/2.04 tff(12434,plain,
% 1.84/2.04 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[9107, 12415, 12412])).
% 1.84/2.04 tff(12435,plain,
% 1.84/2.04 (b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[135, 68, 132, 12434])).
% 1.84/2.04 tff(12436,plain,
% 1.84/2.04 (~b(z, s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[9179, 3656, 1090, 7672])).
% 1.84/2.04 tff(12437,plain,
% 1.84/2.04 (r(z, s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[100, 12436])).
% 1.84/2.04 tff(12438,plain,
% 1.84/2.04 (~r(s(s(z)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3196, 196, 3188])).
% 1.84/2.04 tff(12439,plain,
% 1.84/2.04 (b(s(s(z)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2726, 12438])).
% 1.84/2.04 tff(12440,plain,
% 1.84/2.04 (~r(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3455, 196, 689])).
% 1.84/2.04 tff(12441,plain,
% 1.84/2.04 (b(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[281, 12440])).
% 1.84/2.04 tff(12442,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2846, 12441, 12439, 77, 1])).
% 1.84/2.04 tff(12443,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12444,plain,
% 1.84/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12443, 12413, 3656, 12437, 12415])).
% 1.84/2.04 tff(12445,plain,
% 1.84/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[249, 12444])).
% 1.84/2.04 tff(12446,plain,
% 1.84/2.04 (~b(s(s(z)), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6362, 12445, 12435, 12433])).
% 1.84/2.04 tff(12447,plain,
% 1.84/2.04 (r(s(s(z)), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[265, 12446, 1108])).
% 1.84/2.04 tff(12448,plain,
% 1.84/2.04 (~r(s(z), s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5333, 12447, 12412])).
% 1.84/2.04 tff(12449,plain,
% 1.84/2.04 (b(s(z), s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1071, 12448])).
% 1.84/2.04 tff(12450,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12451,plain,
% 1.84/2.04 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12452,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12451])).
% 1.84/2.04 tff(12453,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[12452, 12450])).
% 1.84/2.04 tff(12454,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(12455,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12454, 12453])).
% 1.84/2.04 tff(12456,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12455, 224, 3656, 12445, 1090, 7672, 12449])).
% 1.84/2.04 tff(12457,plain,((~r(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12458,plain,
% 1.84/2.04 (~r(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12457, 7066, 12090, 2, 3, 11, 7067])).
% 1.84/2.04 tff(12459,plain,
% 1.84/2.04 (b(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[454, 12458, 91])).
% 1.84/2.04 tff(12460,plain,
% 1.84/2.04 (~r(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12457, 7672, 12090, 2, 3, 157, 688])).
% 1.84/2.04 tff(12461,plain,
% 1.84/2.04 (b(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[454, 12460, 91])).
% 1.84/2.04 tff(12462,plain,
% 1.84/2.04 (b(s(elem!1), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12334, 688, 83, 3, 12090, 7672, 157])).
% 1.84/2.04 tff(12463,plain,
% 1.84/2.04 (~b(s(z), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12410, 688, 3, 7672, 2, 12090, 157])).
% 1.84/2.04 tff(12464,plain,
% 1.84/2.04 (r(s(z), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[653, 12463])).
% 1.84/2.04 tff(12465,plain,
% 1.84/2.04 (~r(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12343, 4223, 327, 12462, 688, 561, 12461])).
% 1.84/2.04 tff(12466,plain,
% 1.84/2.04 (b(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[625, 12465])).
% 1.84/2.04 tff(12467,plain,
% 1.84/2.04 (~r(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10648, 4223, 12464])).
% 1.84/2.04 tff(12468,plain,
% 1.84/2.04 (b(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[593, 12467])).
% 1.84/2.04 tff(12469,plain,
% 1.84/2.04 (~r(z, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10916, 4223, 91, 688, 3])).
% 1.84/2.04 tff(12470,plain,
% 1.84/2.04 (b(z, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[752, 12469])).
% 1.84/2.04 tff(12471,plain,
% 1.84/2.04 (~r(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12457, 7672, 1090, 2, 3, 157, 688])).
% 1.84/2.04 tff(12472,plain,
% 1.84/2.04 (b(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[454, 12471, 91])).
% 1.84/2.04 tff(12473,plain,
% 1.84/2.04 (~r(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12343, 179, 327, 12335, 688, 561, 12472])).
% 1.84/2.04 tff(12474,plain,
% 1.84/2.04 (b(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[625, 12473])).
% 1.84/2.04 tff(12475,plain,
% 1.84/2.04 (~r(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10648, 179, 12412])).
% 1.84/2.04 tff(12476,plain,
% 1.84/2.04 (b(s(s(elem!1)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[593, 12475])).
% 1.84/2.04 tff(12477,plain,
% 1.84/2.04 (~r(z, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10916, 179, 91, 688, 3])).
% 1.84/2.04 tff(12478,plain,
% 1.84/2.04 (b(z, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[752, 12477])).
% 1.84/2.04 tff(12479,plain,
% 1.84/2.04 (~r(elem!1, s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[7684, 3340, 7672, 2, 688])).
% 1.84/2.04 tff(12480,plain,
% 1.84/2.04 (b(s(elem!1), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1476, 483, 409])).
% 1.84/2.04 tff(12481,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[539, 12355, 1181])).
% 1.84/2.04 tff(12482,plain,
% 1.84/2.04 (~b(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4322, 543, 1181, 1240, 2505, 363])).
% 1.84/2.04 tff(12483,plain,
% 1.84/2.04 (~r(z, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[604, 543, 363])).
% 1.84/2.04 tff(12484,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[625, 12483, 12482])).
% 1.84/2.04 tff(12485,plain,((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12486,plain,
% 1.84/2.04 (~r(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12485, 12355, 1181, 1240, 526])).
% 1.84/2.04 tff(12487,plain,
% 1.84/2.04 (b(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[403, 12486, 157])).
% 1.84/2.04 tff(12488,plain,
% 1.84/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[613, 12487, 1240, 1180])).
% 1.84/2.04 tff(12489,plain,
% 1.84/2.04 (~r(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[10522, 12488, 3, 12353, 12481, 12480])).
% 1.84/2.04 tff(12490,plain,
% 1.84/2.04 (b(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1277, 12489, 88])).
% 1.84/2.04 tff(12491,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12492,plain,
% 1.84/2.04 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(12493,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12492])).
% 1.84/2.04 tff(12494,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[12493, 12491])).
% 1.84/2.04 tff(12495,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(12496,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12495, 12494])).
% 1.84/2.04 tff(12497,plain,
% 1.84/2.04 (~b(elem!1, s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12496, 224, 12487, 12490, 1090, 7672])).
% 1.84/2.04 tff(12498,plain,
% 1.84/2.04 (elem!1 = s(s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[388, 12497, 2440])).
% 1.84/2.04 tff(12499,plain,
% 1.84/2.04 (s(s(s(z))) = elem!1),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3418, 12498])).
% 1.84/2.04 tff(12500,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4136, 12499, 12480])).
% 1.84/2.04 tff(12501,plain,
% 1.84/2.04 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12498])).
% 1.84/2.04 tff(12502,plain,
% 1.84/2.04 (b(s(s(s(z))), s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12490, 12501])).
% 1.84/2.04 tff(12503,plain,
% 1.84/2.04 (s(elem!1) = s(s(s(s(z))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12498])).
% 1.84/2.04 tff(12504,plain,
% 1.84/2.04 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12503])).
% 1.84/2.04 tff(12505,plain,
% 1.84/2.04 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[12498])).
% 1.84/2.04 tff(12506,plain,
% 1.84/2.04 (b(s(elem!1), s(s(s(z))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[1488, 12505])).
% 1.84/2.04 tff(12507,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[12506, 12504])).
% 1.84/2.04 tff(12508,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1579, 12507, 12502, 1090, 12500])).
% 1.84/2.04 tff(12509,plain,((~r(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | r(elem!1, s(s(s(z)))) | (~b(s(s(s(z))), z)) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (elem!1 = z) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(12510,plain,
% 1.84/2.04 (~r(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[12509, 12479, 12335, 1090, 7672, 83, 3, 12476, 12478, 157, 3340, 12472, 179])).
% 1.84/2.04 tff(12511,plain,
% 1.84/2.04 (b(s(elem!1), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[498, 12510])).
% 1.84/2.04 tff(12512,plain,
% 1.84/2.04 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4320, 12511, 12476, 12474])).
% 1.84/2.04 tff(12513,plain,
% 1.84/2.04 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[530, 12512, 526])).
% 1.84/2.04 tff(12514,plain,
% 1.84/2.04 (~r(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[664, 12513, 12412])).
% 1.84/2.04 tff(12515,plain,
% 1.84/2.04 (b(elem!1, s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[541, 12512, 3, 354])).
% 1.84/2.04 tff(12516,plain,
% 1.84/2.04 (~b(s(z), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4221, 12515, 12335, 12472])).
% 1.84/2.05 tff(12517,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[670, 12516, 12514, 561])).
% 1.84/2.05 tff(12518,plain,(b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12519,plain,
% 1.84/2.05 (b(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12518, 4223, 12090, 7672, 157, 3, 2, 688])).
% 1.84/2.05 tff(12520,plain,
% 1.84/2.05 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[613, 12357, 1240, 1180])).
% 1.84/2.05 tff(12521,plain,
% 1.84/2.05 (r(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[558, 12520, 3])).
% 1.84/2.05 tff(12522,plain,
% 1.84/2.05 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[553, 12521, 12355])).
% 1.84/2.05 tff(12523,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[530, 12522, 526])).
% 1.84/2.05 tff(12524,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12525,plain,
% 1.84/2.05 (((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12526,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12525])).
% 1.84/2.05 tff(12527,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[12526, 12524])).
% 1.84/2.05 tff(12528,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(12529,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12528, 12527])).
% 1.84/2.05 tff(12530,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12529, 224, 12523, 12357, 1240, 390, 407])).
% 1.84/2.05 tff(12531,plain,((~r(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (elem!1 = z) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12532,plain,
% 1.84/2.05 (~r(s(elem!1), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12531, 12468, 12519, 12466, 3, 12470, 157, 12462, 12461, 4223])).
% 1.84/2.05 tff(12533,plain,
% 1.84/2.05 (b(s(elem!1), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[498, 12532])).
% 1.84/2.05 tff(12534,plain,
% 1.84/2.05 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4320, 12533, 12468, 12466])).
% 1.84/2.05 tff(12535,plain,
% 1.84/2.05 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[530, 12534, 526])).
% 1.84/2.05 tff(12536,plain,
% 1.84/2.05 (~r(s(z), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[664, 12535, 12464])).
% 1.84/2.05 tff(12537,plain,
% 1.84/2.05 (b(s(z), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[670, 12536, 561])).
% 1.84/2.05 tff(12538,plain,
% 1.84/2.05 (~b(elem!1, s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4221, 12537, 12462, 12461])).
% 1.84/2.05 tff(12539,plain,
% 1.84/2.05 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4154, 12533, 12468, 12470])).
% 1.84/2.05 tff(12540,plain,
% 1.84/2.05 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1521, 12539, 319])).
% 1.84/2.05 tff(12541,plain,
% 1.84/2.05 (~(s(elem!1) = s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3988, 4208])).
% 1.84/2.05 tff(12542,plain,
% 1.84/2.05 (~(elem!1 = z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3984, 12541])).
% 1.84/2.05 tff(12543,plain,
% 1.84/2.05 (~(z = elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[338, 12542])).
% 1.84/2.05 tff(12544,plain,
% 1.84/2.05 (r(z, elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[289, 12543, 4538])).
% 1.84/2.05 tff(12545,plain,
% 1.84/2.05 (~r(elem!1, z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2665, 12541, 1700, 1488, 682, 390, 129, 4223])).
% 1.84/2.05 tff(12546,plain,
% 1.84/2.05 (b(elem!1, z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[403, 12545, 12542])).
% 1.84/2.05 tff(12547,plain,
% 1.84/2.05 (~b(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[613, 12546, 682, 1240])).
% 1.84/2.05 tff(12548,plain,
% 1.84/2.05 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[580, 68, 12547])).
% 1.84/2.05 tff(12549,plain,
% 1.84/2.05 (r(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12548, 567])).
% 1.84/2.05 tff(12550,plain,
% 1.84/2.05 (~r(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3061, 4223, 12544, 12549])).
% 1.84/2.05 tff(12551,plain,
% 1.84/2.05 (b(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[653, 12550])).
% 1.84/2.05 tff(12552,plain,
% 1.84/2.05 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12553,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12552])).
% 1.84/2.05 tff(12554,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[12553, 629])).
% 1.84/2.05 tff(12555,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(12556,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12555, 12554])).
% 1.84/2.05 tff(12557,plain,
% 1.84/2.05 (~b(s(z), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12556, 224, 682, 12551, 390])).
% 1.84/2.05 tff(12558,plain,
% 1.84/2.05 (r(s(z), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[454, 12557, 129])).
% 1.84/2.05 tff(12559,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2464, 112, 4223, 12558, 12544])).
% 1.84/2.05 tff(12560,plain,(b(s(z), z) | (s(z) = elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12561,plain,
% 1.84/2.05 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12560, 12540, 91, 12462, 3998, 12519, 12468, 4538])).
% 1.84/2.05 tff(12562,plain,
% 1.84/2.05 (r(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[558, 12561, 3])).
% 1.84/2.05 tff(12563,plain,
% 1.84/2.05 (~r(elem!1, s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[553, 12562, 12535])).
% 1.84/2.05 tff(12564,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[515, 12563, 12538, 327])).
% 1.84/2.05 tff(12565,plain,(b(s(z), z) | (elem!1 = s(s(elem!1))) | b(z, elem!1) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12566,plain,
% 1.84/2.05 (b(s(z), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12565, 11, 4538, 3, 7066, 2, 7067])).
% 1.84/2.05 tff(12567,plain,
% 1.84/2.05 (~b(z, s(s(s(z))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[9179, 12566, 12090, 7066])).
% 1.84/2.05 tff(12568,plain,
% 1.84/2.05 (r(z, s(s(s(z))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[100, 12567])).
% 1.84/2.05 tff(12569,plain,
% 1.84/2.05 (s(s(s(z))) = elem!1),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12304, 12568, 12090, 12459, 7067])).
% 1.84/2.05 tff(12570,plain,
% 1.84/2.05 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12569])).
% 1.84/2.05 tff(12571,plain,
% 1.84/2.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.05 inference(symmetry,[status(thm)],[12570])).
% 1.84/2.05 tff(12572,plain,
% 1.84/2.05 (s(s(s(s(z)))) = s(elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12569])).
% 1.84/2.05 tff(12573,plain,
% 1.84/2.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12572])).
% 1.84/2.05 tff(12574,plain,
% 1.84/2.05 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.84/2.05 inference(symmetry,[status(thm)],[12573])).
% 1.84/2.05 tff(12575,plain,
% 1.84/2.05 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[12574, 12571])).
% 1.84/2.05 tff(12576,plain,
% 1.84/2.05 (b(s(elem!1), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12334, 7067, 83, 3, 12090, 7066, 11])).
% 1.84/2.05 tff(12577,plain,
% 1.84/2.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12576, 12575])).
% 1.84/2.05 tff(12578,plain,
% 1.84/2.05 (~b(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12410, 7067, 3, 7066, 2, 12090, 11])).
% 1.84/2.05 tff(12579,plain,
% 1.84/2.05 (r(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[653, 12578])).
% 1.84/2.05 tff(12580,plain,
% 1.84/2.05 (r(s(s(s(z))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12569])).
% 1.84/2.05 tff(12581,plain,
% 1.84/2.05 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.05 inference(symmetry,[status(thm)],[12580])).
% 1.84/2.05 tff(12582,plain,
% 1.84/2.05 (r(z, s(s(s(z))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[100, 12091])).
% 1.84/2.05 tff(12583,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[11579, 9139, 7672, 12582])).
% 1.84/2.05 tff(12584,plain,
% 1.84/2.05 (b(s(elem!1), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12334, 688, 88, 3, 1090, 7672, 157])).
% 1.84/2.05 tff(12585,plain,
% 1.84/2.05 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2346, 9146, 688])).
% 1.84/2.05 tff(12586,plain,
% 1.84/2.05 (b(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[360, 12585, 353])).
% 1.84/2.05 tff(12587,plain,
% 1.84/2.05 (~b(z, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12427, 12586, 1, 656, 12584, 9146, 3, 157, 88])).
% 1.84/2.05 tff(12588,plain,
% 1.84/2.05 (r(z, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[5459, 12587])).
% 1.84/2.05 tff(12589,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4621, 12588, 12582])).
% 1.84/2.05 tff(12590,plain,
% 1.84/2.05 (b(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[925, 12589])).
% 1.84/2.05 tff(12591,plain,
% 1.84/2.05 (~r(s(s(elem!1)), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[5928, 12588, 9146])).
% 1.84/2.05 tff(12592,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[901, 12591])).
% 1.84/2.05 tff(12593,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3206, 12592, 12590, 1090, 12583])).
% 1.84/2.05 tff(12594,plain,(b(s(s(elem!1)), z) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (elem!1 = s(z)) | (~r(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12595,plain,
% 1.84/2.05 (b(s(s(elem!1)), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12594, 12566, 12090, 12579, 3, 11, 83, 7067, 7066])).
% 1.84/2.05 tff(12596,plain,
% 1.84/2.05 (b(elem!1, z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12299, 12569, 7066])).
% 1.84/2.05 tff(12597,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12598,plain,
% 1.84/2.05 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12599,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12598])).
% 1.84/2.05 tff(12600,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[12599, 12597])).
% 1.84/2.05 tff(12601,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(12602,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12601, 12600])).
% 1.84/2.05 tff(12603,plain,
% 1.84/2.05 (~b(s(z), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12602, 224, 12576, 12596, 12566, 12459])).
% 1.84/2.05 tff(12604,plain,
% 1.84/2.05 (r(s(z), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[670, 12603, 4204])).
% 1.84/2.05 tff(12605,plain,
% 1.84/2.05 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[664, 12604, 12579])).
% 1.84/2.05 tff(12606,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[530, 12605, 526])).
% 1.84/2.05 tff(12607,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12608,plain,
% 1.84/2.05 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(12609,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12608])).
% 1.84/2.05 tff(12610,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[12609, 12607])).
% 1.84/2.05 tff(12611,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(12612,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12611, 12610])).
% 1.84/2.05 tff(12613,plain,
% 1.84/2.05 (~b(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12612, 224, 12576, 12606, 12596, 12595])).
% 1.84/2.05 tff(12614,plain,
% 1.84/2.05 (r(elem!1, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[9608, 12613, 7066, 12568, 12595, 12569])).
% 1.84/2.05 tff(12615,plain,
% 1.84/2.05 (r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12614, 12581])).
% 1.84/2.05 tff(12616,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[9107, 12615, 12579])).
% 1.84/2.05 tff(12617,plain,
% 1.84/2.05 (b(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[925, 12616])).
% 1.84/2.05 tff(12618,plain,
% 1.84/2.05 (~b(s(s(s(s(z)))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1579, 12617, 12090, 12577])).
% 1.84/2.05 tff(12619,plain,
% 1.84/2.05 (r(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[360, 12613, 353])).
% 1.84/2.05 tff(12620,plain,
% 1.84/2.05 (~r(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3500, 12619, 7067])).
% 1.84/2.05 tff(12621,plain,
% 1.84/2.05 (b(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[752, 12620])).
% 1.84/2.05 tff(12622,plain,
% 1.84/2.05 (~b(z, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[10953, 12615, 7066, 12566, 12595, 12621])).
% 1.84/2.05 tff(12623,plain,
% 1.84/2.05 (r(z, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[5459, 12622])).
% 1.84/2.05 tff(12624,plain,
% 1.84/2.05 (~r(elem!1, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[9964, 112, 12614, 12579])).
% 1.84/2.05 tff(12625,plain,
% 1.84/2.05 (b(elem!1, s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1277, 12624, 83])).
% 1.84/2.05 tff(12626,plain,
% 1.84/2.05 (~r(s(elem!1), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[5658, 12625, 7067, 12569, 353, 12459, 3, 12623])).
% 1.84/2.05 tff(12627,plain,
% 1.84/2.05 (b(s(elem!1), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1476, 12626, 160])).
% 1.84/2.05 tff(12628,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4136, 12627, 12618, 12569])).
% 1.84/2.05 tff(12629,plain,((z = elem!1) | (elem!1 = s(s(elem!1))) | b(z, elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12630,plain,
% 1.84/2.05 (z = elem!1),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12629, 4538, 3, 2])).
% 1.84/2.05 tff(12631,plain,
% 1.84/2.05 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12630])).
% 1.84/2.05 tff(12632,plain,
% 1.84/2.05 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.84/2.05 inference(symmetry,[status(thm)],[12631])).
% 1.84/2.05 tff(12633,plain,
% 1.84/2.05 (s(z) = s(elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12630])).
% 1.84/2.05 tff(12634,plain,
% 1.84/2.05 (s(s(z)) = s(s(elem!1))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12633])).
% 1.84/2.05 tff(12635,plain,
% 1.84/2.05 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12634])).
% 1.84/2.05 tff(12636,plain,
% 1.84/2.05 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12635])).
% 1.84/2.05 tff(12637,plain,
% 1.84/2.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.84/2.05 inference(symmetry,[status(thm)],[12636])).
% 1.84/2.05 tff(12638,plain,
% 1.84/2.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.84/2.05 inference(transitivity,[status(thm)],[12637, 12632])).
% 1.84/2.05 tff(12639,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.84/2.05 tff(12640,plain,
% 1.84/2.05 (s(s(s(elem!1))) = z),
% 1.84/2.05 inference(transitivity,[status(thm)],[12639, 1701])).
% 1.84/2.05 tff(12641,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1362, 12640])).
% 1.84/2.05 tff(12642,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(12643,plain,
% 1.84/2.05 (~(s(s(s(elem!1))) = elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[12642, 12630])).
% 1.84/2.05 tff(12644,plain,
% 1.84/2.05 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.84/2.05 inference(symmetry,[status(thm)],[1926])).
% 1.84/2.05 tff(12645,plain,
% 1.84/2.05 (b(s(elem!1), s(s(s(z))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[1090, 4645])).
% 1.84/2.05 tff(12646,plain,
% 1.84/2.05 (b(s(elem!1), s(s(s(elem!1))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12645, 4644])).
% 1.84/2.05 tff(12647,plain,
% 1.84/2.05 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[1619, 1617])).
% 1.84/2.05 tff(12648,plain,
% 1.84/2.05 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.84/2.05 inference(symmetry,[status(thm)],[12647])).
% 1.84/2.05 tff(12649,plain,
% 1.84/2.05 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.84/2.05 inference(symmetry,[status(thm)],[11406])).
% 1.84/2.05 tff(12650,plain,
% 1.84/2.05 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12649])).
% 1.84/2.05 tff(12651,plain,
% 1.84/2.05 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.84/2.05 inference(transitivity,[status(thm)],[1631, 1655])).
% 1.84/2.05 tff(12652,plain,
% 1.84/2.05 (r(s(s(s(elem!1))), elem!1)),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[73, 12651])).
% 1.84/2.05 tff(12653,plain,
% 1.84/2.05 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1662, 112, 10081, 12652])).
% 1.84/2.05 tff(12654,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[12653, 12650])).
% 1.84/2.05 tff(12655,plain,
% 1.84/2.05 (b(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[925, 12654])).
% 1.84/2.05 tff(12656,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.84/2.05 inference(symmetry,[status(thm)],[11250])).
% 1.84/2.05 tff(12657,plain,
% 1.84/2.05 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.05 tff(12658,plain,
% 1.84/2.05 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[12657])).
% 1.84/2.05 tff(12659,plain,
% 1.84/2.05 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.84/2.05 inference(symmetry,[status(thm)],[1634])).
% 1.84/2.05 tff(12660,plain,
% 1.84/2.05 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.84/2.05 inference(symmetry,[status(thm)],[1633])).
% 1.84/2.05 tff(12661,plain,
% 1.84/2.05 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12660, 12659])).
% 1.84/2.06 tff(12662,plain,
% 1.84/2.06 (r(s(s(elem!1)), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[333, 102, 1668])).
% 1.84/2.06 tff(12663,plain,
% 1.84/2.06 (~r(s(elem!1), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6557, 12662, 408])).
% 1.84/2.06 tff(12664,plain,
% 1.84/2.06 (b(s(elem!1), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1521, 12663, 319])).
% 1.84/2.06 tff(12665,plain,
% 1.84/2.06 (~r(s(z), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[10648, 102, 1648])).
% 1.84/2.06 tff(12666,plain,
% 1.84/2.06 (b(s(z), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[653, 12665])).
% 1.84/2.06 tff(12667,plain,
% 1.84/2.06 (~r(s(s(s(z))), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[5988, 12666, 2, 1090, 12662])).
% 1.84/2.06 tff(12668,plain,
% 1.84/2.06 (b(s(s(s(z))), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[374, 12667, 4549])).
% 1.84/2.06 tff(12669,plain,
% 1.84/2.06 (b(s(s(s(elem!1))), elem!1)),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12668, 10978])).
% 1.84/2.06 tff(12670,plain,
% 1.84/2.06 (~r(s(s(elem!1)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[895, 102, 1648])).
% 1.84/2.06 tff(12671,plain,
% 1.84/2.06 (b(s(s(elem!1)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[901, 12670])).
% 1.84/2.06 tff(12672,plain,
% 1.84/2.06 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.84/2.06 inference(symmetry,[status(thm)],[4600])).
% 1.84/2.06 tff(12673,plain,
% 1.84/2.06 (b(s(s(s(z))), z)),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12668, 12672])).
% 1.84/2.06 tff(12674,plain,
% 1.84/2.06 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12671, 11250])).
% 1.84/2.06 tff(12675,plain,
% 1.84/2.06 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11016, 12674, 1717, 1854, 408, 12662, 12664])).
% 1.84/2.06 tff(12676,plain,
% 1.84/2.06 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1777, 12675, 1615])).
% 1.84/2.06 tff(12677,plain,
% 1.84/2.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[5914, 12662, 1644, 1733])).
% 1.84/2.06 tff(12678,plain,
% 1.84/2.06 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[1241, 11250])).
% 1.84/2.06 tff(12679,plain,
% 1.84/2.06 (~r(elem!1, s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[7935, 543, 335, 12678, 1181])).
% 1.84/2.06 tff(12680,plain,
% 1.84/2.06 (b(elem!1, s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[388, 12679, 4561])).
% 1.84/2.06 tff(12681,plain,
% 1.84/2.06 (b(elem!1, s(s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12680, 4559])).
% 1.84/2.06 tff(12682,plain,
% 1.84/2.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11024, 224, 7305, 11073, 12681])).
% 1.84/2.06 tff(12683,plain,
% 1.84/2.06 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 12682])).
% 1.84/2.06 tff(12684,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[4702, 543, 335, 1181, 1390, 12678])).
% 1.84/2.06 tff(12685,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11549, 12684, 335])).
% 1.84/2.06 tff(12686,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1884, 12685])).
% 1.84/2.06 tff(12687,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12686, 1786])).
% 1.84/2.06 tff(12688,plain,
% 1.84/2.06 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11048, 112, 12687, 12683])).
% 1.84/2.06 tff(12689,plain,
% 1.84/2.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 12688])).
% 1.84/2.06 tff(12690,plain,
% 1.84/2.06 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[1687, 1620])).
% 1.84/2.06 tff(12691,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[12690])).
% 1.84/2.06 tff(12692,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[1786, 12691])).
% 1.84/2.06 tff(12693,plain,
% 1.84/2.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12686, 12692])).
% 1.84/2.06 tff(12694,plain,
% 1.84/2.06 (b(s(z), s(s(z)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[1390, 11242])).
% 1.84/2.06 tff(12695,plain,
% 1.84/2.06 (b(s(s(z)), s(z))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[1241, 11251])).
% 1.84/2.06 tff(12696,plain,
% 1.84/2.06 (b(z, s(s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12680, 11564])).
% 1.84/2.06 tff(12697,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.84/2.06 tff(12698,plain,
% 1.84/2.06 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11048, 112, 1788, 12697])).
% 1.84/2.06 tff(12699,plain,
% 1.84/2.06 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 12698])).
% 1.84/2.06 tff(12700,plain,
% 1.84/2.06 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[3206, 560, 1090, 1241])).
% 1.84/2.06 tff(12701,plain,
% 1.84/2.06 (r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[147, 12700, 2])).
% 1.84/2.06 tff(12702,plain,
% 1.84/2.06 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12701, 4639])).
% 1.84/2.06 tff(12703,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12704,plain,
% 1.84/2.06 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12705,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(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(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12704])).
% 1.84/2.06 tff(12706,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(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(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12705, 12703])).
% 1.84/2.06 tff(12707,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(12708,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12707, 12706])).
% 1.84/2.06 tff(12709,plain,
% 1.84/2.06 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12708, 112, 12697, 12702])).
% 1.84/2.06 tff(12710,plain,
% 1.84/2.06 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 12709])).
% 1.84/2.06 tff(12711,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, 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(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12712,plain,
% 1.84/2.06 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12713,plain,
% 1.84/2.06 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12712])).
% 1.84/2.06 tff(12714,plain,
% 1.84/2.06 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12713, 12711])).
% 1.84/2.06 tff(12715,plain,
% 1.84/2.06 ((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(12716,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12715, 12714])).
% 1.84/2.06 tff(12717,plain,
% 1.84/2.06 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12716, 112, 1788, 12702])).
% 1.84/2.06 tff(12718,plain,
% 1.84/2.06 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1422, 68, 12717, 8986])).
% 1.84/2.06 tff(12719,plain,
% 1.84/2.06 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[4798, 560, 335, 12645, 12678, 1787])).
% 1.84/2.06 tff(12720,plain,
% 1.84/2.06 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1401, 68, 2287, 12719])).
% 1.84/2.06 tff(12721,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12722,plain,
% 1.84/2.06 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12723,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12722])).
% 1.84/2.06 tff(12724,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12723, 12721])).
% 1.84/2.06 tff(12725,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(elem!1)))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(12726,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12725, 12724])).
% 1.84/2.06 tff(12727,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12726, 224, 12720, 12718, 12710, 12699])).
% 1.84/2.06 tff(12728,plain,((~b(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(12729,plain,
% 1.84/2.06 (~b(s(s(s(z))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12728, 12683, 2287, 335, 2, 12686, 1090, 1241])).
% 1.84/2.06 tff(12730,plain,
% 1.84/2.06 (r(s(s(s(z))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[925, 12729])).
% 1.84/2.06 tff(12731,plain,
% 1.84/2.06 (~r(s(s(s(s(z)))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[8902, 12730, 7672, 12696, 4567])).
% 1.84/2.06 tff(12732,plain,
% 1.84/2.06 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[3168, 12731])).
% 1.84/2.06 tff(12733,plain,
% 1.84/2.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[5196, 12732, 12695, 12694])).
% 1.84/2.06 tff(12734,plain,
% 1.84/2.06 (r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6185, 12733])).
% 1.84/2.06 tff(12735,plain,
% 1.84/2.06 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11263, 12734, 12693])).
% 1.84/2.06 tff(12736,plain,
% 1.84/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[249, 12735])).
% 1.84/2.06 tff(12737,plain,
% 1.84/2.06 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12736, 7330])).
% 1.84/2.06 tff(12738,plain,
% 1.84/2.06 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[4829, 12730, 335, 12686])).
% 1.84/2.06 tff(12739,plain,
% 1.84/2.06 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1345, 12738, 1832])).
% 1.84/2.06 tff(12740,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12741,plain,
% 1.84/2.06 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12742,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12741])).
% 1.84/2.06 tff(12743,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12742, 12740])).
% 1.84/2.06 tff(12744,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(12745,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12744, 12743])).
% 1.84/2.06 tff(12746,plain,
% 1.84/2.06 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12745, 224, 12678, 12739, 12737, 12646])).
% 1.84/2.06 tff(12747,plain,
% 1.84/2.06 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1422, 68, 8986, 12746])).
% 1.84/2.06 tff(12748,plain,
% 1.84/2.06 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[8075, 12747, 1181])).
% 1.84/2.06 tff(12749,plain,
% 1.84/2.06 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1439, 12748, 1782])).
% 1.84/2.06 tff(12750,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1814, 224, 3919, 12749, 7305, 12689])).
% 1.84/2.06 tff(12751,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (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(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(12752,plain,
% 1.84/2.06 (~r(elem!1, s(elem!1))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[12751, 12677, 12676, 12662, 335, 12673, 7240, 2, 1090, 12671, 12669, 12664])).
% 1.84/2.06 tff(12753,plain,
% 1.84/2.06 (b(elem!1, s(elem!1))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[515, 12752, 327])).
% 1.84/2.06 tff(12754,plain,
% 1.84/2.06 (b(z, s(z))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12753, 12661])).
% 1.84/2.06 tff(12755,plain,
% 1.84/2.06 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[7380])).
% 1.84/2.06 tff(12756,plain,
% 1.84/2.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[11315])).
% 1.84/2.06 tff(12757,plain,
% 1.84/2.06 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12756])).
% 1.84/2.06 tff(12758,plain,
% 1.84/2.06 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[4558])).
% 1.84/2.06 tff(12759,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[4631, 224, 3919, 11073, 7170])).
% 1.84/2.06 tff(12760,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[11549, 12759, 335])).
% 1.84/2.06 tff(12761,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1884, 12760])).
% 1.84/2.06 tff(12762,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[12761, 1786])).
% 1.84/2.06 tff(12763,plain,
% 1.84/2.06 (((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12764,plain,
% 1.84/2.06 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(12765,plain,
% 1.84/2.06 (((~![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(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[12764])).
% 1.84/2.06 tff(12766,plain,
% 1.84/2.06 (((~![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(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[12765, 12763])).
% 1.84/2.06 tff(12767,plain,
% 1.84/2.06 ((~![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(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12768,plain,
% 1.84/2.07 ((~![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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12767, 12766])).
% 1.84/2.07 tff(12769,plain,
% 1.84/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12768, 112, 12762, 11075])).
% 1.84/2.07 tff(12770,plain,
% 1.84/2.07 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4829, 12761, 335, 3188])).
% 1.84/2.07 tff(12771,plain,
% 1.84/2.07 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1345, 12770, 1832])).
% 1.84/2.07 tff(12772,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12773,plain,
% 1.84/2.07 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12774,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[12773])).
% 1.84/2.07 tff(12775,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[12774, 12772])).
% 1.84/2.07 tff(12776,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12777,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12776, 12775])).
% 1.84/2.07 tff(12778,plain,
% 1.84/2.07 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12777, 224, 501, 3919, 12771, 7305])).
% 1.84/2.07 tff(12779,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2047, 68, 2044, 12778, 12769])).
% 1.84/2.07 tff(12780,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(12781,plain,
% 1.84/2.07 (~b(elem!1, s(s(s(elem!1))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12780, 3188, 3919, 7305, 335, 501, 11073])).
% 1.84/2.07 tff(12782,plain,
% 1.84/2.07 (~b(elem!1, s(s(s(z))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12781, 12758])).
% 1.84/2.07 tff(12783,plain,
% 1.84/2.07 (r(elem!1, s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[388, 12782, 4561])).
% 1.84/2.07 tff(12784,plain,
% 1.84/2.07 (r(elem!1, s(s(s(elem!1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12783, 1784])).
% 1.84/2.07 tff(12785,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.84/2.07 tff(12786,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12787,plain,
% 1.84/2.07 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12788,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[12787])).
% 1.84/2.07 tff(12789,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[12788, 12786])).
% 1.84/2.07 tff(12790,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12791,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12790, 12789])).
% 1.84/2.07 tff(12792,plain,
% 1.84/2.07 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12791, 224, 3919, 11073])).
% 1.84/2.07 tff(12793,plain,
% 1.84/2.07 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12792, 4599, 12785])).
% 1.84/2.07 tff(12794,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1345, 12793, 1832])).
% 1.84/2.07 tff(12795,plain,
% 1.84/2.07 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[11419, 112, 12794, 7144])).
% 1.84/2.07 tff(12796,plain,
% 1.84/2.07 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12795, 7381])).
% 1.84/2.07 tff(12797,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[5426, 12796])).
% 1.84/2.07 tff(12798,plain,
% 1.84/2.07 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12797, 11315])).
% 1.84/2.07 tff(12799,plain,
% 1.84/2.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[11927, 4599, 3919, 1181, 335, 2, 3, 2252, 7672])).
% 1.84/2.07 tff(12800,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12799, 12798])).
% 1.84/2.07 tff(12801,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(12802,plain,
% 1.84/2.07 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12801, 11413, 335, 12785, 3919, 11073, 1181, 2, 3, 2252, 7672])).
% 1.84/2.07 tff(12803,plain,
% 1.84/2.07 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[11549, 12802, 335])).
% 1.84/2.07 tff(12804,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1884, 12803])).
% 1.84/2.07 tff(12805,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12804, 1786])).
% 1.84/2.07 tff(12806,plain,
% 1.84/2.07 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1794, 112, 12805, 12784])).
% 1.84/2.07 tff(12807,plain,
% 1.84/2.07 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1439, 12806, 1782])).
% 1.84/2.07 tff(12808,plain,
% 1.84/2.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[11925, 224, 3919, 12807, 11073])).
% 1.84/2.07 tff(12809,plain,
% 1.84/2.07 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12808, 12757])).
% 1.84/2.07 tff(12810,plain,
% 1.84/2.07 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[5426, 12809])).
% 1.84/2.07 tff(12811,plain,
% 1.84/2.07 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12810, 12755])).
% 1.84/2.07 tff(12812,plain,
% 1.84/2.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1814, 224, 3919, 12807, 7305])).
% 1.84/2.07 tff(12813,plain,
% 1.84/2.07 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 12812])).
% 1.84/2.07 tff(12814,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12815,plain,
% 1.84/2.07 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12816,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[12815])).
% 1.84/2.07 tff(12817,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[12816, 12814])).
% 1.84/2.07 tff(12818,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12819,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12818, 12817])).
% 1.84/2.07 tff(12820,plain,
% 1.84/2.07 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12819, 112, 11413, 12813, 12811])).
% 1.84/2.07 tff(12821,plain,
% 1.84/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 12820])).
% 1.84/2.07 tff(12822,plain,
% 1.84/2.07 (~b(z, s(s(s(z))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12781, 11566])).
% 1.84/2.07 tff(12823,plain,
% 1.84/2.07 (b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[11913, 12822, 2, 3, 2252, 7672])).
% 1.84/2.07 tff(12824,plain,
% 1.84/2.07 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12823, 7328])).
% 1.84/2.07 tff(12825,plain,
% 1.84/2.07 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4829, 12804, 335, 3188])).
% 1.84/2.07 tff(12826,plain,
% 1.84/2.07 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1345, 12825, 1832])).
% 1.84/2.07 tff(12827,plain,
% 1.84/2.07 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12745, 224, 1391, 12826, 12824, 12785])).
% 1.84/2.07 tff(12828,plain,
% 1.84/2.07 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1422, 68, 7374, 12827])).
% 1.84/2.07 tff(12829,plain,
% 1.84/2.07 (((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12830,plain,
% 1.84/2.07 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12831,plain,
% 1.84/2.07 (((~![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)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[12830])).
% 1.84/2.07 tff(12832,plain,
% 1.84/2.07 (((~![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)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[12831, 12829])).
% 1.84/2.07 tff(12833,plain,
% 1.84/2.07 ((~![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)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12834,plain,
% 1.84/2.07 ((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12833, 12832])).
% 1.84/2.07 tff(12835,plain,
% 1.84/2.07 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12834, 112, 1181, 12828, 12813])).
% 1.84/2.07 tff(12836,plain,
% 1.84/2.07 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 12835])).
% 1.84/2.07 tff(12837,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~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(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~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(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12838,plain,
% 1.84/2.07 (((~b(s(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(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(12839,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~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(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[12838])).
% 1.84/2.07 tff(12840,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~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(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.07 inference(transitivity,[status(thm)],[12839, 12837])).
% 1.84/2.07 tff(12841,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(12842,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[12841, 12840])).
% 1.84/2.07 tff(12843,plain,
% 1.84/2.07 ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12842, 224, 7305, 11073, 12824])).
% 1.84/2.07 tff(12844,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12843, 12836, 12821])).
% 1.84/2.07 tff(12845,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(12846,plain,
% 1.84/2.07 (~r(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[12845, 12676, 12669, 12662, 335, 12677, 12674, 12646, 2, 3, 12666, 12673, 12753])).
% 1.84/2.07 tff(12847,plain,
% 1.84/2.07 (b(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[925, 12846])).
% 1.84/2.07 tff(12848,plain,
% 1.84/2.07 (~b(z, s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6404, 12847, 1090, 12754])).
% 1.84/2.08 tff(12849,plain,
% 1.84/2.08 (~r(z, s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[3348, 12847, 1090, 1644, 2, 12662, 12754])).
% 1.84/2.08 tff(12850,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[100, 12849, 12848])).
% 1.84/2.08 tff(12851,plain,((~r(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~(z = elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12852,plain,
% 1.84/2.08 (~r(s(s(elem!1)), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12851, 10081, 2, 335, 3, 1090])).
% 1.84/2.08 tff(12853,plain,
% 1.84/2.08 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12852, 12658])).
% 1.84/2.08 tff(12854,plain,
% 1.84/2.08 (b(s(s(elem!1)), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[593, 12852])).
% 1.84/2.08 tff(12855,plain,
% 1.84/2.08 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12691])).
% 1.84/2.08 tff(12856,plain,
% 1.84/2.08 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1294, 1290, 1733])).
% 1.84/2.08 tff(12857,plain,
% 1.84/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7399, 112, 12856, 1739])).
% 1.84/2.08 tff(12858,plain,
% 1.84/2.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12857, 12855])).
% 1.84/2.08 tff(12859,plain,
% 1.84/2.08 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1317, 1290, 1733, 1287])).
% 1.84/2.08 tff(12860,plain,
% 1.84/2.08 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1345, 12859, 1832])).
% 1.84/2.08 tff(12861,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7550, 12860, 335])).
% 1.84/2.08 tff(12862,plain,
% 1.84/2.08 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1579, 12861, 1090, 560])).
% 1.84/2.08 tff(12863,plain,
% 1.84/2.08 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[3252, 12862])).
% 1.84/2.08 tff(12864,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12863, 12858])).
% 1.84/2.08 tff(12865,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12866,plain,
% 1.84/2.08 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12865, 12652, 335, 1090, 12655, 1287])).
% 1.84/2.08 tff(12867,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7095, 1240, 335])).
% 1.84/2.08 tff(12868,plain,
% 1.84/2.08 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[1621])).
% 1.84/2.08 tff(12869,plain,
% 1.84/2.08 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(symmetry,[status(thm)],[12868])).
% 1.84/2.08 tff(12870,plain,
% 1.84/2.08 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[1617])).
% 1.84/2.08 tff(12871,plain,
% 1.84/2.08 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(transitivity,[status(thm)],[12870, 12869])).
% 1.84/2.08 tff(12872,plain,
% 1.84/2.08 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1662, 112, 408, 12652])).
% 1.84/2.08 tff(12873,plain,
% 1.84/2.08 (~r(s(s(s(z))), s(z))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12872, 12650])).
% 1.84/2.08 tff(12874,plain,
% 1.84/2.08 (b(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[925, 12873])).
% 1.84/2.08 tff(12875,plain,
% 1.84/2.08 (b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12874, 12871])).
% 1.84/2.08 tff(12876,plain,
% 1.84/2.08 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[11458, 11007, 7466])).
% 1.84/2.08 tff(12877,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12878,plain,
% 1.84/2.08 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12879,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12878])).
% 1.84/2.08 tff(12880,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[12879, 12877])).
% 1.84/2.08 tff(12881,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(12882,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12881, 12880])).
% 1.84/2.08 tff(12883,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12882, 224, 4651, 1752, 12876, 12785])).
% 1.84/2.08 tff(12884,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12885,plain,
% 1.84/2.08 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12884, 12875, 12646, 1736, 1854, 12652, 408])).
% 1.84/2.08 tff(12886,plain,
% 1.84/2.08 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1777, 12885, 1615])).
% 1.84/2.08 tff(12887,plain,
% 1.84/2.08 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7462, 224, 596, 390, 7305])).
% 1.84/2.08 tff(12888,plain,
% 1.84/2.08 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 12887])).
% 1.84/2.08 tff(12889,plain,
% 1.84/2.08 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7477, 224, 596, 3919, 390])).
% 1.84/2.08 tff(12890,plain,
% 1.84/2.08 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1401, 68, 12889, 7240])).
% 1.84/2.08 tff(12891,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12892,plain,
% 1.84/2.08 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12893,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12892])).
% 1.84/2.08 tff(12894,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[12893, 12891])).
% 1.84/2.08 tff(12895,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(12896,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12895, 12894])).
% 1.84/2.08 tff(12897,plain,
% 1.84/2.08 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12896, 112, 12890, 12888])).
% 1.84/2.08 tff(12898,plain,
% 1.84/2.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 12897])).
% 1.84/2.08 tff(12899,plain,
% 1.84/2.08 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.08 tff(12900,plain,
% 1.84/2.08 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.84/2.08 inference(symmetry,[status(thm)],[12899])).
% 1.84/2.08 tff(12901,plain,
% 1.84/2.08 (r(z, s(elem!1))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[543, 12900])).
% 1.84/2.08 tff(12902,plain,
% 1.84/2.08 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.08 tff(12903,plain,
% 1.84/2.08 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(symmetry,[status(thm)],[12902])).
% 1.84/2.08 tff(12904,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.84/2.08 tff(12905,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1814, 224, 3919, 1412, 7305, 12904])).
% 1.84/2.08 tff(12906,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12907,plain,
% 1.84/2.08 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12906, 12898, 7305, 3919])).
% 1.84/2.08 tff(12908,plain,
% 1.84/2.08 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1439, 12907, 1782])).
% 1.84/2.08 tff(12909,plain,
% 1.84/2.08 (r(z, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12908, 12903])).
% 1.84/2.08 tff(12910,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12911,plain,
% 1.84/2.08 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12912,plain,
% 1.84/2.08 (((~![X0: $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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12911])).
% 1.84/2.08 tff(12913,plain,
% 1.84/2.08 (((~![X0: $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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[12912, 12910])).
% 1.84/2.08 tff(12914,plain,
% 1.84/2.08 ((~![X0: $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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(12915,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12914, 12913])).
% 1.84/2.08 tff(12916,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12915, 112, 408, 568, 4716, 7578])).
% 1.84/2.08 tff(12917,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12918,plain,
% 1.84/2.08 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12917, 12909, 408, 12901])).
% 1.84/2.08 tff(12919,plain,
% 1.84/2.08 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1869, 12918, 1683])).
% 1.84/2.08 tff(12920,plain,
% 1.84/2.08 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[11061, 224, 3919, 12919, 7305, 12898])).
% 1.84/2.08 tff(12921,plain,
% 1.84/2.08 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[11458, 12920, 1854])).
% 1.84/2.08 tff(12922,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7294, 112, 544, 12921, 12888])).
% 1.84/2.08 tff(12923,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12924,plain,
% 1.84/2.08 (~r(elem!1, s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12923, 544, 3919, 12886, 408, 335, 12867, 3])).
% 1.84/2.08 tff(12925,plain,
% 1.84/2.08 (b(elem!1, s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[515, 12924, 327])).
% 1.84/2.08 tff(12926,plain,
% 1.84/2.08 (b(z, s(z))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12925, 12661])).
% 1.84/2.08 tff(12927,plain,
% 1.84/2.08 (~b(z, s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6404, 12926, 1090, 12874])).
% 1.84/2.08 tff(12928,plain,
% 1.84/2.08 (b(z, s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[4020, 12927, 12, 1240, 88, 12926, 328])).
% 1.84/2.08 tff(12929,plain,
% 1.84/2.08 (b(elem!1, s(s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12928, 4706])).
% 1.84/2.08 tff(12930,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(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(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12931,plain,
% 1.84/2.08 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(12932,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12931])).
% 1.84/2.08 tff(12933,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[12932, 12930])).
% 1.84/2.08 tff(12934,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(12935,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12934, 12933])).
% 1.84/2.08 tff(12936,plain,
% 1.84/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12935, 112, 7479, 7464])).
% 1.84/2.08 tff(12937,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.84/2.08 tff(12938,plain,
% 1.84/2.08 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2047, 68, 12937, 12936])).
% 1.84/2.08 tff(12939,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.84/2.08 tff(12940,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12777, 224, 501, 3919, 1409, 7305, 12939])).
% 1.84/2.08 tff(12941,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12942,plain,
% 1.84/2.08 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12941, 12938, 3919, 7305, 501])).
% 1.84/2.08 tff(12943,plain,
% 1.84/2.08 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1345, 12942, 1286])).
% 1.84/2.08 tff(12944,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[3939, 112, 544, 12943, 7479])).
% 1.84/2.08 tff(12945,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12946,plain,
% 1.84/2.08 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12945, 544, 1832, 3919, 12886, 12925, 2044, 1717, 7240, 12867])).
% 1.84/2.08 tff(12947,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12946, 12929])).
% 1.84/2.08 tff(12948,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(z))), z) | (~b(s(s(elem!1)), z)) | (elem!1 = s(z)) | r(s(s(elem!1)), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(12949,plain,
% 1.84/2.08 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12948, 12866, 335, 12, 12854, 83, 12853, 1090, 10081, 3])).
% 1.84/2.08 tff(12950,plain,
% 1.84/2.08 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[530, 12949, 526])).
% 1.84/2.08 tff(12951,plain,
% 1.84/2.08 (b(s(s(elem!1)), s(z))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12950, 12656])).
% 1.84/2.08 tff(12952,plain,
% 1.84/2.08 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[3206, 12951, 1090, 12655])).
% 1.84/2.08 tff(12953,plain,
% 1.84/2.08 (r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[147, 12952, 2])).
% 1.84/2.08 tff(12954,plain,
% 1.84/2.08 (r(s(s(z)), s(s(s(z))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12953, 10982])).
% 1.84/2.08 tff(12955,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.84/2.08 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.08 tff(12956,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.84/2.08 inference(symmetry,[status(thm)],[12955])).
% 1.84/2.08 tff(12957,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.08 inference(monotonicity,[status(thm)],[1687])).
% 1.84/2.08 tff(12958,plain,
% 1.84/2.08 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.84/2.08 inference(symmetry,[status(thm)],[12957])).
% 1.84/2.08 tff(12959,plain,
% 1.84/2.08 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.84/2.08 inference(transitivity,[status(thm)],[12958, 12956])).
% 1.84/2.08 tff(12960,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), z)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12866, 12959])).
% 1.84/2.08 tff(12961,plain,
% 1.84/2.08 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.84/2.08 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.08 tff(12962,plain,
% 1.84/2.08 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.84/2.08 inference(symmetry,[status(thm)],[12961])).
% 1.84/2.08 tff(12963,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.84/2.08 inference(symmetry,[status(thm)],[11165])).
% 1.84/2.08 tff(12964,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.84/2.08 inference(transitivity,[status(thm)],[12963, 12962])).
% 1.84/2.08 tff(12965,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7095, 12854, 335])).
% 1.84/2.08 tff(12966,plain,
% 1.84/2.08 (b(s(s(z)), z)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12965, 12964])).
% 1.84/2.08 tff(12967,plain,
% 1.84/2.08 (r(s(s(s(elem!1))), elem!1)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[177, 12651])).
% 1.84/2.08 tff(12968,plain,
% 1.84/2.08 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1662, 112, 408, 12967])).
% 1.84/2.08 tff(12969,plain,
% 1.84/2.08 (~r(s(s(s(z))), s(z))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12968, 12650])).
% 1.84/2.08 tff(12970,plain,
% 1.84/2.08 (b(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[925, 12969])).
% 1.84/2.08 tff(12971,plain,
% 1.84/2.08 (b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[12970, 12871])).
% 1.84/2.08 tff(12972,plain,
% 1.84/2.08 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[12884, 12971, 12646, 1736, 1854, 12967, 408])).
% 1.84/2.08 tff(12973,plain,
% 1.84/2.08 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1777, 12972, 1615])).
% 1.84/2.08 tff(12974,plain,
% 1.84/2.08 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.84/2.08 inference(symmetry,[status(thm)],[7258])).
% 1.84/2.08 tff(12975,plain,
% 1.84/2.08 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[12974])).
% 1.84/2.08 tff(12976,plain,
% 1.84/2.08 (~r(s(z), s(s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[10635, 12975])).
% 1.84/2.08 tff(12977,plain,
% 1.84/2.08 (r(z, s(s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[545, 7244])).
% 1.84/2.08 tff(12978,plain,
% 1.84/2.08 (~b(s(z), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[7338, 12977, 177, 308, 4569])).
% 1.84/2.08 tff(12979,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[653, 12978, 12976])).
% 1.84/2.08 tff(12980,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(z))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(12981,plain,
% 1.84/2.09 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12980, 4567, 308, 177, 335, 408])).
% 1.84/2.09 tff(12982,plain,
% 1.84/2.09 (b(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[558, 12981, 3])).
% 1.84/2.09 tff(12983,plain,
% 1.84/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7462, 224, 12982, 390, 12973])).
% 1.84/2.09 tff(12984,plain,
% 1.84/2.09 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 12983])).
% 1.84/2.09 tff(12985,plain,
% 1.84/2.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7477, 224, 12982, 3919, 390])).
% 1.84/2.09 tff(12986,plain,
% 1.84/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1401, 68, 12985, 7240])).
% 1.84/2.09 tff(12987,plain,
% 1.84/2.09 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12896, 112, 12986, 12984])).
% 1.84/2.09 tff(12988,plain,
% 1.84/2.09 (b(s(s(s(s(z)))), z)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[3919, 12959])).
% 1.84/2.09 tff(12989,plain,
% 1.84/2.09 (b(s(s(z)), z)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[390, 12964])).
% 1.84/2.09 tff(12990,plain,
% 1.84/2.09 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.09 tff(12991,plain,
% 1.84/2.09 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.84/2.09 inference(symmetry,[status(thm)],[12990])).
% 1.84/2.09 tff(12992,plain,
% 1.84/2.09 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[1619])).
% 1.84/2.09 tff(12993,plain,
% 1.84/2.09 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.84/2.09 inference(symmetry,[status(thm)],[12992])).
% 1.84/2.09 tff(12994,plain,
% 1.84/2.09 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.84/2.09 inference(transitivity,[status(thm)],[12993, 12991])).
% 1.84/2.09 tff(12995,plain,
% 1.84/2.09 (b(z, s(s(z)))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[12982, 12994])).
% 1.84/2.09 tff(12996,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.84/2.09 tff(12997,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6090, 224, 2191, 1118, 5188, 12996])).
% 1.84/2.09 tff(12998,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(12999,plain,
% 1.84/2.09 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12998, 12995, 12989, 12988])).
% 1.84/2.09 tff(13000,plain,
% 1.84/2.09 (r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6185, 12999])).
% 1.84/2.09 tff(13001,plain,
% 1.84/2.09 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11263, 13000, 196])).
% 1.84/2.09 tff(13002,plain,
% 1.84/2.09 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3252, 13001])).
% 1.84/2.09 tff(13003,plain,
% 1.84/2.09 (~b(s(s(s(s(z)))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1579, 13002, 1090, 12970])).
% 1.84/2.09 tff(13004,plain,
% 1.84/2.09 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7550, 13003, 335])).
% 1.84/2.09 tff(13005,plain,
% 1.84/2.09 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1345, 13004, 1832])).
% 1.84/2.09 tff(13006,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13007,plain,
% 1.84/2.09 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13008,plain,
% 1.84/2.09 (((~![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(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[13007])).
% 1.84/2.09 tff(13009,plain,
% 1.84/2.09 (((~![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(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[13008, 13006])).
% 1.84/2.09 tff(13010,plain,
% 1.84/2.09 ((~![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(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(13011,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13010, 13009])).
% 1.84/2.09 tff(13012,plain,
% 1.84/2.09 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13011, 112, 543, 13005])).
% 1.84/2.09 tff(13013,plain,
% 1.84/2.09 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1439, 13012, 1782])).
% 1.84/2.09 tff(13014,plain,
% 1.84/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12906, 13013, 12973, 3919])).
% 1.84/2.09 tff(13015,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1838, 68, 1835, 13014, 12987])).
% 1.84/2.09 tff(13016,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13017,plain,
% 1.84/2.09 (~r(elem!1, s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13016, 12866, 335, 1090, 12954, 12965, 3, 132, 73, 10081])).
% 1.84/2.09 tff(13018,plain,
% 1.84/2.09 (b(elem!1, s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[515, 13017, 327])).
% 1.84/2.09 tff(13019,plain,
% 1.84/2.09 (b(z, s(z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13018, 12661])).
% 1.84/2.09 tff(13020,plain,
% 1.84/2.09 (~b(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6404, 13019, 1090, 12655])).
% 1.84/2.09 tff(13021,plain,
% 1.84/2.09 (r(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[100, 13020])).
% 1.84/2.09 tff(13022,plain,
% 1.84/2.09 (~r(z, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3074, 13021, 12953])).
% 1.84/2.09 tff(13023,plain,
% 1.84/2.09 (~r(z, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7250, 13022, 335])).
% 1.84/2.09 tff(13024,plain,
% 1.84/2.09 (b(z, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1088, 13023])).
% 1.84/2.09 tff(13025,plain,
% 1.84/2.09 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12998, 13024, 12966, 12960])).
% 1.84/2.09 tff(13026,plain,
% 1.84/2.09 (r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6185, 13025])).
% 1.84/2.09 tff(13027,plain,
% 1.84/2.09 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11263, 13026, 12954])).
% 1.84/2.09 tff(13028,plain,
% 1.84/2.09 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3252, 13027])).
% 1.84/2.09 tff(13029,plain,
% 1.84/2.09 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[335])).
% 1.84/2.09 tff(13030,plain,
% 1.84/2.09 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.84/2.09 inference(symmetry,[status(thm)],[13029])).
% 1.84/2.09 tff(13031,plain,
% 1.84/2.09 (b(z, s(elem!1))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13018, 13030])).
% 1.84/2.09 tff(13032,plain,
% 1.84/2.09 (b(z, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[4020, 13020, 12, 12854, 83, 13019, 12853])).
% 1.84/2.09 tff(13033,plain,
% 1.84/2.09 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[4124, 13032, 12950, 13031])).
% 1.84/2.09 tff(13034,plain,
% 1.84/2.09 (~b(s(z), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11153, 13033, 335])).
% 1.84/2.09 tff(13035,plain,
% 1.84/2.09 (r(s(z), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1071, 13034])).
% 1.84/2.09 tff(13036,plain,
% 1.84/2.09 (~r(s(s(s(s(z)))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6083, 13026, 12017, 13035])).
% 1.84/2.09 tff(13037,plain,
% 1.84/2.09 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3168, 13036])).
% 1.84/2.09 tff(13038,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1579, 13037, 13028, 1090, 12655])).
% 1.84/2.09 tff(13039,plain,(b(s(s(s(z))), z) | (~b(s(z), s(s(s(z))))) | (~(z = elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13040,plain,
% 1.84/2.09 (b(s(s(s(z))), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13039, 1287, 335, 3, 2, 1090])).
% 1.84/2.09 tff(13041,plain,
% 1.84/2.09 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[1620, 1687])).
% 1.84/2.09 tff(13042,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.09 inference(symmetry,[status(thm)],[13041])).
% 1.84/2.09 tff(13043,plain,
% 1.84/2.09 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[11315, 13042])).
% 1.84/2.09 tff(13044,plain,
% 1.84/2.09 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.84/2.09 inference(symmetry,[status(thm)],[7329])).
% 1.84/2.09 tff(13045,plain,
% 1.84/2.09 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[11551, 13044])).
% 1.84/2.09 tff(13046,plain,
% 1.84/2.09 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[13045])).
% 1.84/2.09 tff(13047,plain,
% 1.84/2.09 (b(s(s(s(z))), elem!1)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13040, 4600])).
% 1.84/2.09 tff(13048,plain,
% 1.84/2.09 (~r(s(s(elem!1)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12851, 408, 2, 335, 3, 1090])).
% 1.84/2.09 tff(13049,plain,
% 1.84/2.09 (b(s(s(elem!1)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[593, 13048])).
% 1.84/2.09 tff(13050,plain,
% 1.84/2.09 (b(s(s(elem!1)), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7095, 13049, 335])).
% 1.84/2.09 tff(13051,plain,
% 1.84/2.09 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1869, 12137, 1683])).
% 1.84/2.09 tff(13052,plain,
% 1.84/2.09 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11309, 1409, 408, 1835, 1854, 1798, 13051])).
% 1.84/2.09 tff(13053,plain,
% 1.84/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1777, 13052, 1615])).
% 1.84/2.09 tff(13054,plain,
% 1.84/2.09 (~r(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11633, 4567, 1668, 4575, 1090])).
% 1.84/2.09 tff(13055,plain,
% 1.84/2.09 (b(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[100, 13054])).
% 1.84/2.09 tff(13056,plain,
% 1.84/2.09 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[10929, 13055, 13049, 7672])).
% 1.84/2.09 tff(13057,plain,
% 1.84/2.09 (r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[147, 13056, 2])).
% 1.84/2.09 tff(13058,plain,
% 1.84/2.09 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13057, 4639])).
% 1.84/2.09 tff(13059,plain,
% 1.84/2.09 (b(elem!1, s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13055, 10974])).
% 1.84/2.09 tff(13060,plain,
% 1.84/2.09 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.84/2.09 inference(transitivity,[status(thm)],[4600, 10978])).
% 1.84/2.09 tff(13061,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[7672, 13060])).
% 1.84/2.09 tff(13062,plain,
% 1.84/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11024, 224, 13053, 13061, 13059])).
% 1.84/2.09 tff(13063,plain,
% 1.84/2.09 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 13062])).
% 1.84/2.09 tff(13064,plain,
% 1.84/2.09 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12708, 112, 13063, 13058])).
% 1.84/2.09 tff(13065,plain,
% 1.84/2.09 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 13064])).
% 1.84/2.09 tff(13066,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[7462, 224, 682, 390, 7305, 7304])).
% 1.84/2.09 tff(13067,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13068,plain,
% 1.84/2.09 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13067, 13065, 13053, 13050])).
% 1.84/2.09 tff(13069,plain,
% 1.84/2.09 (r(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[558, 13068, 3])).
% 1.84/2.09 tff(13070,plain,
% 1.84/2.09 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[553, 13069, 543])).
% 1.84/2.09 tff(13071,plain,
% 1.84/2.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1397, 224, 1391, 10636, 1409])).
% 1.84/2.09 tff(13072,plain,
% 1.84/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1401, 68, 13071, 2287])).
% 1.84/2.09 tff(13073,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11366, 112, 543, 545, 1798, 13072])).
% 1.84/2.09 tff(13074,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13075,plain,
% 1.84/2.09 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13074, 13069, 1798, 7240, 543, 1409, 319, 408])).
% 1.84/2.09 tff(13076,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[530, 13075, 13070, 526])).
% 1.84/2.09 tff(13077,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13078,plain,
% 1.84/2.09 (~r(elem!1, s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13077, 12856, 12860, 10081, 3, 335, 2, 13040, 1090])).
% 1.84/2.09 tff(13079,plain,
% 1.84/2.09 (b(elem!1, s(elem!1))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[515, 13078, 327])).
% 1.84/2.09 tff(13080,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13040, 13060])).
% 1.84/2.09 tff(13081,plain,
% 1.84/2.09 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[10270, 12856, 10081])).
% 1.84/2.09 tff(13082,plain,
% 1.84/2.09 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1869, 13081, 1683])).
% 1.84/2.09 tff(13083,plain,
% 1.84/2.09 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11309, 12860, 10081, 1835, 1854, 12856, 13082])).
% 1.84/2.09 tff(13084,plain,
% 1.84/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1777, 13083, 1615])).
% 1.84/2.09 tff(13085,plain,
% 1.84/2.09 (b(s(s(z)), elem!1)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[390, 12963])).
% 1.84/2.09 tff(13086,plain,
% 1.84/2.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11497, 112, 544, 11413])).
% 1.84/2.09 tff(13087,plain,
% 1.84/2.09 (r(s(s(z)), s(z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[544, 12648])).
% 1.84/2.09 tff(13088,plain,
% 1.84/2.09 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3196, 3188, 13087])).
% 1.84/2.09 tff(13089,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[249, 13088])).
% 1.84/2.09 tff(13090,plain,
% 1.84/2.09 (~b(elem!1, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2412, 13089, 1109, 787])).
% 1.84/2.09 tff(13091,plain,
% 1.84/2.09 (r(elem!1, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[388, 13090, 4561])).
% 1.84/2.09 tff(13092,plain,
% 1.84/2.09 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13089, 7330])).
% 1.84/2.09 tff(13093,plain,
% 1.84/2.09 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3915, 13092, 1798, 545, 335, 13091])).
% 1.84/2.09 tff(13094,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3905, 13093, 13086, 7255])).
% 1.84/2.09 tff(13095,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13096,plain,
% 1.84/2.09 (~r(s(s(s(z))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13095, 545, 1798, 335, 544, 13085, 787])).
% 1.84/2.09 tff(13097,plain,
% 1.84/2.09 (b(s(s(s(z))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[925, 13096])).
% 1.84/2.09 tff(13098,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13097, 12871])).
% 1.84/2.09 tff(13099,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13100,plain,
% 1.84/2.09 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13101,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[13100])).
% 1.84/2.09 tff(13102,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[13101, 13099])).
% 1.84/2.09 tff(13103,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(13104,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13103, 13102])).
% 1.84/2.09 tff(13105,plain,
% 1.84/2.09 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13104, 224, 501, 390, 13098, 11073])).
% 1.84/2.09 tff(13106,plain,
% 1.84/2.09 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[1629, 1784])).
% 1.84/2.09 tff(13107,plain,
% 1.84/2.09 (b(z, s(z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[501, 12661])).
% 1.84/2.09 tff(13108,plain,
% 1.84/2.09 (~b(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6404, 13097, 1090, 13107])).
% 1.84/2.09 tff(13109,plain,
% 1.84/2.09 (r(z, s(s(s(z))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[100, 13108])).
% 1.84/2.09 tff(13110,plain,
% 1.84/2.09 (r(elem!1, s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[13109, 13106])).
% 1.84/2.09 tff(13111,plain,
% 1.84/2.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3896, 13110, 545])).
% 1.84/2.09 tff(13112,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3905, 13111, 13105, 7255])).
% 1.84/2.09 tff(13113,plain,((~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(13114,plain,
% 1.84/2.09 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13113, 544, 390, 11073, 335, 1090, 1798, 501, 787])).
% 1.84/2.09 tff(13115,plain,
% 1.84/2.09 (b(elem!1, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[558, 13114, 3])).
% 1.84/2.09 tff(13116,plain,
% 1.84/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[13067, 13115, 7305, 390])).
% 1.84/2.09 tff(13117,plain,
% 1.84/2.09 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1763, 68, 1717, 13116])).
% 1.84/2.09 tff(13118,plain,
% 1.84/2.09 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[12082, 13115, 390, 11073])).
% 1.84/2.09 tff(13119,plain,
% 1.84/2.09 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3905, 13118, 7255])).
% 1.84/2.09 tff(13120,plain,
% 1.84/2.09 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[11349, 112, 13119, 13117])).
% 1.84/2.09 tff(13121,plain,
% 1.84/2.09 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1751, 68, 1736, 13120])).
% 1.84/2.09 tff(13122,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13123,plain,
% 1.84/2.09 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(13124,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[13123])).
% 1.84/2.09 tff(13125,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13124, 13122])).
% 1.84/2.10 tff(13126,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13127,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13126, 13125])).
% 1.84/2.10 tff(13128,plain,
% 1.84/2.10 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13127, 224, 7305, 11073, 12646])).
% 1.84/2.10 tff(13129,plain,
% 1.84/2.10 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13128, 13121])).
% 1.84/2.10 tff(13130,plain,
% 1.84/2.10 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11458, 13129, 1854])).
% 1.84/2.10 tff(13131,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[7294, 112, 544, 13130, 13117])).
% 1.84/2.10 tff(13132,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(13133,plain,
% 1.84/2.10 (~r(s(s(elem!1)), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13132, 13084, 13080, 12965, 3, 335, 1090, 12856, 13079, 13047])).
% 1.84/2.10 tff(13134,plain,
% 1.84/2.10 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[530, 13133, 526])).
% 1.84/2.10 tff(13135,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13136,plain,
% 1.84/2.10 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13137,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[13136])).
% 1.84/2.10 tff(13138,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13137, 13135])).
% 1.84/2.10 tff(13139,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13140,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13139, 13138])).
% 1.84/2.10 tff(13141,plain,
% 1.84/2.10 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13140, 224, 12965, 13080, 12646])).
% 1.84/2.10 tff(13142,plain,
% 1.84/2.10 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13141, 13134])).
% 1.84/2.10 tff(13143,plain,
% 1.84/2.10 (~b(s(s(z)), s(s(s(z))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13142, 13046])).
% 1.84/2.10 tff(13144,plain,
% 1.84/2.10 (r(s(s(z)), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[249, 13143])).
% 1.84/2.10 tff(13145,plain,
% 1.84/2.10 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11211, 224, 13134, 12860, 13082])).
% 1.84/2.10 tff(13146,plain,
% 1.84/2.10 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1422, 68, 7374, 13145])).
% 1.84/2.10 tff(13147,plain,
% 1.84/2.10 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13146, 11317])).
% 1.84/2.10 tff(13148,plain,
% 1.84/2.10 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[5413, 13147, 13144])).
% 1.84/2.10 tff(13149,plain,
% 1.84/2.10 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[5426, 13148])).
% 1.84/2.10 tff(13150,plain,
% 1.84/2.10 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13149, 13043])).
% 1.84/2.10 tff(13151,plain,
% 1.84/2.10 (r(s(s(s(s(z)))), z)),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[12856, 4574])).
% 1.84/2.10 tff(13152,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13153,plain,
% 1.84/2.10 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13154,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[13153])).
% 1.84/2.10 tff(13155,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13154, 13152])).
% 1.84/2.10 tff(13156,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13157,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13156, 13155])).
% 1.84/2.10 tff(13158,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13157, 112, 179, 7575, 2276])).
% 1.84/2.10 tff(13159,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(13160,plain,
% 1.84/2.10 (~r(s(z), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13159, 13151, 12017])).
% 1.84/2.10 tff(13161,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13162,plain,
% 1.84/2.10 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13163,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[13162])).
% 1.84/2.10 tff(13164,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13163, 13161])).
% 1.84/2.10 tff(13165,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13166,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13165, 13164])).
% 1.84/2.10 tff(13167,plain,
% 1.84/2.10 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13166, 224, 13079, 13134, 12965, 13084])).
% 1.84/2.10 tff(13168,plain,
% 1.84/2.10 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11124, 68, 11940, 13167])).
% 1.84/2.10 tff(13169,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13170,plain,
% 1.84/2.10 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13171,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[13170])).
% 1.84/2.10 tff(13172,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13171, 13169])).
% 1.84/2.10 tff(13173,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13174,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13173, 13172])).
% 1.84/2.10 tff(13175,plain,
% 1.84/2.10 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13174, 224, 13079, 12860, 13082])).
% 1.84/2.10 tff(13176,plain,
% 1.84/2.10 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1439, 13175, 1782])).
% 1.84/2.10 tff(13177,plain,
% 1.84/2.10 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13178,plain,
% 1.84/2.10 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(13179,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[13178])).
% 1.84/2.10 tff(13180,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[13179, 13177])).
% 1.84/2.10 tff(13181,plain,
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% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(13182,plain,
% 1.84/2.10 ((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13181, 13180])).
% 1.84/2.10 tff(13183,plain,
% 1.84/2.10 (~r(elem!1, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13182, 112, 13176, 13146, 13168])).
% 1.84/2.10 tff(13184,plain,
% 1.84/2.10 (b(elem!1, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[558, 13183, 3])).
% 1.84/2.10 tff(13185,plain,
% 1.84/2.10 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[12082, 13184, 12965, 13080])).
% 1.84/2.10 tff(13186,plain,
% 1.84/2.10 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3905, 13185, 7255])).
% 1.84/2.10 tff(13187,plain,
% 1.84/2.10 (r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11437, 13186, 335])).
% 1.84/2.10 tff(13188,plain,
% 1.84/2.10 (b(z, s(z))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13079, 12661])).
% 1.84/2.10 tff(13189,plain,
% 1.84/2.10 (b(z, s(elem!1))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13079, 13030])).
% 1.84/2.10 tff(13190,plain,
% 1.84/2.10 (b(z, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11358, 13184, 335])).
% 1.84/2.10 tff(13191,plain,
% 1.84/2.10 (~b(s(z), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[10888, 13190, 13189, 13134, 13188])).
% 1.84/2.10 tff(13192,plain,
% 1.84/2.10 (r(s(z), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[653, 13191])).
% 1.84/2.10 tff(13193,plain,
% 1.84/2.10 (~r(s(s(s(z))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[9107, 13192, 13187])).
% 1.84/2.10 tff(13194,plain,
% 1.84/2.10 (b(s(s(s(z))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[925, 13193])).
% 1.84/2.10 tff(13195,plain,
% 1.84/2.10 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[7573, 13194, 1668, 13160, 12861])).
% 1.84/2.10 tff(13196,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13195, 13150])).
% 1.84/2.10 tff(13197,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~(z = elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(13198,plain,
% 1.84/2.10 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13197, 1287, 3, 1090, 2, 335])).
% 1.84/2.10 tff(13199,plain,
% 1.84/2.10 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13140, 224, 13050, 13061, 12646])).
% 1.84/2.10 tff(13200,plain,
% 1.84/2.10 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13199, 1391])).
% 1.84/2.10 tff(13201,plain,
% 1.84/2.10 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13200, 11552])).
% 1.84/2.10 tff(13202,plain,
% 1.84/2.10 (r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[147, 13201, 2])).
% 1.84/2.10 tff(13203,plain,
% 1.84/2.10 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13202, 4639])).
% 1.84/2.10 tff(13204,plain,
% 1.84/2.10 (b(s(s(z)), z)),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13050, 12964])).
% 1.84/2.10 tff(13205,plain,
% 1.84/2.10 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[4789, 7254])).
% 1.84/2.10 tff(13206,plain,
% 1.84/2.10 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[4795, 112, 4789, 7946])).
% 1.84/2.10 tff(13207,plain,
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% 1.84/2.10 inference(unit_resolution,[status(thm)],[13206, 12027])).
% 1.84/2.10 tff(13208,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(13209,plain,
% 1.84/2.10 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13208, 4789, 335, 6554])).
% 1.84/2.10 tff(13210,plain,
% 1.84/2.10 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 1.84/2.10 tff(13211,plain,
% 1.84/2.10 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[12791, 224, 3919, 13061, 12785])).
% 1.84/2.10 tff(13212,plain,
% 1.84/2.10 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[13211, 13210])).
% 1.84/2.10 tff(13213,plain,
% 1.84/2.10 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1345, 13212, 1832])).
% 1.84/2.10 tff(13214,plain,
% 1.84/2.10 (r(s(s(s(s(z)))), s(z))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13213, 7275])).
% 1.84/2.10 tff(13215,plain,
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% 1.84/2.10 inference(unit_resolution,[status(thm)],[7280, 13214, 13205])).
% 1.84/2.10 tff(13216,plain,
% 1.84/2.10 (b(s(z), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[653, 13215])).
% 1.84/2.10 tff(13217,plain,
% 1.84/2.10 (b(z, s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[11913, 13216, 2, 3, 7672, 6484])).
% 1.84/2.10 tff(13218,plain,
% 1.84/2.10 (b(elem!1, s(s(s(elem!1))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13217, 10974])).
% 1.84/2.10 tff(13219,plain,
% 1.84/2.10 (~b(elem!1, s(s(s(elem!1))))),
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% 1.84/2.10 tff(13220,plain,
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% 1.84/2.10 tff(13221,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | b(s(s(elem!1)), s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(13222,plain,
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% 1.84/2.10 inference(unit_resolution,[status(thm)],[13221, 13201, 2, 3, 7672, 335, 3919, 12646])).
% 1.84/2.10 tff(13223,plain,
% 1.84/2.10 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[13222, 11993])).
% 1.84/2.10 tff(13224,plain,
% 1.84/2.10 (b(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6185, 13223])).
% 1.84/2.10 tff(13225,plain,
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% 1.84/2.10 tff(13226,plain,
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% 1.84/2.10 tff(13228,plain,
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% 1.84/2.10 tff(13229,plain,
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% 1.84/2.10 tff(13230,plain,
% 1.84/2.10 (b(elem!1, s(s(s(elem!1))))),
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% 1.84/2.10 tff(13231,plain,
% 1.84/2.10 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 1.84/2.10 tff(13232,plain,
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% 1.84/2.10 tff(13233,plain,
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% 1.84/2.11 tff(13234,plain,
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% 1.84/2.11 tff(13235,plain,
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% 1.84/2.11 inference(unit_resolution,[status(thm)],[1439, 13256, 1782])).
% 1.84/2.11 tff(13258,plain,
% 1.84/2.11 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(13259,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[13258])).
% 1.84/2.11 tff(13260,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[13259, 3957])).
% 1.84/2.11 tff(13261,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(13262,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13261, 13260])).
% 1.84/2.11 tff(13263,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13262, 224, 3919, 13050, 13257, 13236])).
% 1.84/2.11 tff(13264,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(13265,plain,
% 1.84/2.11 (~b(s(s(elem!1)), s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13264, 13198, 335, 1090, 10081, 2, 3, 13040])).
% 1.84/2.11 tff(13266,plain,
% 1.84/2.11 (r(s(s(elem!1)), s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[530, 13265, 526])).
% 1.84/2.11 tff(13267,plain,
% 1.84/2.11 (r(s(s(z)), s(z))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13266, 12648])).
% 1.84/2.11 tff(13268,plain,
% 1.84/2.11 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[12082, 4261, 12867, 13061])).
% 1.84/2.11 tff(13269,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3905, 13268, 7255])).
% 1.84/2.11 tff(13270,plain,
% 1.84/2.11 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[7477, 224, 4261, 3919, 12867])).
% 1.84/2.11 tff(13271,plain,
% 1.84/2.11 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1401, 68, 13270, 7240])).
% 1.84/2.11 tff(13272,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(13273,plain,
% 1.84/2.11 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(13274,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[13273])).
% 1.84/2.11 tff(13275,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[13274, 13272])).
% 1.84/2.11 tff(13276,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(13277,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13276, 13275])).
% 1.84/2.11 tff(13278,plain,
% 1.84/2.11 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13277, 112, 13271, 13269])).
% 1.84/2.11 tff(13279,plain,
% 1.84/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13278, 7381])).
% 1.84/2.11 tff(13280,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[5426, 13279])).
% 1.84/2.11 tff(13281,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13280, 11315])).
% 1.84/2.11 tff(13282,plain,
% 1.84/2.11 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[7966, 112, 13271, 13269])).
% 1.84/2.11 tff(13283,plain,
% 1.84/2.11 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13282, 12855])).
% 1.84/2.11 tff(13284,plain,
% 1.84/2.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3252, 13283])).
% 1.84/2.11 tff(13285,plain,
% 1.84/2.11 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[11233, 68, 13282, 10988])).
% 1.84/2.11 tff(13286,plain,
% 1.84/2.11 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13211, 13285])).
% 1.84/2.11 tff(13287,plain,
% 1.84/2.11 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1345, 13286, 1832])).
% 1.84/2.11 tff(13288,plain,
% 1.84/2.11 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3939, 112, 544, 1289])).
% 1.84/2.11 tff(13289,plain,
% 1.84/2.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[13288, 11993])).
% 1.84/2.11 tff(13290,plain,
% 1.84/2.11 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3196, 13087, 3188])).
% 1.84/2.11 tff(13291,plain,
% 1.84/2.11 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[249, 13290])).
% 1.84/2.11 tff(13292,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3905, 13086, 7255])).
% 1.84/2.11 tff(13293,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[1619])).
% 1.84/2.11 tff(13294,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[13293])).
% 1.84/2.11 tff(13295,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[1627])).
% 1.84/2.11 tff(13296,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[13295, 13294])).
% 1.84/2.11 tff(13297,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[1698, 13296])).
% 1.84/2.11 tff(13298,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.84/2.11 tff(13299,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13298, 13297])).
% 1.84/2.11 tff(13300,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(z))), s(s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(13301,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[13300, 13292, 335])).
% 1.84/2.11 tff(13302,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(13303,plain,
% 1.95/2.11 (((~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(13304,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[13303])).
% 1.95/2.11 tff(13305,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.95/2.11 inference(transitivity,[status(thm)],[13304, 13302])).
% 1.95/2.11 tff(13306,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(13307,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13306, 13305])).
% 1.95/2.11 tff(13308,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13307, 224, 2212, 1571, 5188, 2211])).
% 1.95/2.11 tff(13309,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(13310,plain,
% 1.95/2.11 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13309, 13301, 1571, 13291])).
% 1.95/2.11 tff(13311,plain,
% 1.95/2.11 (r(s(s(s(s(z)))), s(s(z)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6185, 13310])).
% 1.95/2.11 tff(13312,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13311, 13289])).
% 1.95/2.11 tff(13313,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(13314,plain,
% 1.95/2.11 (~r(s(s(s(z))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13313, 13287, 544, 13284, 335])).
% 1.95/2.11 tff(13315,plain,
% 1.95/2.11 (b(s(s(s(z))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[925, 13314])).
% 1.95/2.11 tff(13316,plain,
% 1.95/2.11 (b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13315, 12871])).
% 1.95/2.11 tff(13317,plain,
% 1.95/2.11 (r(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[11437, 13269, 335])).
% 1.95/2.11 tff(13318,plain,
% 1.95/2.11 ((~r(elem!1, s(s(elem!1)))) <=> (~r(z, s(s(elem!1))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[7244])).
% 1.95/2.11 tff(13319,plain,
% 1.95/2.11 (~r(z, s(s(elem!1)))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[2597, 13318])).
% 1.95/2.11 tff(13320,plain,
% 1.95/2.11 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13221, 13271, 2, 3, 7672, 335, 3919, 12785])).
% 1.95/2.11 tff(13321,plain,
% 1.95/2.11 (~b(z, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[10929, 13320, 1240, 7672])).
% 1.95/2.11 tff(13322,plain,
% 1.95/2.11 (r(z, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[100, 13321])).
% 1.95/2.11 tff(13323,plain,
% 1.95/2.11 (~r(z, s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[11714, 13322, 179, 1240, 7672, 13319, 13317])).
% 1.95/2.11 tff(13324,plain,
% 1.95/2.11 (b(z, s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[5459, 13323])).
% 1.95/2.11 tff(13325,plain,
% 1.95/2.11 (b(elem!1, s(elem!1))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13324, 7348])).
% 1.95/2.11 tff(13326,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(13327,plain,
% 1.95/2.11 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(13328,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[13327])).
% 1.95/2.11 tff(13329,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.95/2.11 inference(transitivity,[status(thm)],[13328, 13326])).
% 1.95/2.11 tff(13330,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(13331,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13330, 13329])).
% 1.95/2.11 tff(13332,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13331, 224, 13325, 3919, 13316, 13061, 13281])).
% 1.95/2.11 tff(13333,plain,(r(elem!1, s(s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(13334,plain,
% 1.95/2.11 (r(elem!1, s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13333, 13198, 335, 13266, 12646, 12017, 12854, 13040, 2, 3])).
% 1.95/2.11 tff(13335,plain,
% 1.95/2.11 (~r(elem!1, s(elem!1))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[553, 13334, 13266])).
% 1.95/2.11 tff(13336,plain,
% 1.95/2.11 (b(elem!1, s(elem!1))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[515, 13335, 327])).
% 1.95/2.11 tff(13337,plain,
% 1.95/2.11 (b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[560, 12871])).
% 1.95/2.11 tff(13338,plain,
% 1.95/2.11 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13104, 224, 501, 390, 13337, 11073])).
% 1.95/2.11 tff(13339,plain,
% 1.95/2.11 (~b(z, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6404, 560, 1090, 13107])).
% 1.95/2.11 tff(13340,plain,
% 1.95/2.11 (r(z, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[100, 13339])).
% 1.95/2.11 tff(13341,plain,
% 1.95/2.11 (r(elem!1, s(s(s(elem!1))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13340, 13106])).
% 1.95/2.11 tff(13342,plain,
% 1.95/2.11 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3896, 13341, 545])).
% 1.95/2.11 tff(13343,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3905, 13342, 13338, 7255])).
% 1.95/2.11 tff(13344,plain,((~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(13345,plain,
% 1.95/2.11 (~b(s(s(s(z))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13344, 13334, 13336, 12965, 13080, 335, 1090])).
% 1.95/2.11 tff(13346,plain,
% 1.95/2.11 (r(s(s(s(z))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[925, 13345])).
% 1.95/2.11 tff(13347,plain,
% 1.95/2.11 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3196, 13346, 13267])).
% 1.95/2.11 tff(13348,plain,
% 1.95/2.11 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[249, 13347])).
% 1.95/2.11 tff(13349,plain,
% 1.95/2.11 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13348, 7330])).
% 1.95/2.11 tff(13350,plain,
% 1.95/2.11 (r(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13346, 11406])).
% 1.95/2.11 tff(13351,plain,
% 1.95/2.11 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[11497, 112, 13266, 13350])).
% 1.95/2.11 tff(13352,plain,
% 1.95/2.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3905, 13351, 7255])).
% 1.95/2.11 tff(13353,plain,
% 1.95/2.11 (~r(s(elem!1), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[4010, 13334, 10081])).
% 1.95/2.11 tff(13354,plain,
% 1.95/2.11 (b(s(elem!1), s(s(elem!1)))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1521, 13353, 319])).
% 1.95/2.11 tff(13355,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[4017, 224, 13354, 13352, 13349, 12646])).
% 1.95/2.11 tff(13356,plain,(b(s(elem!1), elem!1) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(13357,plain,
% 1.95/2.11 (b(s(elem!1), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[13356, 335, 1090, 2, 3])).
% 1.95/2.11 tff(13358,plain,
% 1.95/2.11 (b(s(z), elem!1)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13357, 12644])).
% 1.95/2.11 tff(13359,plain,
% 1.95/2.11 (~r(elem!1, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[7935, 543, 335, 1181, 1391])).
% 1.95/2.11 tff(13360,plain,
% 1.95/2.11 (b(elem!1, s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[388, 13359, 4561])).
% 1.95/2.11 tff(13361,plain,
% 1.95/2.11 (b(z, s(s(s(z))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13360, 11564])).
% 1.95/2.11 tff(13362,plain,
% 1.95/2.11 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.95/2.11 inference(symmetry,[status(thm)],[1631])).
% 1.95/2.11 tff(13363,plain,
% 1.95/2.11 (r(s(s(s(z))), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[4200, 13359, 1090, 4549, 684])).
% 1.95/2.11 tff(13364,plain,
% 1.95/2.11 (r(s(s(s(z))), z)),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[13363, 13362])).
% 1.95/2.11 tff(13365,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6329, 13364, 4567, 102, 2, 13361])).
% 1.95/2.11 tff(13366,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13367,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13366, 7687, 7686, 2, 335, 1090, 13358, 3340, 11372])).
% 1.95/2.12 tff(13368,plain,(b(elem!1, s(elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13369,plain,
% 1.95/2.12 (b(elem!1, s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13368, 354, 335, 1090, 3, 2])).
% 1.95/2.12 tff(13370,plain,
% 1.95/2.12 (b(s(z), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4001, 13357, 11282])).
% 1.95/2.12 tff(13371,plain,
% 1.95/2.12 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(symmetry,[status(thm)],[12870])).
% 1.95/2.12 tff(13372,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(transitivity,[status(thm)],[12868, 13371])).
% 1.95/2.12 tff(13373,plain,
% 1.95/2.12 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13372])).
% 1.95/2.12 tff(13374,plain,
% 1.95/2.12 (b(s(z), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1488, 12644])).
% 1.95/2.12 tff(13375,plain,
% 1.95/2.12 (b(s(z), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4001, 1488, 11282])).
% 1.95/2.12 tff(13376,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(z))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1391, 12656])).
% 1.95/2.12 tff(13377,plain,
% 1.95/2.12 (~r(elem!1, s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13366, 1391, 2, 335, 1090, 13374, 1181, 9146])).
% 1.95/2.12 tff(13378,plain,
% 1.95/2.12 (b(elem!1, s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[515, 13377, 2506])).
% 1.95/2.12 tff(13379,plain,
% 1.95/2.12 (~b(s(elem!1), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3570, 13378, 682, 1391])).
% 1.95/2.12 tff(13380,plain,
% 1.95/2.12 (r(s(elem!1), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1521, 13379, 523])).
% 1.95/2.12 tff(13381,plain,
% 1.95/2.12 (r(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13380, 12974])).
% 1.95/2.12 tff(13382,plain,
% 1.95/2.12 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1654])).
% 1.95/2.12 tff(13383,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4689, 112, 1181, 1739])).
% 1.95/2.12 tff(13384,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13383, 7255])).
% 1.95/2.12 tff(13385,plain,
% 1.95/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13300, 13384, 335])).
% 1.95/2.12 tff(13386,plain,
% 1.95/2.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[2023, 11993])).
% 1.95/2.12 tff(13387,plain,
% 1.95/2.12 (b(s(s(s(s(z)))), s(s(z)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6185, 13386])).
% 1.95/2.12 tff(13388,plain,
% 1.95/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7400, 12855])).
% 1.95/2.12 tff(13389,plain,
% 1.95/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3252, 13388])).
% 1.95/2.12 tff(13390,plain,
% 1.95/2.12 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[4638, 10982])).
% 1.95/2.12 tff(13391,plain,
% 1.95/2.12 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13390])).
% 1.95/2.12 tff(13392,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(13393,plain,
% 1.95/2.12 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(13394,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13393])).
% 1.95/2.12 tff(13395,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[13394, 13392])).
% 1.95/2.12 tff(13396,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(13397,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13396, 13395])).
% 1.95/2.12 tff(13398,plain,
% 1.95/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13397, 112, 1181, 1739])).
% 1.95/2.12 tff(13399,plain,
% 1.95/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13398, 13391])).
% 1.95/2.12 tff(13400,plain,
% 1.95/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[249, 13399])).
% 1.95/2.12 tff(13401,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13309, 13400, 13389, 13387, 13385])).
% 1.95/2.12 tff(13402,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13403,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13402, 1798, 1181, 335])).
% 1.95/2.12 tff(13404,plain,
% 1.95/2.12 (~r(s(s(s(z))), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13403, 13382])).
% 1.95/2.12 tff(13405,plain,
% 1.95/2.12 (r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4200, 13404, 1090, 4549, 684])).
% 1.95/2.12 tff(13406,plain,
% 1.95/2.12 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1806, 13405, 1798])).
% 1.95/2.12 tff(13407,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1884, 13406])).
% 1.95/2.12 tff(13408,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11549, 13407, 335])).
% 1.95/2.12 tff(13409,plain,
% 1.95/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13408, 11258])).
% 1.95/2.12 tff(13410,plain,
% 1.95/2.12 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.95/2.12 inference(monotonicity,[status(thm)],[335])).
% 1.95/2.12 tff(13411,plain,
% 1.95/2.12 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 1.95/2.12 inference(symmetry,[status(thm)],[13410])).
% 1.95/2.12 tff(13412,plain,
% 1.95/2.12 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 1.95/2.12 inference(transitivity,[status(thm)],[1640, 13411])).
% 1.95/2.12 tff(13413,plain,
% 1.95/2.12 (r(s(s(z)), z)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1181, 13412])).
% 1.95/2.12 tff(13414,plain,
% 1.95/2.12 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.95/2.12 inference(transitivity,[status(thm)],[1654, 13362])).
% 1.95/2.12 tff(13415,plain,
% 1.95/2.12 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), z))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13414])).
% 1.95/2.12 tff(13416,plain,
% 1.95/2.12 (~r(s(s(s(z))), z)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13403, 13415])).
% 1.95/2.12 tff(13417,plain,
% 1.95/2.12 (b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[72, 13416])).
% 1.95/2.12 tff(13418,plain,
% 1.95/2.12 (~b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9179, 13417, 1090, 1])).
% 1.95/2.12 tff(13419,plain,
% 1.95/2.12 (r(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[100, 13418])).
% 1.95/2.12 tff(13420,plain,
% 1.95/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3455, 13419, 13413])).
% 1.95/2.12 tff(13421,plain,
% 1.95/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[249, 13420])).
% 1.95/2.12 tff(13422,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11579, 13419, 9139, 13417])).
% 1.95/2.12 tff(13423,plain,
% 1.95/2.12 (~b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3206, 13422, 1090, 1241])).
% 1.95/2.12 tff(13424,plain,
% 1.95/2.12 (r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[925, 13423])).
% 1.95/2.12 tff(13425,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9107, 13424, 656])).
% 1.95/2.12 tff(13426,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11437, 13425, 335])).
% 1.95/2.12 tff(13427,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13426, 7255])).
% 1.95/2.12 tff(13428,plain,
% 1.95/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13300, 13427, 335])).
% 1.95/2.12 tff(13429,plain,
% 1.95/2.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13309, 13428, 13387, 13421])).
% 1.95/2.12 tff(13430,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13429, 13409])).
% 1.95/2.12 tff(13431,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | b(s(s(elem!1)), z) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13432,plain,
% 1.95/2.12 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13431, 13381, 335, 1090, 13376, 9139, 13375, 13374, 1181])).
% 1.95/2.12 tff(13433,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1294, 13432, 1733])).
% 1.95/2.12 tff(13434,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4689, 112, 1181, 12967])).
% 1.95/2.12 tff(13435,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13434, 7255])).
% 1.95/2.12 tff(13436,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(13437,plain,
% 1.95/2.12 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(13438,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13437])).
% 1.95/2.12 tff(13439,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[13438, 13436])).
% 1.95/2.12 tff(13440,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(13441,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13440, 13439])).
% 1.95/2.12 tff(13442,plain,
% 1.95/2.12 (~b(elem!1, s(s(s(elem!1))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13441, 224, 501, 682, 1391, 13435])).
% 1.95/2.12 tff(13443,plain,
% 1.95/2.12 (~b(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13442, 12758])).
% 1.95/2.12 tff(13444,plain,
% 1.95/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13397, 112, 1181, 12967])).
% 1.95/2.12 tff(13445,plain,
% 1.95/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13444, 13391])).
% 1.95/2.12 tff(13446,plain,
% 1.95/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[249, 13445])).
% 1.95/2.12 tff(13447,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13446, 7330])).
% 1.95/2.12 tff(13448,plain,
% 1.95/2.12 (~r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7283, 13447, 2287, 335, 1181, 656, 1632, 501, 1488, 682])).
% 1.95/2.12 tff(13449,plain,
% 1.95/2.12 (b(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[388, 13448, 4561])).
% 1.95/2.12 tff(13450,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13449, 13443])).
% 1.95/2.12 tff(13451,plain,((~r(s(s(s(z))), z)) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13452,plain,
% 1.95/2.12 (~r(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13451, 13381, 2287, 1181, 335, 13378, 1488, 682, 1391])).
% 1.95/2.12 tff(13453,plain,
% 1.95/2.12 (b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[72, 13452])).
% 1.95/2.12 tff(13454,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13453, 13060])).
% 1.95/2.12 tff(13455,plain,
% 1.95/2.12 (~b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9179, 13453, 1090, 13375])).
% 1.95/2.12 tff(13456,plain,
% 1.95/2.12 (r(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[100, 13455])).
% 1.95/2.12 tff(13457,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11579, 13456, 9139, 13453])).
% 1.95/2.12 tff(13458,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13457, 7328])).
% 1.95/2.12 tff(13459,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11403, 13458, 13454, 2287, 335, 1488, 13381, 13378, 13433])).
% 1.95/2.12 tff(13460,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | b(s(s(elem!1)), z) | (~b(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (elem!1 = s(elem!1)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13461,plain,
% 1.95/2.12 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13460, 682, 335, 13357, 11371, 1090, 3340, 7240, 319, 327, 2])).
% 1.95/2.12 tff(13462,plain,
% 1.95/2.12 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[530, 13461, 526])).
% 1.95/2.12 tff(13463,plain,
% 1.95/2.12 (b(elem!1, s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[541, 13461, 3, 354])).
% 1.95/2.12 tff(13464,plain,
% 1.95/2.12 (~b(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[5988, 1632, 2, 1090, 1181])).
% 1.95/2.12 tff(13465,plain,
% 1.95/2.12 (r(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[653, 13464])).
% 1.95/2.12 tff(13466,plain,
% 1.95/2.12 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13402, 12967, 1181, 335])).
% 1.95/2.12 tff(13467,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1294, 13466, 1733])).
% 1.95/2.12 tff(13468,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[2054, 224, 501, 1488, 13467])).
% 1.95/2.12 tff(13469,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1345, 13468, 1832])).
% 1.95/2.12 tff(13470,plain,
% 1.95/2.12 (r(s(s(s(s(z)))), s(z))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1289, 7275])).
% 1.95/2.12 tff(13471,plain,
% 1.95/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3326, 3188, 13470])).
% 1.95/2.12 tff(13472,plain,
% 1.95/2.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13313, 3188, 544, 1289, 335])).
% 1.95/2.12 tff(13473,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3252, 13472, 13471])).
% 1.95/2.12 tff(13474,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13475,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13474, 13469, 544, 335])).
% 1.95/2.12 tff(13476,plain,
% 1.95/2.12 (b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[925, 13475])).
% 1.95/2.12 tff(13477,plain,
% 1.95/2.12 (~b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6404, 13476, 1090, 13107])).
% 1.95/2.12 tff(13478,plain,
% 1.95/2.12 (r(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[100, 13477])).
% 1.95/2.12 tff(13479,plain,
% 1.95/2.12 (r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13478, 1629])).
% 1.95/2.12 tff(13480,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7283, 13479, 13447, 2287, 335, 1181, 13465, 1632, 501, 1488, 682])).
% 1.95/2.12 tff(13481,plain,((~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13482,plain,
% 1.95/2.12 (~r(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13481, 13463, 335, 3340, 7240, 13357, 682, 1090, 13462, 2])).
% 1.95/2.12 tff(13483,plain,
% 1.95/2.12 (b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[72, 13482])).
% 1.95/2.12 tff(13484,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13483, 13060])).
% 1.95/2.12 tff(13485,plain,
% 1.95/2.12 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11382, 224, 13463, 13357, 13484])).
% 1.95/2.12 tff(13486,plain,
% 1.95/2.12 (~b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13485, 13373])).
% 1.95/2.12 tff(13487,plain,
% 1.95/2.12 (~b(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[12100, 13483, 1090, 13370, 2, 3])).
% 1.95/2.12 tff(13488,plain,
% 1.95/2.12 (r(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[653, 13487])).
% 1.95/2.12 tff(13489,plain,
% 1.95/2.12 (~b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9179, 13483, 1090, 13370])).
% 1.95/2.12 tff(13490,plain,
% 1.95/2.12 (r(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[100, 13489])).
% 1.95/2.12 tff(13491,plain,
% 1.95/2.12 (r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13490, 1629])).
% 1.95/2.12 tff(13492,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11579, 13490, 11371, 13483])).
% 1.95/2.12 tff(13493,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13492, 7328])).
% 1.95/2.12 tff(13494,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11403, 13493, 7240, 335, 13357, 13488, 13463, 13484])).
% 1.95/2.12 tff(13495,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1294, 13494, 1733])).
% 1.95/2.12 tff(13496,plain,
% 1.95/2.12 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[2029, 13495, 3340, 13493, 335, 13491])).
% 1.95/2.12 tff(13497,plain,
% 1.95/2.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13496, 7255])).
% 1.95/2.12 tff(13498,plain,
% 1.95/2.12 (r(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11437, 13497, 335])).
% 1.95/2.12 tff(13499,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9107, 13498, 13488])).
% 1.95/2.12 tff(13500,plain,
% 1.95/2.12 (b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[925, 13499])).
% 1.95/2.12 tff(13501,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13500, 13486])).
% 1.95/2.12 tff(13502,plain,((~b(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13503,plain,
% 1.95/2.12 (~b(elem!1, s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13502, 354, 1090, 2, 3, 335])).
% 1.95/2.12 tff(13504,plain,
% 1.95/2.12 (r(elem!1, s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[558, 13503, 3])).
% 1.95/2.12 tff(13505,plain,
% 1.95/2.12 (r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[101, 1629])).
% 1.95/2.12 tff(13506,plain,
% 1.95/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3455, 101, 13413])).
% 1.95/2.12 tff(13507,plain,
% 1.95/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[249, 13506])).
% 1.95/2.12 tff(13508,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13507, 7330])).
% 1.95/2.12 tff(13509,plain,
% 1.95/2.12 (r(elem!1, s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[101, 13106])).
% 1.95/2.12 tff(13510,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3896, 13509, 545])).
% 1.95/2.12 tff(13511,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13510, 7255])).
% 1.95/2.12 tff(13512,plain,
% 1.95/2.12 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 1.95/2.12 inference(monotonicity,[status(thm)],[335])).
% 1.95/2.12 tff(13513,plain,
% 1.95/2.12 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 1.95/2.12 inference(symmetry,[status(thm)],[13512])).
% 1.95/2.12 tff(13514,plain,
% 1.95/2.12 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[13513])).
% 1.95/2.12 tff(13515,plain,
% 1.95/2.12 (~r(z, elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7227, 13514])).
% 1.95/2.12 tff(13516,plain,
% 1.95/2.12 (~r(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[2332, 74, 102, 12977, 3, 83, 13107, 13515])).
% 1.95/2.12 tff(13517,plain,
% 1.95/2.12 (b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[72, 13516])).
% 1.95/2.12 tff(13518,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13517, 13060])).
% 1.95/2.12 tff(13519,plain,
% 1.95/2.12 (~b(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[12100, 13517, 1090, 13370, 2, 3])).
% 1.95/2.12 tff(13520,plain,
% 1.95/2.12 (r(s(z), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[653, 13519])).
% 1.95/2.12 tff(13521,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11403, 13508, 7240, 335, 13357, 13520, 501, 13518])).
% 1.95/2.12 tff(13522,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1294, 13521, 1733])).
% 1.95/2.12 tff(13523,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[2029, 13522, 13511, 1181, 13508, 335, 13505])).
% 1.95/2.12 tff(13524,plain,(b(z, s(s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13525,plain,
% 1.95/2.12 (b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13524, 3340, 335, 13369, 13504, 1090, 2, 3, 11372])).
% 1.95/2.12 tff(13526,plain,
% 1.95/2.12 (~b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[9179, 13525, 1090, 13370])).
% 1.95/2.12 tff(13527,plain,
% 1.95/2.12 (r(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[72, 13526])).
% 1.95/2.12 tff(13528,plain,
% 1.95/2.12 (r(s(s(s(elem!1))), elem!1)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13527, 12651])).
% 1.95/2.12 tff(13529,plain,
% 1.95/2.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[4689, 112, 3340, 13528])).
% 1.95/2.12 tff(13530,plain,
% 1.95/2.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[3905, 13529, 7255])).
% 1.95/2.12 tff(13531,plain,
% 1.95/2.12 (b(z, s(z))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13369, 12661])).
% 1.95/2.12 tff(13532,plain,
% 1.95/2.12 (~b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6404, 13525, 1090, 13531])).
% 1.95/2.12 tff(13533,plain,
% 1.95/2.12 (r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[925, 13532])).
% 1.95/2.12 tff(13534,plain,
% 1.95/2.12 (r(s(s(s(elem!1))), s(elem!1))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13533, 11406])).
% 1.95/2.12 tff(13535,plain,
% 1.95/2.12 (b(elem!1, s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13525, 10974])).
% 1.95/2.12 tff(13536,plain,
% 1.95/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13397, 112, 3340, 13528])).
% 1.95/2.12 tff(13537,plain,
% 1.95/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13536, 13391])).
% 1.95/2.12 tff(13538,plain,
% 1.95/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[249, 13537])).
% 1.95/2.12 tff(13539,plain,
% 1.95/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[13538, 7330])).
% 1.95/2.12 tff(13540,plain,
% 1.95/2.12 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7179, 13539, 13535, 13534, 1717, 13504, 13530, 1736, 11454])).
% 1.95/2.12 tff(13541,plain,
% 1.95/2.12 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11458, 13540, 1854])).
% 1.95/2.12 tff(13542,plain,
% 1.95/2.12 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1772, 13539, 3340, 1736, 1717, 13528, 13530])).
% 1.95/2.12 tff(13543,plain,
% 1.95/2.12 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1777, 13542, 1615])).
% 1.95/2.12 tff(13544,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11966, 13543, 13541, 13357, 13369])).
% 1.95/2.12 tff(13545,plain,(b(s(s(elem!1)), elem!1) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13546,plain,
% 1.95/2.12 (b(s(s(elem!1)), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13545, 12630, 12090, 2, 3])).
% 1.95/2.12 tff(13547,plain,
% 1.95/2.12 (b(s(elem!1), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13356, 12630, 12090, 2, 3])).
% 1.95/2.12 tff(13548,plain,
% 1.95/2.12 (b(s(s(elem!1)), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13545, 335, 1090, 2, 3])).
% 1.95/2.12 tff(13549,plain,
% 1.95/2.12 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[12994])).
% 1.95/2.12 tff(13550,plain,
% 1.95/2.12 (r(elem!1, s(s(s(elem!1))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[689, 13106])).
% 1.95/2.12 tff(13551,plain,
% 1.95/2.12 (~r(s(s(s(s(z)))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[11633, 689, 1668, 4569, 1090])).
% 1.95/2.12 tff(13552,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.95/2.12 tff(13553,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13552, 4575])).
% 1.95/2.12 tff(13554,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(s(s(s(z)))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(13555,plain,
% 1.95/2.12 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[13554, 13551, 335])).
% 1.95/2.12 tff(13556,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1294, 13555, 1733])).
% 1.95/2.12 tff(13557,plain,
% 1.95/2.12 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.95/2.12 inference(monotonicity,[status(thm)],[335])).
% 1.95/2.12 tff(13558,plain,
% 1.95/2.12 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.95/2.12 inference(symmetry,[status(thm)],[13557])).
% 1.95/2.12 tff(13559,plain,
% 1.95/2.12 (b(s(elem!1), z)),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[1488, 13558])).
% 1.95/2.12 tff(13560,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(13561,plain,
% 1.95/2.13 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), 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)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13562,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[13561])).
% 1.95/2.13 tff(13563,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[13562, 13560])).
% 1.95/2.13 tff(13564,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(13565,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13564, 13563])).
% 1.95/2.13 tff(13566,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13565, 224, 1488, 682, 1390, 1240, 500])).
% 1.95/2.13 tff(13567,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13568,plain,
% 1.95/2.13 (~b(s(elem!1), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13567, 682, 1488, 13559, 7333])).
% 1.95/2.13 tff(13569,plain,
% 1.95/2.13 (r(s(elem!1), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1521, 13568, 523])).
% 1.95/2.13 tff(13570,plain,
% 1.95/2.13 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1900, 112, 13569, 7479])).
% 1.95/2.13 tff(13571,plain,
% 1.95/2.13 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1869, 13570, 1683])).
% 1.95/2.13 tff(13572,plain,
% 1.95/2.13 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7610, 112, 13569, 7479])).
% 1.95/2.13 tff(13573,plain,
% 1.95/2.13 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1345, 13572, 1832])).
% 1.95/2.13 tff(13574,plain,
% 1.95/2.13 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4768, 13573, 1090, 335, 1488, 4569, 3919])).
% 1.95/2.13 tff(13575,plain,
% 1.95/2.13 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1884, 13574])).
% 1.95/2.13 tff(13576,plain,
% 1.95/2.13 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13575, 1786])).
% 1.95/2.13 tff(13577,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1794, 112, 13576, 3887])).
% 1.95/2.13 tff(13578,plain,
% 1.95/2.13 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1439, 13577, 1782])).
% 1.95/2.13 tff(13579,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1864, 224, 1488, 3919, 13578, 13571])).
% 1.95/2.13 tff(13580,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13581,plain,
% 1.95/2.13 (~b(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13580, 13556, 13357, 13550, 335, 1090, 4569, 7240, 13548, 319])).
% 1.95/2.13 tff(13582,plain,
% 1.95/2.13 (~b(z, s(s(z)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13581, 13549])).
% 1.95/2.13 tff(13583,plain,
% 1.95/2.13 (r(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[558, 13581, 3])).
% 1.95/2.13 tff(13584,plain,
% 1.95/2.13 (~r(s(s(elem!1)), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1001, 13583, 993])).
% 1.95/2.13 tff(13585,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[901, 13584])).
% 1.95/2.13 tff(13586,plain,
% 1.95/2.13 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3206, 13585, 1090, 5754])).
% 1.95/2.13 tff(13587,plain,
% 1.95/2.13 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[147, 13586, 2])).
% 1.95/2.13 tff(13588,plain,
% 1.95/2.13 (~r(z, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3074, 13587, 689])).
% 1.95/2.13 tff(13589,plain,
% 1.95/2.13 (~r(z, s(s(z)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7250, 13588, 335])).
% 1.95/2.13 tff(13590,plain,
% 1.95/2.13 (b(z, s(s(z)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1088, 13589])).
% 1.95/2.13 tff(13591,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13590, 13582])).
% 1.95/2.13 tff(13592,plain,((~r(z, s(s(s(z))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13593,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13592, 4646, 2, 1090, 335, 3, 4567])).
% 1.95/2.13 tff(13594,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[100, 13593])).
% 1.95/2.13 tff(13595,plain,
% 1.95/2.13 (~b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9179, 13594, 1090, 13370])).
% 1.95/2.13 tff(13596,plain,
% 1.95/2.13 (r(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[72, 13595])).
% 1.95/2.13 tff(13597,plain,
% 1.95/2.13 (r(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13596, 12651])).
% 1.95/2.13 tff(13598,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4608, 13596, 4567])).
% 1.95/2.13 tff(13599,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[925, 13598])).
% 1.95/2.13 tff(13600,plain,
% 1.95/2.13 (b(elem!1, s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13594, 10974])).
% 1.95/2.13 tff(13601,plain,
% 1.95/2.13 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7592, 13600, 335, 4567, 13599, 13597])).
% 1.95/2.13 tff(13602,plain,
% 1.95/2.13 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1294, 13601, 1733])).
% 1.95/2.13 tff(13603,plain,
% 1.95/2.13 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[12990, 12992])).
% 1.95/2.13 tff(13604,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13605,plain,
% 1.95/2.13 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13606,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[13605])).
% 1.95/2.13 tff(13607,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[13606, 13604])).
% 1.95/2.13 tff(13608,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(13609,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13608, 13607])).
% 1.95/2.13 tff(13610,plain,
% 1.95/2.13 (~b(s(elem!1), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13609, 224, 13357, 13548, 13600, 12646])).
% 1.95/2.13 tff(13611,plain,
% 1.95/2.13 (r(s(elem!1), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1521, 13610, 319])).
% 1.95/2.13 tff(13612,plain,
% 1.95/2.13 (r(s(z), s(s(elem!1)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13611, 12974])).
% 1.95/2.13 tff(13613,plain,
% 1.95/2.13 (~r(z, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6325, 13612, 4567])).
% 1.95/2.13 tff(13614,plain,
% 1.95/2.13 (~r(z, s(s(z)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7250, 13613, 335])).
% 1.95/2.13 tff(13615,plain,
% 1.95/2.13 (b(z, s(s(z)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1088, 13614])).
% 1.95/2.13 tff(13616,plain,
% 1.95/2.13 (b(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13615, 13603])).
% 1.95/2.13 tff(13617,plain,
% 1.95/2.13 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7477, 224, 13616, 13602, 13548])).
% 1.95/2.13 tff(13618,plain,
% 1.95/2.13 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1401, 68, 13617, 7240])).
% 1.95/2.13 tff(13619,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13620,plain,
% 1.95/2.13 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13621,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[13620])).
% 1.95/2.13 tff(13622,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[13621, 13619])).
% 1.95/2.13 tff(13623,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(13624,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13623, 13622])).
% 1.95/2.13 tff(13625,plain,
% 1.95/2.13 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13624, 224, 13357, 13602, 13600, 12646])).
% 1.95/2.13 tff(13626,plain,
% 1.95/2.13 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1869, 13625, 1683])).
% 1.95/2.13 tff(13627,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1900, 112, 13611, 13626, 13618])).
% 1.95/2.13 tff(13628,plain,((~r(elem!1, s(elem!1))) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13629,plain,
% 1.95/2.13 (~r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13628, 12630, 12090, 2, 3])).
% 1.95/2.13 tff(13630,plain,
% 1.95/2.13 (b(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[515, 13629, 327])).
% 1.95/2.13 tff(13631,plain,
% 1.95/2.13 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1496, 13630, 13547, 13546])).
% 1.95/2.13 tff(13632,plain,
% 1.95/2.13 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[530, 13631, 526])).
% 1.95/2.13 tff(13633,plain,
% 1.95/2.13 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12630])).
% 1.95/2.13 tff(13634,plain,
% 1.95/2.13 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.95/2.13 inference(symmetry,[status(thm)],[13633])).
% 1.95/2.13 tff(13635,plain,
% 1.95/2.13 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12633])).
% 1.95/2.13 tff(13636,plain,
% 1.95/2.13 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.95/2.13 inference(symmetry,[status(thm)],[13635])).
% 1.95/2.13 tff(13637,plain,
% 1.95/2.13 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 1.95/2.13 inference(transitivity,[status(thm)],[13636, 13634])).
% 1.95/2.13 tff(13638,plain,
% 1.95/2.13 (b(z, s(z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13630, 13637])).
% 1.95/2.13 tff(13639,plain,
% 1.95/2.13 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12634])).
% 1.95/2.13 tff(13640,plain,
% 1.95/2.13 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.95/2.13 inference(symmetry,[status(thm)],[13639])).
% 1.95/2.13 tff(13641,plain,
% 1.95/2.13 (b(s(s(z)), elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13546, 13640])).
% 1.95/2.13 tff(13642,plain,
% 1.95/2.13 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12630])).
% 1.95/2.13 tff(13643,plain,
% 1.95/2.13 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[13642])).
% 1.95/2.13 tff(13644,plain,
% 1.95/2.13 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1334, 13643])).
% 1.95/2.13 tff(13645,plain,
% 1.95/2.13 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1496, 501, 1488, 390])).
% 1.95/2.13 tff(13646,plain,
% 1.95/2.13 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[530, 13645, 526])).
% 1.95/2.13 tff(13647,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13474, 11386, 13646, 335])).
% 1.95/2.13 tff(13648,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[925, 13647])).
% 1.95/2.13 tff(13649,plain,
% 1.95/2.13 (~b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6404, 13648, 1090, 13107])).
% 1.95/2.13 tff(13650,plain,
% 1.95/2.13 (r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[100, 13649])).
% 1.95/2.13 tff(13651,plain,
% 1.95/2.13 (r(elem!1, s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13650, 13106])).
% 1.95/2.13 tff(13652,plain,
% 1.95/2.13 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3964, 13651, 335, 13375, 7333, 13107, 3919])).
% 1.95/2.13 tff(13653,plain,
% 1.95/2.13 (~b(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7481, 3919, 7240, 1488, 1832, 390, 501, 13646])).
% 1.95/2.13 tff(13654,plain,
% 1.95/2.13 (r(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[558, 13653, 3])).
% 1.95/2.13 tff(13655,plain,
% 1.95/2.13 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3896, 13651, 13654])).
% 1.95/2.13 tff(13656,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3905, 13655, 13652, 7255])).
% 1.95/2.13 tff(13657,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13658,plain,
% 1.95/2.13 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13657, 12630, 12090, 13630, 13547, 3, 13546])).
% 1.95/2.13 tff(13659,plain,
% 1.95/2.13 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1294, 13658, 13644])).
% 1.95/2.13 tff(13660,plain,
% 1.95/2.13 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3896, 13550, 545])).
% 1.95/2.13 tff(13661,plain,
% 1.95/2.13 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3074, 689, 12977])).
% 1.95/2.13 tff(13662,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[147, 13661, 2])).
% 1.95/2.13 tff(13663,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13662, 7328])).
% 1.95/2.13 tff(13664,plain,
% 1.95/2.13 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3915, 13663, 1798, 545, 335, 1630])).
% 1.95/2.13 tff(13665,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3905, 13664, 13660, 7255])).
% 1.95/2.13 tff(13666,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13667,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13666, 545, 1798, 335, 2])).
% 1.95/2.13 tff(13668,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[100, 13667])).
% 1.95/2.13 tff(13669,plain,
% 1.95/2.13 (~b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6404, 13668, 1090, 77])).
% 1.95/2.13 tff(13670,plain,
% 1.95/2.13 (r(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[925, 13669])).
% 1.95/2.13 tff(13671,plain,
% 1.95/2.13 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3196, 13670, 13087])).
% 1.95/2.13 tff(13672,plain,
% 1.95/2.13 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[249, 13671])).
% 1.95/2.13 tff(13673,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13672, 7330])).
% 1.95/2.13 tff(13674,plain,
% 1.95/2.13 (b(elem!1, s(s(s(elem!1))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13668, 10974])).
% 1.95/2.13 tff(13675,plain,
% 1.95/2.13 (~b(s(s(s(z))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13095, 13670, 544, 335, 1798, 1109, 545])).
% 1.95/2.13 tff(13676,plain,
% 1.95/2.13 (r(s(s(s(z))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[374, 13675, 4549])).
% 1.95/2.13 tff(13677,plain,
% 1.95/2.13 (r(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13676, 1655])).
% 1.95/2.13 tff(13678,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7429, 13677, 13674, 1386, 1798, 13673, 335, 545])).
% 1.95/2.13 tff(13679,plain,((~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13680,plain,
% 1.95/2.13 (~r(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13679, 13659, 7374, 12630, 13632, 13641, 12090, 13638, 2])).
% 1.95/2.13 tff(13681,plain,
% 1.95/2.13 (b(elem!1, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[558, 13680, 3])).
% 1.95/2.13 tff(13682,plain,
% 1.95/2.13 (~r(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7521, 13681, 12630, 7240, 13547, 13546, 13630, 13632])).
% 1.95/2.13 tff(13683,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.95/2.13 tff(13684,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.95/2.13 tff(13685,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.95/2.13 tff(13686,plain,
% 1.95/2.13 (((~![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))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(13687,plain,
% 1.95/2.13 ((~![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))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(13688,plain,
% 1.95/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13687, 13686])).
% 1.95/2.13 tff(13689,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13688, 68, 13685, 13684, 13683])).
% 1.95/2.13 tff(13690,plain,(b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13691,plain,
% 1.95/2.13 (b(s(s(s(elem!1))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13690, 13682, 12643])).
% 1.95/2.13 tff(13692,plain,
% 1.95/2.13 (b(s(s(s(z))), z)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13691, 12638])).
% 1.95/2.13 tff(13693,plain,
% 1.95/2.13 (b(z, s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[11358, 13681, 12630])).
% 1.95/2.13 tff(13694,plain,
% 1.95/2.13 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12630])).
% 1.95/2.13 tff(13695,plain,
% 1.95/2.13 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.95/2.13 inference(symmetry,[status(thm)],[13694])).
% 1.95/2.13 tff(13696,plain,
% 1.95/2.13 (b(s(s(elem!1)), z)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[13546, 13695])).
% 1.95/2.13 tff(13697,plain,
% 1.95/2.13 (elem!1 = z),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[338, 12630])).
% 1.95/2.13 tff(13698,plain,
% 1.95/2.13 (s(elem!1) = s(z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3984, 13697])).
% 1.95/2.13 tff(13699,plain,
% 1.95/2.13 (s(z) = s(elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3988, 13698])).
% 1.95/2.13 tff(13700,plain,
% 1.95/2.13 (b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4001, 13547, 13699])).
% 1.95/2.13 tff(13701,plain,
% 1.95/2.13 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3878, 12630])).
% 1.95/2.13 tff(13702,plain,
% 1.95/2.13 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[12082, 13691, 13546, 13681])).
% 1.95/2.13 tff(13703,plain,
% 1.95/2.13 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3905, 13702, 13701])).
% 1.95/2.13 tff(13704,plain,
% 1.95/2.13 (r(s(s(s(z))), s(s(elem!1)))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[11437, 13703, 12630])).
% 1.95/2.13 tff(13705,plain,
% 1.95/2.13 (~b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10953, 13704, 13700, 13696, 13638, 13693])).
% 1.95/2.13 tff(13706,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13705, 13692])).
% 1.95/2.13 tff(13707,plain,(b(z, elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13708,plain,
% 1.95/2.13 (b(z, elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13707, 3, 2])).
% 1.95/2.13 tff(13709,plain,
% 1.95/2.13 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[12123])).
% 1.95/2.13 tff(13710,plain,
% 1.95/2.13 (~(elem!1 = s(s(s(z))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[1165, 13709])).
% 1.95/2.13 tff(13711,plain,
% 1.95/2.13 (s(s(s(z))) = s(elem!1)),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[777, 775])).
% 1.95/2.13 tff(13712,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10736, 13711])).
% 1.95/2.13 tff(13713,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13714,plain,
% 1.95/2.13 (~(s(elem!1) = s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13713, 12111])).
% 1.95/2.13 tff(13715,plain,
% 1.95/2.13 (b(z, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9882, 2597, 4, 7066, 170, 354])).
% 1.95/2.13 tff(13716,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[530, 4113, 526])).
% 1.95/2.13 tff(13717,plain,
% 1.95/2.13 (~r(s(z), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2107, 13716, 409, 1181, 408])).
% 1.95/2.13 tff(13718,plain,
% 1.95/2.13 (b(s(z), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[454, 13717, 149])).
% 1.95/2.13 tff(13719,plain,
% 1.95/2.13 (~b(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10588, 4113, 149, 3, 157, 77, 408])).
% 1.95/2.13 tff(13720,plain,
% 1.95/2.13 (r(elem!1, s(elem!1))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[515, 13719, 327])).
% 1.95/2.13 tff(13721,plain,
% 1.95/2.13 (~b(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2904, 13718, 344, 77])).
% 1.95/2.13 tff(13722,plain,
% 1.95/2.13 (r(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1277, 13721, 88])).
% 1.95/2.13 tff(13723,plain,
% 1.95/2.13 (~r(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1604, 13722, 13720])).
% 1.95/2.13 tff(13724,plain,
% 1.95/2.13 (b(s(elem!1), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1476, 13723, 409])).
% 1.95/2.13 tff(13725,plain,
% 1.95/2.13 (~b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6730, 1, 344, 684])).
% 1.95/2.13 tff(13726,plain,
% 1.95/2.13 (r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[403, 13725, 157])).
% 1.95/2.13 tff(13727,plain,
% 1.95/2.13 (~b(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6470, 1, 77, 1347])).
% 1.95/2.13 tff(13728,plain,
% 1.95/2.13 (r(s(elem!1), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[498, 13727])).
% 1.95/2.13 tff(13729,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4310, 13728, 13726, 543])).
% 1.95/2.13 tff(13730,plain,((~b(s(z), z)) | (~r(elem!1, s(elem!1))) | (elem!1 = z) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13731,plain,
% 1.95/2.13 (~b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13730, 13720, 157, 77, 13724, 344, 13718])).
% 1.95/2.13 tff(13732,plain,
% 1.95/2.13 (r(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[194, 13731])).
% 1.95/2.13 tff(13733,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9119, 13732, 178])).
% 1.95/2.13 tff(13734,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[100, 13733])).
% 1.95/2.13 tff(13735,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1028, 13722, 178])).
% 1.95/2.13 tff(13736,plain,
% 1.95/2.13 (b(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[388, 13735, 680])).
% 1.95/2.13 tff(13737,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1259, 13732, 13722])).
% 1.95/2.13 tff(13738,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[403, 13737, 157])).
% 1.95/2.13 tff(13739,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9576, 224, 13738, 13736, 13734, 7672])).
% 1.95/2.13 tff(13740,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (elem!1 = s(z)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13741,plain,
% 1.95/2.13 (~r(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13740, 13715, 11, 176, 7066, 13708, 680, 83, 3340, 3])).
% 1.95/2.13 tff(13742,plain,
% 1.95/2.13 (b(s(elem!1), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[939, 13741, 303])).
% 1.95/2.13 tff(13743,plain,
% 1.95/2.13 (~r(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9119, 689, 178])).
% 1.95/2.13 tff(13744,plain,
% 1.95/2.13 (b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[194, 13743])).
% 1.95/2.13 tff(13745,plain,
% 1.95/2.13 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[11579, 9139, 7672, 689])).
% 1.95/2.13 tff(13746,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2076, 9146, 1181])).
% 1.95/2.13 tff(13747,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[403, 13746, 157])).
% 1.95/2.13 tff(13748,plain,
% 1.95/2.13 (~b(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10882, 13747, 13744, 77])).
% 1.95/2.13 tff(13749,plain,
% 1.95/2.13 (r(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1277, 13748, 88])).
% 1.95/2.13 tff(13750,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1028, 13749, 178])).
% 1.95/2.13 tff(13751,plain,
% 1.95/2.13 (b(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[388, 13750, 680])).
% 1.95/2.13 tff(13752,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10060, 224, 682, 13747, 13751, 13745, 7672])).
% 1.95/2.13 tff(13753,plain,(b(s(s(elem!1)), z) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(z)) | (~b(z, s(z))) | (elem!1 = z) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13754,plain,
% 1.95/2.13 (b(s(s(elem!1)), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13753, 689, 7672, 680, 178, 88, 77, 157, 1181, 682])).
% 1.95/2.13 tff(13755,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[12485, 13754, 1181, 543, 2505])).
% 1.95/2.13 tff(13756,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[403, 13755, 157])).
% 1.95/2.13 tff(13757,plain,
% 1.95/2.13 (~b(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10882, 13756, 13744, 77])).
% 1.95/2.13 tff(13758,plain,
% 1.95/2.13 (~b(s(s(elem!1)), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1249, 13754, 77, 13744])).
% 1.95/2.13 tff(13759,plain,
% 1.95/2.13 (r(s(s(elem!1)), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[901, 13758])).
% 1.95/2.13 tff(13760,plain,
% 1.95/2.13 (~r(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3588, 13759, 1181])).
% 1.95/2.13 tff(13761,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1277, 13760, 13757, 88])).
% 1.95/2.13 tff(13762,plain,((~r(z, s(s(s(z))))) | (elem!1 = s(z)) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(13763,plain,
% 1.95/2.13 (~r(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[13762, 543, 1181, 77, 157, 83, 1923, 7672, 680, 178, 682])).
% 1.95/2.13 tff(13764,plain,
% 1.95/2.13 (b(z, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[100, 13763])).
% 1.95/2.13 tff(13765,plain,
% 1.95/2.13 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[10929, 1240, 7672, 6255])).
% 1.95/2.13 tff(13766,plain,
% 1.95/2.13 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[147, 13765, 2])).
% 1.95/2.13 tff(13767,plain,
% 1.95/2.13 (r(elem!1, s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[9740, 13766, 178, 354, 682])).
% 1.95/2.13 tff(13768,plain,
% 1.95/2.13 (~r(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1028, 13767, 178])).
% 1.95/2.13 tff(13769,plain,
% 1.95/2.13 (b(elem!1, s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[388, 13768, 680])).
% 1.95/2.13 tff(13770,plain,
% 1.95/2.13 (~r(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[12485, 1240, 1181, 543, 2505])).
% 1.95/2.13 tff(13771,plain,
% 1.95/2.13 (b(elem!1, z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[403, 13770, 157])).
% 1.95/2.13 tff(13772,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13773,plain,
% 1.95/2.14 (((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13774,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[13773])).
% 1.95/2.14 tff(13775,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[13774, 13772])).
% 1.95/2.14 tff(13776,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(13777,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[13776, 13775])).
% 1.95/2.14 tff(13778,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13777, 224, 682, 13771, 1240, 13769, 6255])).
% 1.95/2.14 tff(13779,plain,((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13780,plain,
% 1.95/2.14 (~b(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13779, 13764, 682, 680, 178, 354, 2, 157, 7672, 1181, 543, 1923])).
% 1.95/2.14 tff(13781,plain,
% 1.95/2.14 (r(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[593, 13780])).
% 1.95/2.14 tff(13782,plain,
% 1.95/2.14 (~r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2076, 13781, 1181])).
% 1.95/2.14 tff(13783,plain,
% 1.95/2.14 (b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[403, 13782, 157])).
% 1.95/2.14 tff(13784,plain,
% 1.95/2.14 (~r(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[12361, 102, 523, 409, 179])).
% 1.95/2.14 tff(13785,plain,
% 1.95/2.14 (b(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[498, 13784])).
% 1.95/2.14 tff(13786,plain,
% 1.95/2.14 (~r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2076, 102, 1181])).
% 1.95/2.14 tff(13787,plain,
% 1.95/2.14 (b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[403, 13786, 157])).
% 1.95/2.14 tff(13788,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[946, 224, 1488, 13787, 13785, 344])).
% 1.95/2.14 tff(13789,plain,((~r(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (elem!1 = z) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13790,plain,
% 1.95/2.14 (~r(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13789, 13781, 344, 157, 523, 1488, 1181])).
% 1.95/2.14 tff(13791,plain,
% 1.95/2.14 (b(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[194, 13790])).
% 1.95/2.14 tff(13792,plain,
% 1.95/2.14 (~b(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10882, 13791, 13783, 77])).
% 1.95/2.14 tff(13793,plain,
% 1.95/2.14 (r(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1277, 13792, 83])).
% 1.95/2.14 tff(13794,plain,
% 1.95/2.14 (~r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3588, 13793, 1181])).
% 1.95/2.14 tff(13795,plain,
% 1.95/2.14 (~b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6730, 13791, 344, 13783])).
% 1.95/2.14 tff(13796,plain,
% 1.95/2.14 (r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13795, 91])).
% 1.95/2.14 tff(13797,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9569, 13796, 344, 7672, 682, 178, 1108, 13764, 1181, 13781, 83, 13783])).
% 1.95/2.14 tff(13798,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13797, 13794])).
% 1.95/2.14 tff(13799,plain,((~r(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(s(z)))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13800,plain,
% 1.95/2.14 (~r(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13799, 4261, 7066, 13708, 176, 3340, 13715, 11, 319, 13742, 680, 354, 2])).
% 1.95/2.14 tff(13801,plain,
% 1.95/2.14 (b(elem!1, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[515, 13800, 327])).
% 1.95/2.14 tff(13802,plain,
% 1.95/2.14 (~r(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13789, 179, 344, 157, 523, 1488, 1181])).
% 1.95/2.14 tff(13803,plain,
% 1.95/2.14 (b(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[593, 13802])).
% 1.95/2.14 tff(13804,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10929, 13803, 7672, 6255])).
% 1.95/2.14 tff(13805,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[147, 13804, 2])).
% 1.95/2.14 tff(13806,plain,
% 1.95/2.14 (r(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9740, 13805, 178, 354, 682])).
% 1.95/2.14 tff(13807,plain,
% 1.95/2.14 (~r(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1028, 13806, 178])).
% 1.95/2.14 tff(13808,plain,
% 1.95/2.14 (b(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[388, 13807, 680])).
% 1.95/2.14 tff(13809,plain,
% 1.95/2.14 (~b(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6542, 501, 344, 1488])).
% 1.95/2.14 tff(13810,plain,
% 1.95/2.14 (r(z, s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[625, 13809])).
% 1.95/2.14 tff(13811,plain,
% 1.95/2.14 (~r(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4231, 179, 13810])).
% 1.95/2.14 tff(13812,plain,
% 1.95/2.14 (b(s(z), s(elem!1))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[670, 13811, 561])).
% 1.95/2.14 tff(13813,plain,
% 1.95/2.14 (~b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4221, 13812, 1488, 501])).
% 1.95/2.14 tff(13814,plain,
% 1.95/2.14 (r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13813, 91])).
% 1.95/2.14 tff(13815,plain,
% 1.95/2.14 (~r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2841, 13814, 179])).
% 1.95/2.14 tff(13816,plain,
% 1.95/2.14 (b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[403, 13815, 157])).
% 1.95/2.14 tff(13817,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13777, 224, 682, 13816, 13803, 13808, 6255])).
% 1.95/2.14 tff(13818,plain,((~r(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = z) | (~r(s(z), s(s(s(z))))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13819,plain,
% 1.95/2.14 (~r(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13818, 6255, 682, 680, 157, 178, 354, 2, 1488, 501, 7672, 344, 523, 1181])).
% 1.95/2.14 tff(13820,plain,
% 1.95/2.14 (b(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[194, 13819])).
% 1.95/2.14 tff(13821,plain,
% 1.95/2.14 (~b(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10882, 13787, 1, 77])).
% 1.95/2.14 tff(13822,plain,
% 1.95/2.14 (r(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1277, 13821, 88])).
% 1.95/2.14 tff(13823,plain,
% 1.95/2.14 (~r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3588, 13822, 1181])).
% 1.95/2.14 tff(13824,plain,
% 1.95/2.14 (~b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6730, 13787, 344, 1])).
% 1.95/2.14 tff(13825,plain,
% 1.95/2.14 (r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13824, 149])).
% 1.95/2.14 tff(13826,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9569, 13825, 344, 7672, 682, 178, 1108, 6255, 1181, 102, 88, 13787])).
% 1.95/2.14 tff(13827,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13826, 13823])).
% 1.95/2.14 tff(13828,plain,((~r(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13829,plain,
% 1.95/2.14 (~r(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13828, 6255, 7672, 682, 178, 344, 1181, 83, 13820, 77, 157])).
% 1.95/2.14 tff(13830,plain,
% 1.95/2.14 (b(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[593, 13829])).
% 1.95/2.14 tff(13831,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10929, 13830, 7672, 6255])).
% 1.95/2.14 tff(13832,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[147, 13831, 2])).
% 1.95/2.14 tff(13833,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1249, 13830, 77, 13820])).
% 1.95/2.14 tff(13834,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13833])).
% 1.95/2.14 tff(13835,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4039, 13834, 13832, 178])).
% 1.95/2.14 tff(13836,plain,((~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (elem!1 = s(s(s(z)))) | b(s(s(elem!1)), elem!1) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13837,plain,
% 1.95/2.14 (~b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13836, 13715, 2, 176, 7066, 4261, 13708, 3340, 11, 680, 354, 13742, 13801, 319])).
% 1.95/2.14 tff(13838,plain,
% 1.95/2.14 (r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[100, 13837])).
% 1.95/2.14 tff(13839,plain,
% 1.95/2.14 (~r(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9119, 13838, 176])).
% 1.95/2.14 tff(13840,plain,
% 1.95/2.14 (b(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[194, 13839])).
% 1.95/2.14 tff(13841,plain,
% 1.95/2.14 (b(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13753, 13838, 7066, 680, 176, 83, 13715, 11, 3340, 4261])).
% 1.95/2.14 tff(13842,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1249, 13841, 13715, 13840])).
% 1.95/2.14 tff(13843,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13842])).
% 1.95/2.14 tff(13844,plain,
% 1.95/2.14 (~r(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3588, 13843, 3340])).
% 1.95/2.14 tff(13845,plain,
% 1.95/2.14 (b(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1277, 13844, 83])).
% 1.95/2.14 tff(13846,plain,
% 1.95/2.14 (~r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4065, 13843, 3340])).
% 1.95/2.14 tff(13847,plain,
% 1.95/2.14 (b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13846, 91])).
% 1.95/2.14 tff(13848,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2904, 13847, 13845, 13708, 13715])).
% 1.95/2.14 tff(13849,plain,(r(elem!1, s(s(elem!1))) | (elem!1 = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (z = elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13850,plain,
% 1.95/2.14 (r(elem!1, s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13849, 13710, 2, 354, 3, 4, 170])).
% 1.95/2.14 tff(13851,plain,
% 1.95/2.14 (~r(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[5470, 689, 178])).
% 1.95/2.14 tff(13852,plain,
% 1.95/2.14 (b(z, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[5459, 13851])).
% 1.95/2.14 tff(13853,plain,
% 1.95/2.14 (~b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6730, 405, 344, 1])).
% 1.95/2.14 tff(13854,plain,
% 1.95/2.14 (r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13853, 129])).
% 1.95/2.14 tff(13855,plain,
% 1.95/2.14 (~r(s(s(s(z))), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2374, 13854, 178])).
% 1.95/2.14 tff(13856,plain,
% 1.95/2.14 (b(s(s(s(z))), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[374, 13855, 362])).
% 1.95/2.14 tff(13857,plain,
% 1.95/2.14 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13858,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[13857])).
% 1.95/2.14 tff(13859,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.14 inference(transitivity,[status(thm)],[13858, 9443])).
% 1.95/2.14 tff(13860,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(13861,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[13860, 13859])).
% 1.95/2.14 tff(13862,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13861, 224, 405, 344, 13856, 7672])).
% 1.95/2.14 tff(13863,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13864,plain,
% 1.95/2.14 (~b(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13863, 13744, 7672, 362, 178, 149, 344])).
% 1.95/2.14 tff(13865,plain,
% 1.95/2.14 (r(elem!1, z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[403, 13864, 157])).
% 1.95/2.14 tff(13866,plain,
% 1.95/2.14 (~r(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2076, 13865, 1181])).
% 1.95/2.14 tff(13867,plain,
% 1.95/2.14 (b(s(s(elem!1)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[593, 13866])).
% 1.95/2.14 tff(13868,plain,
% 1.95/2.14 (~b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1249, 13867, 13852, 13744])).
% 1.95/2.14 tff(13869,plain,
% 1.95/2.14 (r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13868])).
% 1.95/2.14 tff(13870,plain,
% 1.95/2.14 (~r(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[3588, 13869, 1181])).
% 1.95/2.14 tff(13871,plain,
% 1.95/2.14 (b(elem!1, s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1277, 13870, 88])).
% 1.95/2.14 tff(13872,plain,
% 1.95/2.14 (~r(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[4065, 13869, 1181])).
% 1.95/2.14 tff(13873,plain,
% 1.95/2.14 (b(s(z), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[454, 13872, 149])).
% 1.95/2.14 tff(13874,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2904, 13873, 13871, 344, 13852])).
% 1.95/2.14 tff(13875,plain,((~r(z, s(s(s(z))))) | (~b(z, elem!1)) | (elem!1 = s(z)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(13876,plain,
% 1.95/2.14 (~r(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13875, 362, 83, 3340, 157, 7672, 13708, 176])).
% 1.95/2.14 tff(13877,plain,
% 1.95/2.14 (b(z, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[100, 13876])).
% 1.95/2.14 tff(13878,plain,
% 1.95/2.14 (~r(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[895, 102, 179])).
% 1.95/2.14 tff(13879,plain,
% 1.95/2.14 (b(s(s(elem!1)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[901, 13878])).
% 1.95/2.14 tff(13880,plain,
% 1.95/2.14 (~r(s(z), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[10648, 102, 179])).
% 1.95/2.14 tff(13881,plain,
% 1.95/2.14 (b(s(z), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[653, 13880])).
% 1.95/2.14 tff(13882,plain,
% 1.95/2.14 (~b(s(s(z)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9984, 102, 157, 170, 9138, 3, 6255, 2])).
% 1.95/2.14 tff(13883,plain,
% 1.95/2.14 (r(s(s(z)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[249, 13882])).
% 1.95/2.14 tff(13884,plain,
% 1.95/2.14 (~r(s(s(z)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6257, 13883, 176])).
% 1.95/2.14 tff(13885,plain,
% 1.95/2.14 (b(s(s(z)), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[2726, 13884])).
% 1.95/2.14 tff(13886,plain,
% 1.95/2.14 (~b(s(s(z)), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9920, 13885, 13881, 13879])).
% 1.95/2.14 tff(13887,plain,
% 1.95/2.14 (r(s(s(z)), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[265, 13886, 1108])).
% 1.95/2.14 tff(13888,plain,
% 1.95/2.14 (~r(s(s(z)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[276, 13887, 102])).
% 1.95/2.14 tff(13889,plain,
% 1.95/2.14 (b(s(s(z)), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[281, 13888])).
% 1.95/2.14 tff(13890,plain,
% 1.95/2.14 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[8623, 13889, 7672, 6255, 13887])).
% 1.95/2.14 tff(13891,plain,
% 1.95/2.14 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[147, 13890, 2])).
% 1.95/2.14 tff(13892,plain,
% 1.95/2.14 (~r(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[12361, 102, 319, 409, 179])).
% 1.95/2.14 tff(13893,plain,
% 1.95/2.14 (b(s(elem!1), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[498, 13892])).
% 1.95/2.14 tff(13894,plain,
% 1.95/2.14 (~b(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13789, 102, 13708, 157, 319, 179, 1181])).
% 1.95/2.14 tff(13895,plain,
% 1.95/2.14 (r(s(elem!1), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[939, 13894, 303])).
% 1.95/2.14 tff(13896,plain,
% 1.95/2.14 (~r(s(elem!1), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6557, 13895, 1181])).
% 1.95/2.14 tff(13897,plain,
% 1.95/2.14 (b(s(elem!1), s(s(elem!1)))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1521, 13896, 319])).
% 1.95/2.14 tff(13898,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13899,plain,
% 1.95/2.14 (((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13900,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[13899])).
% 1.95/2.14 tff(13901,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[13900, 13898])).
% 1.95/2.14 tff(13902,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(13903,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[13902, 13901])).
% 1.95/2.14 tff(13904,plain,
% 1.95/2.14 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13903, 224, 13897, 13893, 13891, 7672])).
% 1.95/2.14 tff(13905,plain,
% 1.95/2.14 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[1534, 13904, 7733])).
% 1.95/2.14 tff(13906,plain,
% 1.95/2.14 (~b(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[9576, 224, 13787, 6255, 7672])).
% 1.95/2.14 tff(13907,plain,
% 1.95/2.14 (r(elem!1, s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[388, 13906, 680])).
% 1.95/2.14 tff(13908,plain,
% 1.95/2.14 (((~![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(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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13909,plain,
% 1.95/2.14 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(13910,plain,
% 1.95/2.14 (((~![X0: $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(elem!1), s(s(s(z))))) | (~r(elem!1, 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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[13909])).
% 1.95/2.14 tff(13911,plain,
% 1.95/2.14 (((~![X0: $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(elem!1), s(s(s(z))))) | (~r(elem!1, 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(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[13910, 13908])).
% 1.95/2.14 tff(13912,plain,
% 1.95/2.14 ((~![X0: $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(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(13913,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[13912, 13911])).
% 1.95/2.14 tff(13914,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[13913, 112, 13895, 13907, 13905])).
% 1.95/2.14 tff(13915,plain,((~r(s(s(elem!1)), z)) | (s(elem!1) = s(s(s(z)))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(s(z), z)) | b(s(z), s(s(s(z)))) | b(z, s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13916,plain,
% 1.95/2.15 (~r(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13915, 9138, 680, 7672, 13877, 2, 3340, 157, 179, 170, 7733, 3])).
% 1.95/2.15 tff(13917,plain,
% 1.95/2.15 (b(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[593, 13916])).
% 1.95/2.15 tff(13918,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10929, 13917, 7672, 13877])).
% 1.95/2.15 tff(13919,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[147, 13918, 2])).
% 1.95/2.15 tff(13920,plain,
% 1.95/2.15 (~r(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[835, 13919, 176])).
% 1.95/2.15 tff(13921,plain,
% 1.95/2.15 (b(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[653, 13920])).
% 1.95/2.15 tff(13922,plain,
% 1.95/2.15 (~r(s(elem!1), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6557, 408, 1181])).
% 1.95/2.15 tff(13923,plain,
% 1.95/2.15 (b(s(elem!1), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1521, 13922, 523])).
% 1.95/2.15 tff(13924,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13925,plain,
% 1.95/2.15 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13926,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13925])).
% 1.95/2.15 tff(13927,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13926, 13924])).
% 1.95/2.15 tff(13928,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13929,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13928, 13927])).
% 1.95/2.15 tff(13930,plain,
% 1.95/2.15 (~b(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13929, 224, 4114, 13923, 2252])).
% 1.95/2.15 tff(13931,plain,
% 1.95/2.15 (r(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[670, 13930, 666])).
% 1.95/2.15 tff(13932,plain,
% 1.95/2.15 (~r(z, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4231, 13931, 179])).
% 1.95/2.15 tff(13933,plain,
% 1.95/2.15 (b(z, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[625, 13932])).
% 1.95/2.15 tff(13934,plain,
% 1.95/2.15 (~b(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4320, 13933, 1240, 4114])).
% 1.95/2.15 tff(13935,plain,
% 1.95/2.15 (r(s(elem!1), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[498, 13934])).
% 1.95/2.15 tff(13936,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12351, 112, 179, 13935, 13931])).
% 1.95/2.15 tff(13937,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (s(z) = s(elem!1)) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13938,plain,
% 1.95/2.15 (~r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13937, 13917, 179, 561, 13921, 3340, 319])).
% 1.95/2.15 tff(13939,plain,
% 1.95/2.15 (b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[939, 13938, 303])).
% 1.95/2.15 tff(13940,plain,
% 1.95/2.15 (b(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1277, 5750, 88])).
% 1.95/2.15 tff(13941,plain,
% 1.95/2.15 (b(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[454, 6910, 149])).
% 1.95/2.15 tff(13942,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6548, 13941, 13940, 3, 344, 354, 4569, 166, 1240, 1488])).
% 1.95/2.15 tff(13943,plain,((~r(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | b(s(s(elem!1)), elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13944,plain,
% 1.95/2.15 (~r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13943, 9147, 13708, 354, 3, 409, 13917, 13939, 83, 179])).
% 1.95/2.15 tff(13945,plain,
% 1.95/2.15 (b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[403, 13944, 157])).
% 1.95/2.15 tff(13946,plain,
% 1.95/2.15 (~b(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9576, 224, 13945, 13877, 7672])).
% 1.95/2.15 tff(13947,plain,
% 1.95/2.15 (r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[388, 13946, 680])).
% 1.95/2.15 tff(13948,plain,
% 1.95/2.15 (~r(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1028, 13947, 176])).
% 1.95/2.15 tff(13949,plain,
% 1.95/2.15 (b(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1277, 13948, 83])).
% 1.95/2.15 tff(13950,plain,
% 1.95/2.15 (~b(s(s(s(z))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9448, 224, 13945, 13708, 7672])).
% 1.95/2.15 tff(13951,plain,
% 1.95/2.15 (r(s(s(s(z))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[374, 13950, 362])).
% 1.95/2.15 tff(13952,plain,
% 1.95/2.15 (~r(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2374, 13951, 176])).
% 1.95/2.15 tff(13953,plain,
% 1.95/2.15 (b(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[454, 13952, 91])).
% 1.95/2.15 tff(13954,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6548, 13953, 13949, 3, 13708, 354, 9147, 409, 13917, 13939])).
% 1.95/2.15 tff(13955,plain,(b(z, s(z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13956,plain,
% 1.95/2.15 (b(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13955, 179, 354, 362, 680, 7672, 157, 3, 2, 170, 7733])).
% 1.95/2.15 tff(13957,plain,
% 1.95/2.15 (~r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13740, 13956, 157, 176, 7672, 13708, 680, 83, 3340, 3])).
% 1.95/2.15 tff(13958,plain,
% 1.95/2.15 (b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[939, 13957, 303])).
% 1.95/2.15 tff(13959,plain,
% 1.95/2.15 (~r(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13789, 13958, 13708, 157, 319, 179, 3340])).
% 1.95/2.15 tff(13960,plain,
% 1.95/2.15 (b(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[593, 13959])).
% 1.95/2.15 tff(13961,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10929, 13960, 7672, 13877])).
% 1.95/2.15 tff(13962,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[147, 13961, 2])).
% 1.95/2.15 tff(13963,plain,
% 1.95/2.15 (~r(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[835, 13962, 176])).
% 1.95/2.15 tff(13964,plain,
% 1.95/2.15 (b(s(z), s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[653, 13963])).
% 1.95/2.15 tff(13965,plain,
% 1.95/2.15 (~r(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4039, 13962, 176])).
% 1.95/2.15 tff(13966,plain,
% 1.95/2.15 (b(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[901, 13965])).
% 1.95/2.15 tff(13967,plain,
% 1.95/2.15 (~b(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10876, 13966, 13956, 13964])).
% 1.95/2.15 tff(13968,plain,
% 1.95/2.15 (r(z, s(s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[752, 13967])).
% 1.95/2.15 tff(13969,plain,
% 1.95/2.15 (((~![X0: $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, z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13970,plain,
% 1.95/2.15 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(13971,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[13970])).
% 1.95/2.15 tff(13972,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[13971, 13969])).
% 1.95/2.15 tff(13973,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(13974,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[13973, 13972])).
% 1.95/2.15 tff(13975,plain,
% 1.95/2.15 (~r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13974, 112, 545, 13968])).
% 1.95/2.15 tff(13976,plain,
% 1.95/2.15 (b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[403, 13975, 157])).
% 1.95/2.15 tff(13977,plain,
% 1.95/2.15 (~b(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9576, 224, 13976, 13877, 7672])).
% 1.95/2.15 tff(13978,plain,
% 1.95/2.15 (r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[388, 13977, 680])).
% 1.95/2.15 tff(13979,plain,
% 1.95/2.15 (~r(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1028, 13978, 176])).
% 1.95/2.15 tff(13980,plain,
% 1.95/2.15 (b(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1277, 13979, 83])).
% 1.95/2.15 tff(13981,plain,
% 1.95/2.15 (~b(s(s(s(z))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9448, 224, 13976, 13708, 7672])).
% 1.95/2.15 tff(13982,plain,
% 1.95/2.15 (r(s(s(s(z))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[374, 13981, 362])).
% 1.95/2.15 tff(13983,plain,
% 1.95/2.15 (~r(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2374, 13982, 176])).
% 1.95/2.15 tff(13984,plain,
% 1.95/2.15 (b(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[454, 13983, 91])).
% 1.95/2.15 tff(13985,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2904, 13984, 13980, 13708, 13956])).
% 1.95/2.15 tff(13986,plain,((~r(s(z), z)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | b(s(z), s(s(s(z)))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(13987,plain,
% 1.95/2.15 (~r(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13986, 12126, 13710, 7066, 11, 13850, 2, 3, 354, 170, 13714])).
% 1.95/2.15 tff(13988,plain,
% 1.95/2.15 (b(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[194, 13987])).
% 1.95/2.15 tff(13989,plain,
% 1.95/2.15 (~b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13863, 13988, 7066, 12126, 176, 91, 13708])).
% 1.95/2.15 tff(13990,plain,
% 1.95/2.15 (r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[403, 13989, 11])).
% 1.95/2.15 tff(13991,plain,
% 1.95/2.15 (~r(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2076, 13990, 3340])).
% 1.95/2.15 tff(13992,plain,
% 1.95/2.15 (b(s(s(elem!1)), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[593, 13991])).
% 1.95/2.15 tff(13993,plain,
% 1.95/2.15 (~r(z, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13875, 12126, 83, 3340, 11, 7066, 13708, 176])).
% 1.95/2.15 tff(13994,plain,
% 1.95/2.15 (b(z, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[100, 13993])).
% 1.95/2.15 tff(13995,plain,
% 1.95/2.15 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[10929, 13992, 7066, 13994])).
% 1.95/2.15 tff(13996,plain,
% 1.95/2.15 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[147, 13995, 2])).
% 1.95/2.15 tff(13997,plain,
% 1.95/2.15 (~r(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4039, 13996, 176])).
% 1.95/2.15 tff(13998,plain,
% 1.95/2.15 (b(s(s(elem!1)), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[901, 13997])).
% 1.95/2.15 tff(13999,plain,
% 1.95/2.15 (~b(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1249, 13998, 13988, 13992])).
% 1.95/2.15 tff(14000,plain,
% 1.95/2.15 (r(z, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[5459, 13999])).
% 1.95/2.15 tff(14001,plain,
% 1.95/2.15 (~r(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[5749, 14000, 13990])).
% 1.95/2.15 tff(14002,plain,
% 1.95/2.15 (b(elem!1, s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1277, 14001, 83])).
% 1.95/2.15 tff(14003,plain,
% 1.95/2.15 (~r(elem!1, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[12485, 13992, 3340, 13990, 526])).
% 1.95/2.15 tff(14004,plain,
% 1.95/2.15 (b(elem!1, s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[515, 14003, 327])).
% 1.95/2.15 tff(14005,plain,
% 1.95/2.15 (~r(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2107, 11508, 166, 1181, 408])).
% 1.95/2.15 tff(14006,plain,
% 1.95/2.15 (b(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[454, 14005, 129])).
% 1.95/2.15 tff(14007,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14008,plain,
% 1.95/2.15 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14009,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[14008])).
% 1.95/2.15 tff(14010,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[14009, 14007])).
% 1.95/2.15 tff(14011,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(14012,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[14011, 14010])).
% 1.95/2.15 tff(14013,plain,
% 1.95/2.15 ((~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14012, 224, 501, 1, 2696])).
% 1.95/2.15 tff(14014,plain,
% 1.95/2.15 (~b(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14013, 14006])).
% 1.95/2.15 tff(14015,plain,
% 1.95/2.15 (r(s(z), s(elem!1))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[670, 14014, 415])).
% 1.95/2.15 tff(14016,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14017,plain,
% 1.95/2.15 (((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14018,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[14017])).
% 1.95/2.15 tff(14019,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[14018, 14016])).
% 1.95/2.15 tff(14020,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(14021,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[14020, 14019])).
% 1.95/2.15 tff(14022,plain,
% 1.95/2.15 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14021, 224, 2696, 6255, 7672])).
% 1.95/2.15 tff(14023,plain,
% 1.95/2.15 (r(s(elem!1), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1534, 14022, 7733])).
% 1.95/2.15 tff(14024,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7719, 112, 178, 14023, 14015])).
% 1.95/2.15 tff(14025,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (s(z) = elem!1) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(s(z)))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(14026,plain,
% 1.95/2.15 (~r(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14025, 14004, 176, 13988, 91, 160, 3340, 13714, 526, 13994, 7066, 13990])).
% 1.95/2.15 tff(14027,plain,
% 1.95/2.15 (b(s(elem!1), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[939, 14026, 303])).
% 1.95/2.15 tff(14028,plain,
% 1.95/2.15 (~b(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6548, 14027, 3, 13708, 354, 14000, 160, 13992, 14002])).
% 1.95/2.15 tff(14029,plain,
% 1.95/2.15 (r(s(z), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[454, 14028, 91])).
% 1.95/2.15 tff(14030,plain,
% 1.95/2.15 (~b(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9411, 14029, 4, 12126, 14000, 176])).
% 1.95/2.15 tff(14031,plain,
% 1.95/2.15 (r(elem!1, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[388, 14030, 13710])).
% 1.95/2.15 tff(14032,plain,
% 1.95/2.15 (((~![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))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14033,plain,
% 1.95/2.15 (((~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))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(14034,plain,
% 1.95/2.15 (((~![X0: $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)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[14033])).
% 1.95/2.15 tff(14035,plain,
% 1.95/2.15 (((~![X0: $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))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[14034, 14032])).
% 1.95/2.15 tff(14036,plain,
% 1.95/2.15 ((~![X0: $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)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(14037,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[14036, 14035])).
% 1.95/2.15 tff(14038,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14037, 112, 14029, 14031, 176])).
% 1.95/2.15 tff(14039,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (z = elem!1) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(14040,plain,
% 1.95/2.15 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14039, 354, 3, 4, 2, 170])).
% 1.95/2.15 tff(14041,plain,
% 1.95/2.15 (~r(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[2076, 102, 3340])).
% 1.95/2.15 tff(14042,plain,
% 1.95/2.15 (b(elem!1, z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[403, 14041, 157])).
% 1.95/2.15 tff(14043,plain,
% 1.95/2.15 (~b(s(s(s(z))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[9448, 224, 14042, 13708, 7672])).
% 1.95/2.15 tff(14044,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[13875, 5800, 101, 88, 1181, 157, 7672, 344, 178])).
% 1.95/2.15 tff(14045,plain,(b(z, s(s(s(z)))) | (elem!1 = s(z)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(14046,plain,
% 1.95/2.15 (b(z, s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[14045, 3340, 83, 157, 7672, 13708, 176])).
% 1.95/2.16 tff(14047,plain,
% 1.95/2.16 (~b(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9984, 9138, 157, 170, 102, 3, 14046, 2])).
% 1.95/2.16 tff(14048,plain,
% 1.95/2.16 (r(s(s(z)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[249, 14047])).
% 1.95/2.16 tff(14049,plain,
% 1.95/2.16 (~r(s(s(z)), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6257, 14048, 176])).
% 1.95/2.16 tff(14050,plain,
% 1.95/2.16 (b(s(s(z)), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2726, 14049])).
% 1.95/2.16 tff(14051,plain,
% 1.95/2.16 (s(s(s(z))) = elem!1),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[374, 9406, 5799])).
% 1.95/2.16 tff(14052,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14051])).
% 1.95/2.16 tff(14053,plain,
% 1.95/2.16 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14052])).
% 1.95/2.16 tff(14054,plain,
% 1.95/2.16 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14053])).
% 1.95/2.16 tff(14055,plain,
% 1.95/2.16 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[354, 14054])).
% 1.95/2.16 tff(14056,plain,
% 1.95/2.16 (~r(s(z), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6496, 416, 1181])).
% 1.95/2.16 tff(14057,plain,
% 1.95/2.16 (b(s(z), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[653, 14056])).
% 1.95/2.16 tff(14058,plain,
% 1.95/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9920, 14057, 1241, 2844])).
% 1.95/2.16 tff(14059,plain,
% 1.95/2.16 (r(s(s(z)), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[265, 14058, 259])).
% 1.95/2.16 tff(14060,plain,
% 1.95/2.16 (~r(s(s(z)), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[276, 14059, 102])).
% 1.95/2.16 tff(14061,plain,
% 1.95/2.16 (b(s(s(z)), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[281, 14060])).
% 1.95/2.16 tff(14062,plain,
% 1.95/2.16 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[8623, 14061, 6255, 7672, 14059])).
% 1.95/2.16 tff(14063,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[147, 14062, 2])).
% 1.95/2.16 tff(14064,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14063, 14055])).
% 1.95/2.16 tff(14065,plain,((~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | b(s(s(s(z))), elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(14066,plain,
% 1.95/2.16 (~r(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14065, 14050, 2, 1108, 7672, 354, 14046, 102, 14043, 9916, 3340, 176])).
% 1.95/2.16 tff(14067,plain,
% 1.95/2.16 (b(s(z), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[454, 14066, 91])).
% 1.95/2.16 tff(14068,plain,
% 1.95/2.16 (~(elem!1 = s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2477, 14067, 170])).
% 1.95/2.16 tff(14069,plain,
% 1.95/2.16 (~(s(s(s(z))) = elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2487, 14068])).
% 1.95/2.16 tff(14070,plain,
% 1.95/2.16 (~b(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6730, 14067, 13708, 14042])).
% 1.95/2.16 tff(14071,plain,
% 1.95/2.16 (r(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[194, 14070])).
% 1.95/2.16 tff(14072,plain,
% 1.95/2.16 (s(elem!1) = s(s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13955, 14071, 354, 9138, 14068, 7672, 157, 3, 2, 170, 14069])).
% 1.95/2.16 tff(14073,plain,
% 1.95/2.16 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14072])).
% 1.95/2.16 tff(14074,plain,
% 1.95/2.16 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14073])).
% 1.95/2.16 tff(14075,plain,
% 1.95/2.16 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14074])).
% 1.95/2.16 tff(14076,plain,
% 1.95/2.16 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14075])).
% 1.95/2.16 tff(14077,plain,
% 1.95/2.16 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14076])).
% 1.95/2.16 tff(14078,plain,
% 1.95/2.16 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.95/2.16 inference(symmetry,[status(thm)],[14077])).
% 1.95/2.16 tff(14079,plain,
% 1.95/2.16 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14076])).
% 1.95/2.16 tff(14080,plain,
% 1.95/2.16 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14079])).
% 1.95/2.16 tff(14081,plain,
% 1.95/2.16 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14072])).
% 1.95/2.16 tff(14082,plain,
% 1.95/2.16 (elem!1 = s(s(z))),
% 1.95/2.16 inference(transitivity,[status(thm)],[155, 14081, 31])).
% 1.95/2.16 tff(14083,plain,
% 1.95/2.16 (s(s(z)) = elem!1),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2769, 2588])).
% 1.95/2.16 tff(14084,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2796, 14083])).
% 1.95/2.16 tff(14085,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(14086,plain,
% 1.95/2.16 (s(s(z)) = elem!1),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14085, 14082])).
% 1.95/2.16 tff(14087,plain,
% 1.95/2.16 (~b(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13789, 14071, 13708, 157, 319, 102, 3340])).
% 1.95/2.16 tff(14088,plain,
% 1.95/2.16 (r(s(elem!1), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[939, 14087, 303])).
% 1.95/2.16 tff(14089,plain,
% 1.95/2.16 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14072])).
% 1.95/2.16 tff(14090,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14089])).
% 1.95/2.16 tff(14091,plain,
% 1.95/2.16 (~b(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9576, 224, 14042, 14046, 7672])).
% 1.95/2.16 tff(14092,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[388, 14068, 14091])).
% 1.95/2.16 tff(14093,plain,
% 1.95/2.16 (r(elem!1, s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14092, 14090])).
% 1.95/2.16 tff(14094,plain,
% 1.95/2.16 (r(elem!1, s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10079, 9138, 2, 157, 170, 102, 3])).
% 1.95/2.16 tff(14095,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14072])).
% 1.95/2.16 tff(14096,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14095])).
% 1.95/2.16 tff(14097,plain,
% 1.95/2.16 (~r(s(z), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[10648, 14071, 102])).
% 1.95/2.16 tff(14098,plain,
% 1.95/2.16 (b(s(z), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[653, 14097])).
% 1.95/2.16 tff(14099,plain,
% 1.95/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[9920, 14098, 14050, 9916])).
% 1.95/2.16 tff(14100,plain,
% 1.95/2.16 (r(s(s(z)), s(s(elem!1)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[265, 14099, 1108])).
% 1.95/2.16 tff(14101,plain,
% 1.95/2.16 (~r(s(s(z)), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[276, 14100, 102])).
% 1.95/2.16 tff(14102,plain,
% 1.95/2.16 (b(s(s(z)), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[281, 14101])).
% 1.95/2.16 tff(14103,plain,
% 1.95/2.16 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[8623, 14102, 7672, 14046, 14100])).
% 1.95/2.16 tff(14104,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[147, 14103, 2])).
% 1.95/2.16 tff(14105,plain,
% 1.95/2.16 (b(s(s(elem!1)), s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14104, 14096])).
% 1.95/2.16 tff(14106,plain,
% 1.95/2.16 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14072])).
% 1.95/2.16 tff(14107,plain,
% 1.95/2.16 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14106, 1147])).
% 1.95/2.16 tff(14108,plain,
% 1.95/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14107])).
% 1.95/2.16 tff(14109,plain,
% 1.95/2.16 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14108])).
% 1.95/2.16 tff(14110,plain,
% 1.95/2.16 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1165, 14109])).
% 1.95/2.16 tff(14111,plain,
% 1.95/2.16 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1317, 1290, 1288, 1287])).
% 1.95/2.16 tff(14112,plain,
% 1.95/2.16 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13074, 5889, 1391, 2287, 545, 543, 523, 408])).
% 1.95/2.16 tff(14113,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1345, 14112, 14111, 1286])).
% 1.95/2.16 tff(14114,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(14115,plain,
% 1.95/2.16 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14114, 14110, 14105, 7240, 14094, 14093, 319, 14088, 1288, 14087])).
% 1.95/2.16 tff(14116,plain,
% 1.95/2.16 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[5887, 14115, 14086])).
% 1.95/2.16 tff(14117,plain,
% 1.95/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1170])).
% 1.95/2.16 tff(14118,plain,
% 1.95/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14117, 1143])).
% 1.95/2.16 tff(14119,plain,
% 1.95/2.16 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14118])).
% 1.95/2.16 tff(14120,plain,
% 1.95/2.16 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1165, 14119])).
% 1.95/2.16 tff(14121,plain,
% 1.95/2.16 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[5881, 1170])).
% 1.95/2.16 tff(14122,plain,
% 1.95/2.16 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14121])).
% 1.95/2.16 tff(14123,plain,
% 1.95/2.16 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[2226, 14122])).
% 1.95/2.16 tff(14124,plain,
% 1.95/2.16 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1345, 14123, 14120])).
% 1.95/2.16 tff(14125,plain,
% 1.95/2.16 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[5994])).
% 1.95/2.16 tff(14126,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14125])).
% 1.95/2.16 tff(14127,plain,
% 1.95/2.16 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1169])).
% 1.95/2.16 tff(14128,plain,
% 1.95/2.16 (r(elem!1, s(s(s(z))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[196, 14127])).
% 1.95/2.16 tff(14129,plain,
% 1.95/2.16 (r(elem!1, s(elem!1))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14128, 14126])).
% 1.95/2.16 tff(14130,plain,
% 1.95/2.16 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[13011, 112, 14129, 14124])).
% 1.95/2.16 tff(14131,plain,
% 1.95/2.16 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1169])).
% 1.95/2.16 tff(14132,plain,
% 1.95/2.16 (b(s(z), elem!1)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[6298, 14131])).
% 1.95/2.16 tff(14133,plain,
% 1.95/2.16 (~b(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[461, 224, 405, 14132, 344])).
% 1.95/2.16 tff(14134,plain,
% 1.95/2.16 (r(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[194, 14133])).
% 1.95/2.16 tff(14135,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14136,plain,
% 1.95/2.16 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14137,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14136])).
% 1.95/2.16 tff(14138,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14137, 14135])).
% 1.95/2.16 tff(14139,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(14140,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14139, 14138])).
% 1.95/2.16 tff(14141,plain,
% 1.95/2.16 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14140, 112, 14134, 3557, 14124])).
% 1.95/2.16 tff(14142,plain,
% 1.95/2.16 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 14141])).
% 1.95/2.16 tff(14143,plain,
% 1.95/2.16 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4892, 112, 3557, 14124])).
% 1.95/2.16 tff(14144,plain,
% 1.95/2.16 (b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4896, 68, 1364, 14143])).
% 1.95/2.16 tff(14145,plain,
% 1.95/2.16 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[1169])).
% 1.95/2.16 tff(14146,plain,
% 1.95/2.16 (~r(s(s(z)), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6257, 196, 178])).
% 1.95/2.16 tff(14147,plain,
% 1.95/2.16 (b(s(s(z)), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[2726, 14146])).
% 1.95/2.16 tff(14148,plain,
% 1.95/2.16 (b(elem!1, s(z))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14147, 14145])).
% 1.95/2.16 tff(14149,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14150,plain,
% 1.95/2.16 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14151,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14150])).
% 1.95/2.16 tff(14152,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14151, 14149])).
% 1.95/2.16 tff(14153,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(14154,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14153, 14152])).
% 1.95/2.16 tff(14155,plain,
% 1.95/2.16 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14154, 224, 14148, 14144, 14142])).
% 1.95/2.16 tff(14156,plain,
% 1.95/2.16 (elem!1 = s(s(s(s(elem!1))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1439, 14155, 14130])).
% 1.95/2.16 tff(14157,plain,
% 1.95/2.16 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[1169, 14156])).
% 1.95/2.16 tff(14158,plain,
% 1.95/2.16 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14157])).
% 1.95/2.16 tff(14159,plain,
% 1.95/2.16 (s(z) = s(s(s(elem!1)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[50, 14158, 989])).
% 1.95/2.16 tff(14160,plain,
% 1.95/2.16 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14159])).
% 1.95/2.16 tff(14161,plain,
% 1.95/2.16 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14160])).
% 1.95/2.16 tff(14162,plain,
% 1.95/2.16 (s(s(elem!1)) = z),
% 1.95/2.16 inference(transitivity,[status(thm)],[1376, 14161, 27])).
% 1.95/2.16 tff(14163,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[566, 14162])).
% 1.95/2.16 tff(14164,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(14165,plain,
% 1.95/2.16 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14164, 14086, 13708, 14042, 176, 14048])).
% 1.95/2.16 tff(14166,plain,
% 1.95/2.16 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14082])).
% 1.95/2.16 tff(14167,plain,
% 1.95/2.16 (b(z, s(s(z)))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[13708, 14166])).
% 1.95/2.16 tff(14168,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14169,plain,
% 1.95/2.16 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14170,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14169])).
% 1.95/2.16 tff(14171,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14170, 14168])).
% 1.95/2.16 tff(14172,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(14173,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14172, 14171])).
% 1.95/2.16 tff(14174,plain,
% 1.95/2.16 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[14173, 224, 7672, 14167, 14165, 14116])).
% 1.95/2.16 tff(14175,plain,
% 1.95/2.16 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14174, 14080])).
% 1.95/2.16 tff(14176,plain,
% 1.95/2.16 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1338, 14175])).
% 1.95/2.16 tff(14177,plain,
% 1.95/2.16 (r(s(s(s(s(s(s(z)))))), z)),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[14176, 14078])).
% 1.95/2.16 tff(14178,plain,
% 1.95/2.16 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14076])).
% 1.95/2.16 tff(14179,plain,
% 1.95/2.16 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[14178, 2260])).
% 1.95/2.16 tff(14180,plain,
% 1.95/2.16 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.95/2.16 inference(symmetry,[status(thm)],[14179])).
% 1.95/2.16 tff(14181,plain,
% 1.95/2.16 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14180])).
% 1.95/2.16 tff(14182,plain,
% 1.95/2.16 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[1364, 14181])).
% 1.95/2.16 tff(14183,plain,
% 1.95/2.16 (~r(s(z), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6296, 14048, 176])).
% 1.95/2.16 tff(14184,plain,
% 1.95/2.16 (b(s(z), s(s(z)))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[1071, 14183])).
% 1.95/2.16 tff(14185,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14186,plain,
% 1.95/2.16 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(14187,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[14186])).
% 1.95/2.16 tff(14188,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[14187, 14185])).
% 1.95/2.17 tff(14189,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(14190,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14189, 14188])).
% 1.95/2.17 tff(14191,plain,
% 1.95/2.17 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14190, 224, 14184, 14050, 14116])).
% 1.95/2.17 tff(14192,plain,
% 1.95/2.17 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2314, 68, 14191])).
% 1.95/2.17 tff(14193,plain,
% 1.95/2.17 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14192, 14182])).
% 1.95/2.17 tff(14194,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), 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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14195,plain,
% 1.95/2.17 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14196,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14195])).
% 1.95/2.17 tff(14197,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[14196, 14194])).
% 1.95/2.17 tff(14198,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(14199,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14198, 14197])).
% 1.95/2.17 tff(14200,plain,
% 1.95/2.17 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14199, 112, 14071])).
% 1.95/2.17 tff(14201,plain,
% 1.95/2.17 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14200, 14193])).
% 1.95/2.17 tff(14202,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14201, 14177])).
% 1.95/2.17 tff(14203,plain,(b(z, s(z)) | (~b(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(14204,plain,
% 1.95/2.17 (b(z, s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14203, 102, 1288, 2, 7672, 157, 354, 3, 170])).
% 1.95/2.17 tff(14205,plain,
% 1.95/2.17 (elem!1 = s(s(s(z)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[13740, 408, 157, 176, 7672, 344, 77, 88, 1181, 3])).
% 1.95/2.17 tff(14206,plain,
% 1.95/2.17 (~b(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2477, 14205, 170])).
% 1.95/2.17 tff(14207,plain,
% 1.95/2.17 (r(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[454, 14206, 149])).
% 1.95/2.17 tff(14208,plain,
% 1.95/2.17 (~b(z, s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1205, 14207, 1181, 77])).
% 1.95/2.17 tff(14209,plain,
% 1.95/2.17 (r(z, s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[752, 14208])).
% 1.95/2.17 tff(14210,plain,
% 1.95/2.17 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2107, 14207, 409, 1181, 408])).
% 1.95/2.17 tff(14211,plain,
% 1.95/2.17 (r(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[530, 14210, 526])).
% 1.95/2.17 tff(14212,plain,
% 1.95/2.17 (~b(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[449, 14207, 409, 77, 408])).
% 1.95/2.17 tff(14213,plain,
% 1.95/2.17 (r(z, s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[625, 14212])).
% 1.95/2.17 tff(14214,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[576, 14213, 14211, 14209])).
% 1.95/2.17 tff(14215,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | b(s(z), s(s(s(z)))) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(14216,plain,
% 1.95/2.17 (~r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14215, 14204, 3340, 170, 157, 7672, 13708, 83, 3])).
% 1.95/2.17 tff(14217,plain,
% 1.95/2.17 (b(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[939, 14216, 303])).
% 1.95/2.17 tff(14218,plain,
% 1.95/2.17 (~r(s(z), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[13789, 14217, 13708, 157, 319, 102, 3340])).
% 1.95/2.17 tff(14219,plain,
% 1.95/2.17 (b(s(z), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[194, 14218])).
% 1.95/2.17 tff(14220,plain,
% 1.95/2.17 (~b(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6730, 14219, 13708, 14042])).
% 1.95/2.17 tff(14221,plain,
% 1.95/2.17 (r(s(z), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[454, 14220, 91])).
% 1.95/2.17 tff(14222,plain,
% 1.95/2.17 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[5914, 14221, 3340, 1288])).
% 1.95/2.17 tff(14223,plain,
% 1.95/2.17 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1324, 224, 14222, 14042, 13708])).
% 1.95/2.17 tff(14224,plain,
% 1.95/2.17 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1338, 14223])).
% 1.95/2.17 tff(14225,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14226,plain,
% 1.95/2.17 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14227,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14226])).
% 1.95/2.17 tff(14228,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[14227, 14225])).
% 1.95/2.17 tff(14229,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(14230,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14229, 14228])).
% 1.95/2.17 tff(14231,plain,
% 1.95/2.17 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14230, 112, 3340, 102, 14224])).
% 1.95/2.17 tff(14232,plain,
% 1.95/2.17 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1401, 68, 7240, 14231])).
% 1.95/2.17 tff(14233,plain,
% 1.95/2.17 (s(s(s(z))) = elem!1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[13863, 14219, 7672, 14042, 176, 91, 13708])).
% 1.95/2.17 tff(14234,plain,
% 1.95/2.17 (s(s(s(s(z)))) = s(elem!1)),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14233])).
% 1.95/2.17 tff(14235,plain,
% 1.95/2.17 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14234])).
% 1.95/2.17 tff(14236,plain,
% 1.95/2.17 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14235])).
% 1.95/2.17 tff(14237,plain,
% 1.95/2.17 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14236])).
% 1.95/2.17 tff(14238,plain,
% 1.95/2.17 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14237])).
% 1.95/2.17 tff(14239,plain,
% 1.95/2.17 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14238])).
% 1.95/2.17 tff(14240,plain,
% 1.95/2.17 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14234])).
% 1.95/2.17 tff(14241,plain,
% 1.95/2.17 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.95/2.17 inference(transitivity,[status(thm)],[14240, 11069])).
% 1.95/2.17 tff(14242,plain,
% 1.95/2.17 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14241])).
% 1.95/2.17 tff(14243,plain,
% 1.95/2.17 (elem!1 = s(s(s(z)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2487, 14233])).
% 1.95/2.17 tff(14244,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.95/2.17 tff(14245,plain,
% 1.95/2.17 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14244])).
% 1.95/2.17 tff(14246,plain,
% 1.95/2.17 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[1679, 14245, 1705])).
% 1.95/2.17 tff(14247,plain,
% 1.95/2.17 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14246])).
% 1.95/2.17 tff(14248,plain,
% 1.95/2.17 (s(s(z)) = s(s(elem!1))),
% 1.95/2.17 inference(transitivity,[status(thm)],[32, 14247, 292, 3027])).
% 1.95/2.17 tff(14249,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[259, 14248])).
% 1.95/2.17 tff(14250,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(s(elem!1))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(14251,plain,
% 1.95/2.17 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14250, 14243, 1108])).
% 1.95/2.17 tff(14252,plain,
% 1.95/2.17 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14251, 14242])).
% 1.95/2.17 tff(14253,plain,
% 1.95/2.17 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14252, 14239])).
% 1.95/2.17 tff(14254,plain,
% 1.95/2.17 (~b(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[946, 224, 14217, 14042, 13708])).
% 1.95/2.17 tff(14255,plain,
% 1.95/2.17 (r(s(elem!1), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[498, 14254])).
% 1.95/2.17 tff(14256,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14257,plain,
% 1.95/2.17 (((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(14258,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14257])).
% 1.95/2.17 tff(14259,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[14258, 14256])).
% 1.95/2.17 tff(14260,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
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% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14260, 14259])).
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% 1.95/2.17 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1345, 14262, 14253])).
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% 1.95/2.17 (~r(s(s(elem!1)), s(elem!1))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[955, 112, 102, 14255])).
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% 1.95/2.17 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
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% 1.95/2.17 inference(monotonicity,[status(thm)],[14306])).
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% 1.95/2.17 inference(monotonicity,[status(thm)],[14307])).
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% 1.95/2.17 inference(monotonicity,[status(thm)],[14314])).
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% 1.95/2.17 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
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% 1.95/2.17 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[14307])).
% 1.95/2.17 tff(14344,plain,
% 1.95/2.17 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
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% 1.95/2.17 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14325, 14344])).
% 1.95/2.17 tff(14346,plain,
% 1.95/2.17 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
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% 1.95/2.17 tff(14347,plain,
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% 1.95/2.17 inference(unit_resolution,[status(thm)],[2841, 14350, 416])).
% 1.95/2.17 tff(14352,plain,
% 1.95/2.17 (b(elem!1, z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[403, 14351, 11])).
% 1.95/2.17 tff(14353,plain,
% 1.95/2.17 (~b(s(s(s(z))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[9448, 224, 14352, 344, 7672])).
% 1.95/2.17 tff(14354,plain,
% 1.95/2.17 (s(s(s(z))) = elem!1),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[374, 14353, 14292])).
% 1.95/2.17 tff(14355,plain,
% 1.95/2.17 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.95/2.17 inference(monotonicity,[status(thm)],[86])).
% 1.95/2.17 tff(14356,plain,
% 1.95/2.17 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.95/2.17 inference(symmetry,[status(thm)],[14355])).
% 1.95/2.17 tff(14357,plain,
% 1.95/2.17 (~(elem!1 = s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1306, 10386])).
% 1.95/2.17 tff(14358,plain,
% 1.95/2.17 (~(s(elem!1) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[302, 14357])).
% 1.95/2.17 tff(14359,plain,
% 1.95/2.17 (~(s(elem!1) = s(s(elem!1)))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[318, 14357])).
% 1.95/2.17 tff(14360,plain,
% 1.95/2.17 (~b(z, elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[9460, 86, 9138])).
% 1.95/2.17 tff(14361,plain,
% 1.95/2.17 (r(z, elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[289, 14360, 4])).
% 1.95/2.17 tff(14362,plain,
% 1.95/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[352, 14357])).
% 1.95/2.17 tff(14363,plain,
% 1.95/2.17 (r(s(s(elem!1)), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[360, 14362, 354])).
% 1.95/2.17 tff(14364,plain,
% 1.95/2.17 (~r(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[4126, 14363, 14361, 14359])).
% 1.95/2.17 tff(14365,plain,
% 1.95/2.17 (b(s(elem!1), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[939, 14364, 14358])).
% 1.95/2.17 tff(14366,plain,
% 1.95/2.17 (b(s(s(z)), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7872, 14365, 86])).
% 1.95/2.17 tff(14367,plain,
% 1.95/2.17 (b(s(s(z)), s(z))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[14366, 14356])).
% 1.95/2.17 tff(14368,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2724, 14367])).
% 1.95/2.17 tff(14369,plain,((~(s(z) = elem!1)) | b(s(s(z)), s(z)) | b(s(s(elem!1)), elem!1) | (z = elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(14370,plain,
% 1.95/2.17 (~(s(z) = elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[14369, 2724, 354, 4, 9138])).
% 1.95/2.17 tff(14371,plain,
% 1.95/2.17 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[131, 14370])).
% 1.95/2.18 tff(14372,plain,
% 1.95/2.18 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[310, 14371])).
% 1.95/2.18 tff(14373,plain,
% 1.95/2.18 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[147, 14372, 9721])).
% 1.95/2.18 tff(14374,plain,
% 1.95/2.18 (r(s(s(z)), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2726, 2724])).
% 1.95/2.18 tff(14375,plain,
% 1.95/2.18 (~r(s(s(z)), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6167, 14374, 9147])).
% 1.95/2.18 tff(14376,plain,
% 1.95/2.18 (b(s(s(z)), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[281, 14375])).
% 1.95/2.18 tff(14377,plain,
% 1.95/2.18 (~b(s(s(z)), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9201, 14376, 7672, 6255])).
% 1.95/2.18 tff(14378,plain,
% 1.95/2.18 (r(s(s(z)), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[249, 14377])).
% 1.95/2.18 tff(14379,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14380,plain,
% 1.95/2.18 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14381,plain,
% 1.95/2.18 (((~![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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14380])).
% 1.95/2.18 tff(14382,plain,
% 1.95/2.18 (((~![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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14381, 14379])).
% 1.95/2.18 tff(14383,plain,
% 1.95/2.18 ((~![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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(14384,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14383, 14382])).
% 1.95/2.18 tff(14385,plain,
% 1.95/2.18 (~r(s(s(elem!1)), s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14384, 112, 14378, 14373])).
% 1.95/2.18 tff(14386,plain,
% 1.95/2.18 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3547, 68, 14385])).
% 1.95/2.18 tff(14387,plain,
% 1.95/2.18 (b(s(s(elem!1)), s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14386, 3623])).
% 1.95/2.18 tff(14388,plain,
% 1.95/2.18 (~r(z, s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6072, 112, 9147, 14374])).
% 1.95/2.18 tff(14389,plain,
% 1.95/2.18 (b(z, s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1088, 14388])).
% 1.95/2.18 tff(14390,plain,
% 1.95/2.18 (((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14391,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14390])).
% 1.95/2.18 tff(14392,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14391, 3761])).
% 1.95/2.18 tff(14393,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(14394,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14393, 14392])).
% 1.95/2.18 tff(14395,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14394, 224, 1240, 14389, 14376, 14387])).
% 1.95/2.18 tff(14396,plain,(b(s(s(z)), s(z)) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (z = elem!1) | b(z, s(z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(14397,plain,
% 1.95/2.18 (b(s(s(z)), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14396, 9138, 7672, 354, 6255, 4, 1240])).
% 1.95/2.18 tff(14398,plain,
% 1.95/2.18 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[10038, 14354, 14290])).
% 1.95/2.18 tff(14399,plain,
% 1.95/2.18 (s(s(s(s(z)))) = s(elem!1)),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14354])).
% 1.95/2.18 tff(14400,plain,
% 1.95/2.18 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14399])).
% 1.95/2.18 tff(14401,plain,
% 1.95/2.18 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14400])).
% 1.95/2.18 tff(14402,plain,
% 1.95/2.18 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(symmetry,[status(thm)],[14401])).
% 1.95/2.18 tff(14403,plain,
% 1.95/2.18 (~b(s(s(z)), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9920, 14397, 14294, 14290])).
% 1.95/2.18 tff(14404,plain,
% 1.95/2.18 (r(s(s(z)), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[265, 14403, 169])).
% 1.95/2.18 tff(14405,plain,
% 1.95/2.18 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14404, 14402])).
% 1.95/2.18 tff(14406,plain,
% 1.95/2.18 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4511, 14354, 14294])).
% 1.95/2.18 tff(14407,plain,
% 1.95/2.18 (~b(s(s(z)), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[8623, 14404, 7672, 6255, 827])).
% 1.95/2.18 tff(14408,plain,
% 1.95/2.18 (r(s(s(z)), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[281, 14407])).
% 1.95/2.18 tff(14409,plain,
% 1.95/2.18 (~r(s(z), s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9974, 14350, 14408])).
% 1.95/2.18 tff(14410,plain,
% 1.95/2.18 (b(s(z), s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1071, 14409])).
% 1.95/2.18 tff(14411,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14399, 14400])).
% 1.95/2.18 tff(14412,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14411, 519])).
% 1.95/2.18 tff(14413,plain,
% 1.95/2.18 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.95/2.18 inference(symmetry,[status(thm)],[14412])).
% 1.95/2.18 tff(14414,plain,
% 1.95/2.18 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14413])).
% 1.95/2.18 tff(14415,plain,
% 1.95/2.18 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[526, 14414])).
% 1.95/2.18 tff(14416,plain,
% 1.95/2.18 (~b(s(s(s(s(z)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[8879, 14415, 14410, 14406, 14405, 14398, 14397])).
% 1.95/2.18 tff(14417,plain,
% 1.95/2.18 (~b(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[946, 224, 14297, 14352, 344])).
% 1.95/2.18 tff(14418,plain,
% 1.95/2.18 (r(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[498, 14417])).
% 1.95/2.18 tff(14419,plain,
% 1.95/2.18 (~r(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[482, 112, 14350, 14418])).
% 1.95/2.18 tff(14420,plain,
% 1.95/2.18 (b(s(elem!1), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1476, 14419, 160])).
% 1.95/2.18 tff(14421,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4136, 14420, 14416, 14354])).
% 1.95/2.18 tff(14422,plain,(b(z, s(z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(z) = elem!1) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (z = elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(14423,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14422, 416, 7672, 344, 3, 354, 14291, 129, 1408, 1240, 6255, 827, 4, 170])).
% 1.95/2.18 tff(14424,plain,
% 1.95/2.18 (~b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1249, 14423, 1240, 14290])).
% 1.95/2.18 tff(14425,plain,
% 1.95/2.18 (r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[194, 14424])).
% 1.95/2.18 tff(14426,plain,
% 1.95/2.18 (~r(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2841, 14425, 416])).
% 1.95/2.18 tff(14427,plain,
% 1.95/2.18 (b(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[403, 14426, 11])).
% 1.95/2.18 tff(14428,plain,
% 1.95/2.18 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1324, 224, 14291, 14427, 344])).
% 1.95/2.18 tff(14429,plain,
% 1.95/2.18 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1338, 14428])).
% 1.95/2.18 tff(14430,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14431,plain,
% 1.95/2.18 (((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14432,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14431])).
% 1.95/2.18 tff(14433,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14432, 14430])).
% 1.95/2.18 tff(14434,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(14435,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14434, 14433])).
% 1.95/2.18 tff(14436,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14435, 112, 14425, 14429])).
% 1.95/2.18 tff(14437,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 14436])).
% 1.95/2.18 tff(14438,plain,
% 1.95/2.18 (~b(s(s(s(z))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9448, 224, 14427, 344, 7672])).
% 1.95/2.18 tff(14439,plain,
% 1.95/2.18 (s(s(s(z))) = elem!1),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[374, 14438, 14292])).
% 1.95/2.18 tff(14440,plain,
% 1.95/2.18 (s(s(s(s(z)))) = s(elem!1)),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14439])).
% 1.95/2.18 tff(14441,plain,
% 1.95/2.18 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14440])).
% 1.95/2.18 tff(14442,plain,
% 1.95/2.18 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14441])).
% 1.95/2.18 tff(14443,plain,
% 1.95/2.18 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14442])).
% 1.95/2.18 tff(14444,plain,
% 1.95/2.18 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14443])).
% 1.95/2.18 tff(14445,plain,
% 1.95/2.18 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14444])).
% 1.95/2.18 tff(14446,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14440])).
% 1.95/2.18 tff(14447,plain,
% 1.95/2.18 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14446, 11069])).
% 1.95/2.18 tff(14448,plain,
% 1.95/2.18 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14447])).
% 1.95/2.18 tff(14449,plain,
% 1.95/2.18 (elem!1 = s(s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2487, 14439])).
% 1.95/2.18 tff(14450,plain,
% 1.95/2.18 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14250, 14449, 169])).
% 1.95/2.18 tff(14451,plain,
% 1.95/2.18 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14450, 14448])).
% 1.95/2.18 tff(14452,plain,
% 1.95/2.18 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14451, 14445])).
% 1.95/2.18 tff(14453,plain,
% 1.95/2.18 (~b(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[946, 224, 14297, 14427, 344])).
% 1.95/2.18 tff(14454,plain,
% 1.95/2.18 (r(s(elem!1), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[498, 14453])).
% 1.95/2.18 tff(14455,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14261, 112, 14454, 14429])).
% 1.95/2.18 tff(14456,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1345, 14455, 14452])).
% 1.95/2.18 tff(14457,plain,
% 1.95/2.18 (~r(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[12351, 112, 14425, 14454])).
% 1.95/2.18 tff(14458,plain,
% 1.95/2.18 (b(s(z), s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[670, 14457, 4204])).
% 1.95/2.18 tff(14459,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14460,plain,
% 1.95/2.18 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14461,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14460])).
% 1.95/2.18 tff(14462,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14461, 14459])).
% 1.95/2.18 tff(14463,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(14464,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14463, 14462])).
% 1.95/2.18 tff(14465,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14464, 224, 14297, 14291, 14458, 14456, 14437])).
% 1.95/2.18 tff(14466,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (s(z) = elem!1) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (z = elem!1) | b(s(z), s(s(s(z)))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(14467,plain,
% 1.95/2.18 (~r(s(z), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14466, 14269, 7066, 13708, 3, 354, 91, 14270, 14272, 4, 170, 14040])).
% 1.95/2.18 tff(14468,plain,
% 1.95/2.18 (b(s(z), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[454, 14467, 91])).
% 1.95/2.18 tff(14469,plain,
% 1.95/2.18 (~(elem!1 = s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2477, 14468, 170])).
% 1.95/2.18 tff(14470,plain,
% 1.95/2.18 (~(s(s(s(z))) = elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[2487, 14469])).
% 1.95/2.18 tff(14471,plain,
% 1.95/2.18 (r(elem!1, s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[13849, 14469, 2, 354, 3, 4, 170])).
% 1.95/2.18 tff(14472,plain,
% 1.95/2.18 (~r(s(z), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[835, 14272, 176])).
% 1.95/2.18 tff(14473,plain,
% 1.95/2.18 (b(s(z), s(s(elem!1)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[653, 14472])).
% 1.95/2.18 tff(14474,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14475,plain,
% 1.95/2.18 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(14476,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14475])).
% 1.95/2.18 tff(14477,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.95/2.18 inference(transitivity,[status(thm)],[14476, 14474])).
% 1.95/2.18 tff(14478,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(14479,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14478, 14477])).
% 1.95/2.18 tff(14480,plain,
% 1.95/2.18 (~b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14479, 224, 14269, 14473, 14468, 13708])).
% 1.95/2.18 tff(14481,plain,
% 1.95/2.18 (r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[194, 14480])).
% 1.95/2.18 tff(14482,plain,
% 1.95/2.18 (s(elem!1) = s(s(s(z)))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[13986, 14481, 14469, 7066, 11, 14471, 2, 3, 354, 170, 14470])).
% 1.95/2.18 tff(14483,plain,
% 1.95/2.18 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14482])).
% 1.95/2.18 tff(14484,plain,
% 1.95/2.18 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 1.95/2.18 inference(symmetry,[status(thm)],[14483])).
% 1.95/2.18 tff(14485,plain,
% 1.95/2.18 (b(z, s(elem!1))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14270, 14484])).
% 1.95/2.18 tff(14486,plain,
% 1.95/2.18 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14482])).
% 1.95/2.18 tff(14487,plain,
% 1.95/2.18 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.95/2.18 inference(symmetry,[status(thm)],[14486])).
% 1.95/2.18 tff(14488,plain,
% 1.95/2.18 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[14487])).
% 1.95/2.18 tff(14489,plain,
% 1.95/2.18 (~b(s(s(elem!1)), s(elem!1))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[14271, 14488])).
% 1.95/2.18 tff(14490,plain,
% 1.95/2.18 (b(elem!1, s(elem!1))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[541, 14489, 3, 354])).
% 1.95/2.18 tff(14491,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6542, 14490, 14485, 13708, 14288])).
% 1.95/2.18 tff(14492,plain,(b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(14493,plain,
% 1.95/2.18 (b(s(s(elem!1)), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[14492, 170, 2, 3, 4])).
% 1.95/2.18 tff(14494,plain,
% 1.95/2.18 (~r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[9119, 101, 178])).
% 1.95/2.18 tff(14495,plain,
% 1.95/2.18 (b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[194, 14494])).
% 1.95/2.18 tff(14496,plain,
% 1.95/2.18 (~r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5470, 101, 178])).
% 1.95/2.18 tff(14497,plain,
% 1.95/2.18 (b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5459, 14496])).
% 1.95/2.18 tff(14498,plain,
% 1.95/2.18 (~b(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[10094, 224, 14497, 14495, 7672])).
% 1.95/2.18 tff(14499,plain,
% 1.95/2.18 (r(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[925, 14498])).
% 1.95/2.18 tff(14500,plain,
% 1.95/2.18 (~(s(s(s(z))) = elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[347, 74, 13708])).
% 1.95/2.18 tff(14501,plain,
% 1.95/2.18 (~b(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[13863, 14495, 7672, 14500, 178, 91, 13708])).
% 1.95/2.18 tff(14502,plain,
% 1.95/2.18 (r(elem!1, z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[403, 14501, 157])).
% 1.95/2.19 tff(14503,plain,
% 1.95/2.19 (~b(s(z), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[11913, 6484, 2, 3, 7672, 74])).
% 1.95/2.19 tff(14504,plain,
% 1.95/2.19 (~r(s(z), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[835, 6554, 178])).
% 1.95/2.19 tff(14505,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[653, 14504, 14503])).
% 1.95/2.19 tff(14506,plain,(b(s(s(elem!1)), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14507,plain,
% 1.95/2.19 (b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14506, 74, 2, 3, 7672, 178])).
% 1.95/2.19 tff(14508,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14509,plain,
% 1.95/2.19 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14510,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14509])).
% 1.95/2.19 tff(14511,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[14510, 14508])).
% 1.95/2.19 tff(14512,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(14513,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14512, 14511])).
% 1.95/2.19 tff(14514,plain,
% 1.95/2.19 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14513, 224, 13708, 390, 7672])).
% 1.95/2.19 tff(14515,plain,
% 1.95/2.19 (~b(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14514, 14507])).
% 1.95/2.19 tff(14516,plain,
% 1.95/2.19 (r(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[593, 14515])).
% 1.95/2.19 tff(14517,plain,
% 1.95/2.19 (~r(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2512, 14516, 1488, 526, 390, 327, 14502])).
% 1.95/2.19 tff(14518,plain,
% 1.95/2.19 (b(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[625, 14517])).
% 1.95/2.19 tff(14519,plain,
% 1.95/2.19 (~b(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6542, 14518, 13708, 1488])).
% 1.95/2.19 tff(14520,plain,
% 1.95/2.19 (r(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[515, 14519, 327])).
% 1.95/2.19 tff(14521,plain,
% 1.95/2.19 (~r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4310, 14520, 14502])).
% 1.95/2.19 tff(14522,plain,
% 1.95/2.19 (b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[498, 14521])).
% 1.95/2.19 tff(14523,plain,
% 1.95/2.19 (~b(s(elem!1), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6470, 14522, 14495, 14497])).
% 1.95/2.19 tff(14524,plain,
% 1.95/2.19 (r(s(elem!1), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1476, 14523, 409])).
% 1.95/2.19 tff(14525,plain,
% 1.95/2.19 (~r(s(s(s(z))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[9022, 112, 14524, 14499])).
% 1.95/2.19 tff(14526,plain,
% 1.95/2.19 (~r(elem!1, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1604, 14524, 14520])).
% 1.95/2.19 tff(14527,plain,
% 1.95/2.19 (b(elem!1, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1277, 14526, 83])).
% 1.95/2.19 tff(14528,plain,
% 1.95/2.19 (~b(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2904, 14527, 13708, 14497])).
% 1.95/2.19 tff(14529,plain,
% 1.95/2.19 (r(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[454, 14528, 91])).
% 1.95/2.19 tff(14530,plain,
% 1.95/2.19 (~r(s(s(s(z))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2374, 14529, 178])).
% 1.95/2.19 tff(14531,plain,
% 1.95/2.19 (b(s(s(s(z))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[374, 14530, 14500])).
% 1.95/2.19 tff(14532,plain,
% 1.95/2.19 (~b(s(s(s(z))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[10823, 224, 1488, 14531, 14518, 7672])).
% 1.95/2.19 tff(14533,plain,
% 1.95/2.19 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[816, 68, 14532])).
% 1.95/2.19 tff(14534,plain,
% 1.95/2.19 (s(s(s(z))) = s(elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14533, 14525])).
% 1.95/2.19 tff(14535,plain,
% 1.95/2.19 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14534])).
% 1.95/2.19 tff(14536,plain,
% 1.95/2.19 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[14535])).
% 1.95/2.19 tff(14537,plain,
% 1.95/2.19 (elem!1 = s(s(z))),
% 1.95/2.19 inference(transitivity,[status(thm)],[155, 14536, 31])).
% 1.95/2.19 tff(14538,plain,
% 1.95/2.19 (~r(s(s(z)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[12443, 14499, 101, 14497, 14495])).
% 1.95/2.19 tff(14539,plain,
% 1.95/2.19 (b(s(s(z)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[249, 14538])).
% 1.95/2.19 tff(14540,plain,
% 1.95/2.19 (~b(s(s(elem!1)), s(s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2395, 224, 14539, 390, 14531, 14507])).
% 1.95/2.19 tff(14541,plain,
% 1.95/2.19 (~(s(s(z)) = elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2402, 14540, 390])).
% 1.95/2.19 tff(14542,plain,
% 1.95/2.19 (~(elem!1 = s(s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14085, 14541])).
% 1.95/2.19 tff(14543,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14542, 14537])).
% 1.95/2.19 tff(14544,plain,(b(z, s(s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14545,plain,
% 1.95/2.19 (b(z, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14544, 1488, 14493, 7066, 176, 2, 3, 11])).
% 1.95/2.19 tff(14546,plain,
% 1.95/2.19 (~b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2904, 2896, 344, 684])).
% 1.95/2.19 tff(14547,plain,
% 1.95/2.19 (r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5459, 14546])).
% 1.95/2.19 tff(14548,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5576, 5704, 6532, 523, 14547])).
% 1.95/2.19 tff(14549,plain,((~b(elem!1, s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14550,plain,
% 1.95/2.19 (~b(elem!1, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14549, 684, 409, 523, 390, 1488, 344])).
% 1.95/2.19 tff(14551,plain,
% 1.95/2.19 (r(elem!1, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1277, 14550, 88])).
% 1.95/2.19 tff(14552,plain,
% 1.95/2.19 (~(elem!1 = s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2477, 684, 170])).
% 1.95/2.19 tff(14553,plain,
% 1.95/2.19 (~r(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1028, 14551, 176])).
% 1.95/2.19 tff(14554,plain,
% 1.95/2.19 (b(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[388, 14553, 14552])).
% 1.95/2.19 tff(14555,plain,
% 1.95/2.19 (~b(elem!1, z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[8978, 224, 14554, 6255, 7672])).
% 1.95/2.19 tff(14556,plain,
% 1.95/2.19 (r(elem!1, z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[403, 14555, 157])).
% 1.95/2.19 tff(14557,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14558,plain,
% 1.95/2.19 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14559,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14558])).
% 1.95/2.19 tff(14560,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[14559, 14557])).
% 1.95/2.19 tff(14561,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(14562,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14561, 14560])).
% 1.95/2.19 tff(14563,plain,
% 1.95/2.19 (~b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14562, 224, 684, 344, 14554, 6255])).
% 1.95/2.19 tff(14564,plain,
% 1.95/2.19 (r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5459, 14563])).
% 1.95/2.19 tff(14565,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5749, 14564, 14556, 14551])).
% 1.95/2.19 tff(14566,plain,((~b(s(z), elem!1)) | (elem!1 = z) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (elem!1 = s(z)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14567,plain,
% 1.95/2.19 (~b(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14566, 14545, 13708, 11, 7066, 83, 319, 14493, 1488, 170])).
% 1.95/2.19 tff(14568,plain,
% 1.95/2.19 (r(s(z), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[454, 14567, 91])).
% 1.95/2.19 tff(14569,plain,
% 1.95/2.19 (~r(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2841, 363, 416])).
% 1.95/2.19 tff(14570,plain,
% 1.95/2.19 (b(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[194, 14569])).
% 1.95/2.19 tff(14571,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14572,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(14573,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14572, 14571])).
% 1.95/2.19 tff(14574,plain,
% 1.95/2.19 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14573, 224, 1, 344, 390])).
% 1.95/2.19 tff(14575,plain,
% 1.95/2.19 (~b(s(s(elem!1)), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14574, 1240])).
% 1.95/2.19 tff(14576,plain,
% 1.95/2.19 (r(s(s(elem!1)), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[901, 14575])).
% 1.95/2.19 tff(14577,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4039, 14576, 13766, 178])).
% 1.95/2.19 tff(14578,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14579,plain,
% 1.95/2.19 (~b(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14578, 14570, 2, 178, 344, 390, 7672, 6255])).
% 1.95/2.19 tff(14580,plain,
% 1.95/2.19 (r(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[593, 14579])).
% 1.95/2.19 tff(14581,plain,
% 1.95/2.19 (~r(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2512, 14580, 1488, 2505, 390, 2506, 363])).
% 1.95/2.19 tff(14582,plain,
% 1.95/2.19 (b(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[625, 14581])).
% 1.95/2.19 tff(14583,plain,
% 1.95/2.19 (~b(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6542, 14582, 344, 1488])).
% 1.95/2.19 tff(14584,plain,
% 1.95/2.19 (r(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[515, 14583, 2506])).
% 1.95/2.19 tff(14585,plain,
% 1.95/2.19 (~r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4310, 14584, 363])).
% 1.95/2.19 tff(14586,plain,
% 1.95/2.19 (b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[498, 14585])).
% 1.95/2.19 tff(14587,plain,
% 1.95/2.19 (~b(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[10118, 224, 14570, 14586, 14582])).
% 1.95/2.19 tff(14588,plain,
% 1.95/2.19 (r(s(z), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[670, 14587, 666])).
% 1.95/2.19 tff(14589,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[12231, 112, 14584, 416, 14588])).
% 1.95/2.19 tff(14590,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (s(z) = s(elem!1)) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14591,plain,
% 1.95/2.19 (~r(elem!1, z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14590, 14568, 4204, 327, 13708, 1488, 526, 14493, 2, 176, 7066, 14545])).
% 1.95/2.19 tff(14592,plain,
% 1.95/2.19 (b(elem!1, z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[403, 14591, 11])).
% 1.95/2.19 tff(14593,plain,
% 1.95/2.19 (~(s(s(s(z))) = elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[12299, 3633, 7066])).
% 1.95/2.19 tff(14594,plain,
% 1.95/2.19 (~(elem!1 = s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3418, 14593])).
% 1.95/2.19 tff(14595,plain,
% 1.95/2.19 (~b(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[9411, 14593, 4, 14568, 9147, 176])).
% 1.95/2.19 tff(14596,plain,
% 1.95/2.19 (r(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[388, 14595, 14594])).
% 1.95/2.19 tff(14597,plain,
% 1.95/2.19 (~r(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2841, 3634, 14568])).
% 1.95/2.19 tff(14598,plain,
% 1.95/2.19 (b(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[194, 14597])).
% 1.95/2.19 tff(14599,plain,
% 1.95/2.19 (~b(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14578, 14598, 2, 176, 13708, 14493, 7066, 14545])).
% 1.95/2.19 tff(14600,plain,
% 1.95/2.19 (r(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[593, 14599])).
% 1.95/2.19 tff(14601,plain,
% 1.95/2.19 (~r(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2512, 14600, 1488, 526, 14493, 327, 3634])).
% 1.95/2.19 tff(14602,plain,
% 1.95/2.19 (b(z, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[625, 14601])).
% 1.95/2.19 tff(14603,plain,
% 1.95/2.19 (~b(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6542, 14602, 13708, 1488])).
% 1.95/2.19 tff(14604,plain,
% 1.95/2.19 (r(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[515, 14603, 327])).
% 1.95/2.19 tff(14605,plain,
% 1.95/2.19 (~r(s(elem!1), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7891, 14604, 14596])).
% 1.95/2.19 tff(14606,plain,
% 1.95/2.19 (~r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4310, 14604, 3634])).
% 1.95/2.19 tff(14607,plain,
% 1.95/2.19 (b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[498, 14606])).
% 1.95/2.19 tff(14608,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14609,plain,
% 1.95/2.19 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(14610,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14609])).
% 1.95/2.19 tff(14611,plain,
% 1.95/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[14610, 14608])).
% 1.95/2.19 tff(14612,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(14613,plain,
% 1.95/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14612, 14611])).
% 1.95/2.19 tff(14614,plain,
% 1.95/2.19 ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14613, 224, 1488, 13708, 7066])).
% 1.95/2.19 tff(14615,plain,
% 1.95/2.19 (~b(s(elem!1), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14614, 14607])).
% 1.95/2.19 tff(14616,plain,
% 1.95/2.19 (s(elem!1) = s(s(s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1534, 14615, 14605])).
% 1.95/2.19 tff(14617,plain,
% 1.95/2.19 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14616])).
% 1.95/2.19 tff(14618,plain,
% 1.95/2.19 (elem!1 = s(s(z))),
% 1.95/2.19 inference(transitivity,[status(thm)],[155, 14617, 31])).
% 1.95/2.19 tff(14619,plain,
% 1.95/2.19 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14618])).
% 1.95/2.19 tff(14620,plain,
% 1.95/2.19 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.95/2.19 inference(symmetry,[status(thm)],[14619])).
% 1.95/2.19 tff(14621,plain,
% 1.95/2.19 (~b(s(s(z)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[9984, 14600, 11, 170, 9138, 3, 14545, 2])).
% 1.95/2.19 tff(14622,plain,
% 1.95/2.19 (r(s(s(z)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[249, 14621])).
% 1.95/2.19 tff(14623,plain,
% 1.95/2.19 (~r(s(z), s(s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6296, 14622, 176])).
% 1.95/2.19 tff(14624,plain,
% 1.95/2.19 (b(s(z), s(s(z)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1071, 14623])).
% 1.95/2.19 tff(14625,plain,
% 1.95/2.19 (b(s(z), elem!1)),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14624, 14620])).
% 1.95/2.19 tff(14626,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14567, 14625])).
% 1.95/2.19 tff(14627,plain,(b(elem!1, z) | (~b(s(elem!1), elem!1)) | b(s(z), s(s(s(z)))) | b(z, s(z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(14628,plain,
% 1.95/2.19 (b(elem!1, z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[14627, 9138, 170, 1488, 3, 2, 4])).
% 1.95/2.19 tff(14629,plain,
% 1.95/2.19 (~b(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[946, 224, 1488, 14628, 13708])).
% 1.95/2.19 tff(14630,plain,
% 1.95/2.19 (r(s(elem!1), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[498, 14629])).
% 1.95/2.19 tff(14631,plain,
% 1.95/2.19 (~b(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3407, 14628, 13708, 14493])).
% 1.95/2.19 tff(14632,plain,
% 1.95/2.19 (r(s(s(elem!1)), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[593, 14631])).
% 1.95/2.19 tff(14633,plain,
% 1.95/2.19 (~r(s(s(elem!1)), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[955, 112, 14632, 14630])).
% 1.95/2.19 tff(14634,plain,
% 1.95/2.19 (b(s(s(elem!1)), s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[530, 14633, 526])).
% 1.95/2.19 tff(14635,plain,
% 1.95/2.19 (~b(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1496, 14634, 14493, 1488])).
% 1.95/2.19 tff(14636,plain,
% 1.95/2.19 (r(elem!1, s(elem!1))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[515, 14635, 327])).
% 1.95/2.19 tff(14637,plain,
% 1.95/2.19 (~r(s(s(s(z))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[2374, 14568, 176])).
% 1.95/2.19 tff(14638,plain,
% 1.95/2.19 (~b(s(s(s(z))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[9448, 224, 14628, 13708, 7066])).
% 1.95/2.19 tff(14639,plain,
% 1.95/2.19 (s(s(s(z))) = elem!1),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[374, 14638, 14637])).
% 1.95/2.19 tff(14640,plain,
% 1.95/2.19 (~r(s(s(elem!1)), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[5928, 14632, 9147])).
% 1.95/2.19 tff(14641,plain,
% 1.95/2.19 (b(s(s(elem!1)), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[901, 14640])).
% 1.95/2.19 tff(14642,plain,
% 1.95/2.19 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[10038, 14639, 14641])).
% 1.95/2.19 tff(14643,plain,
% 1.95/2.19 (s(s(s(s(z)))) = s(elem!1)),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14639])).
% 1.95/2.19 tff(14644,plain,
% 1.95/2.19 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14643])).
% 1.95/2.19 tff(14645,plain,
% 1.95/2.19 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[14643, 14644])).
% 1.95/2.19 tff(14646,plain,
% 1.95/2.19 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[14645])).
% 1.95/2.19 tff(14647,plain,
% 1.95/2.19 (~r(s(elem!1), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1513, 112, 14632, 14630])).
% 1.95/2.19 tff(14648,plain,
% 1.95/2.19 (b(s(elem!1), s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1521, 14647, 319])).
% 1.95/2.19 tff(14649,plain,
% 1.95/2.19 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[14648, 14646])).
% 1.95/2.19 tff(14650,plain,
% 1.95/2.19 (~b(z, s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[9952, 656, 3, 344, 416])).
% 1.95/2.19 tff(14651,plain,
% 1.95/2.19 (~r(z, s(s(elem!1)))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6325, 656, 4569])).
% 1.95/2.19 tff(14652,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[752, 14651, 14650])).
% 1.95/2.19 tff(14653,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.20 tff(14654,plain,
% 1.95/2.20 (~r(s(z), s(s(elem!1)))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[14653, 9147, 3, 13708, 14568])).
% 1.95/2.20 tff(14655,plain,
% 1.95/2.20 (b(s(z), s(s(elem!1)))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[653, 14654])).
% 1.95/2.20 tff(14656,plain,
% 1.95/2.20 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[4511, 14655, 14639])).
% 1.95/2.20 tff(14657,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.20 tff(14658,plain,
% 1.95/2.20 ($false),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[8864, 224, 1570, 4495, 4494, 14657])).
% 1.95/2.20 tff(14659,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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.20 tff(14660,plain,
% 1.95/2.20 (~b(s(s(s(s(z)))), s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[14659, 14656, 14649, 14642])).
% 1.95/2.20 tff(14661,plain,
% 1.95/2.20 (~b(s(elem!1), s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[4136, 14660, 14639])).
% 1.95/2.20 tff(14662,plain,
% 1.95/2.20 (r(s(elem!1), s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1476, 14661, 160])).
% 1.95/2.20 tff(14663,plain,
% 1.95/2.20 (~r(elem!1, s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1604, 14662, 14636])).
% 1.95/2.20 tff(14664,plain,
% 1.95/2.20 (b(elem!1, s(z))),
% 1.95/2.20 inference(unit_resolution,[status(thm)],[1277, 14663, 83])).
% 1.95/2.20 tff(14665,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(14666,plain,
% 1.95/2.20 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.20 inference(rewrite,[status(thm)],[])).
% 1.95/2.20 tff(14667,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.95/2.20 inference(monotonicity,[status(thm)],[14666])).
% 1.95/2.20 tff(14668,plain,
% 1.95/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.95/2.20 inference(transitivity,[status(thm)],[14667, 14665])).
% 1.95/2.20 tff(14669,plain,
% 1.95/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.95/2.20 inference(quant_inst,[status(thm)],[])).
% 1.95/2.20 tff(14670,plain,
% 1.95/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.95/2.20 inference(modus_ponens,[status(thm)],[14669, 14668])).
% 2.03/2.20 tff(14671,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14670, 224, 1488, 14634, 14641, 14664, 14493])).
% 2.03/2.20 tff(14672,plain,(b(z, s(z)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(14673,plain,
% 2.03/2.20 (b(z, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14672, 1488, 3, 170, 2, 4])).
% 2.03/2.20 tff(14674,plain,
% 2.03/2.20 (~b(s(s(elem!1)), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3407, 14592, 13708, 14493])).
% 2.03/2.20 tff(14675,plain,
% 2.03/2.20 (r(s(s(elem!1)), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[593, 14674])).
% 2.03/2.20 tff(14676,plain,
% 2.03/2.20 (~b(s(elem!1), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[946, 224, 1488, 14592, 13708])).
% 2.03/2.20 tff(14677,plain,
% 2.03/2.20 (r(s(elem!1), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[498, 14676])).
% 2.03/2.20 tff(14678,plain,
% 2.03/2.20 (~r(s(z), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[12361, 14677, 319, 160, 14675])).
% 2.03/2.20 tff(14679,plain,
% 2.03/2.20 (b(s(z), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[194, 14678])).
% 2.03/2.20 tff(14680,plain,
% 2.03/2.20 (~b(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[10882, 14679, 14673, 14592])).
% 2.03/2.20 tff(14681,plain,
% 2.03/2.20 (r(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1277, 14680, 83])).
% 2.03/2.20 tff(14682,plain,
% 2.03/2.20 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[955, 112, 14675, 14677])).
% 2.03/2.20 tff(14683,plain,
% 2.03/2.20 (b(s(s(elem!1)), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[530, 14682, 526])).
% 2.03/2.20 tff(14684,plain,
% 2.03/2.20 (~b(elem!1, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1496, 14683, 14493, 1488])).
% 2.03/2.20 tff(14685,plain,
% 2.03/2.20 (r(elem!1, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[515, 14684, 327])).
% 2.03/2.20 tff(14686,plain,
% 2.03/2.20 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1513, 112, 14675, 14677])).
% 2.03/2.20 tff(14687,plain,
% 2.03/2.20 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1521, 14686, 319])).
% 2.03/2.20 tff(14688,plain,
% 2.03/2.20 (~r(s(z), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[12427, 14679, 11, 14493, 1488, 14673, 3, 14675, 83])).
% 2.03/2.20 tff(14689,plain,
% 2.03/2.20 (b(s(z), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[653, 14688])).
% 2.03/2.20 tff(14690,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14691,plain,
% 2.03/2.20 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14692,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[14691])).
% 2.03/2.20 tff(14693,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.03/2.20 inference(transitivity,[status(thm)],[14692, 14690])).
% 2.03/2.20 tff(14694,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(14695,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14694, 14693])).
% 2.03/2.20 tff(14696,plain,
% 2.03/2.20 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14695, 224, 1488, 14689, 14493])).
% 2.03/2.20 tff(14697,plain,
% 2.03/2.20 (~b(s(elem!1), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14696, 14687])).
% 2.03/2.20 tff(14698,plain,
% 2.03/2.20 (r(s(elem!1), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1476, 14697, 160])).
% 2.03/2.20 tff(14699,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1604, 14698, 14685, 14681])).
% 2.03/2.20 tff(14700,plain,((~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(14701,plain,
% 2.03/2.20 (~b(s(elem!1), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14700, 170, 2, 3, 4])).
% 2.03/2.20 tff(14702,plain,
% 2.03/2.20 (~r(s(elem!1), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2694, 14502, 408])).
% 2.03/2.20 tff(14703,plain,
% 2.03/2.20 (b(s(elem!1), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[498, 14702])).
% 2.03/2.20 tff(14704,plain,
% 2.03/2.20 (~b(s(elem!1), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[6470, 14703, 14497, 14495])).
% 2.03/2.20 tff(14705,plain,
% 2.03/2.20 (r(s(elem!1), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1476, 14704, 409])).
% 2.03/2.20 tff(14706,plain,
% 2.03/2.20 (~r(s(z), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[436, 14705, 408])).
% 2.03/2.20 tff(14707,plain,
% 2.03/2.20 (b(s(z), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[454, 14706, 91])).
% 2.03/2.20 tff(14708,plain,
% 2.03/2.20 (~b(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2904, 14707, 13708, 14497])).
% 2.03/2.20 tff(14709,plain,
% 2.03/2.20 (r(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1277, 14708, 83])).
% 2.03/2.20 tff(14710,plain,
% 2.03/2.20 (~r(elem!1, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1604, 14709, 14705])).
% 2.03/2.20 tff(14711,plain,
% 2.03/2.20 (b(elem!1, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[515, 14710, 327])).
% 2.03/2.20 tff(14712,plain,
% 2.03/2.20 (s(z) = elem!1),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[10588, 501, 77, 408, 3, 10122, 157])).
% 2.03/2.20 tff(14713,plain,
% 2.03/2.20 (r(s(s(elem!1)), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[358, 68, 353, 354])).
% 2.03/2.20 tff(14714,plain,
% 2.03/2.20 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4102, 112, 408, 14713])).
% 2.03/2.20 tff(14715,plain,
% 2.03/2.20 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1521, 14714, 319])).
% 2.03/2.20 tff(14716,plain,
% 2.03/2.20 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3570, 14715, 1391, 501])).
% 2.03/2.20 tff(14717,plain,
% 2.03/2.20 (r(elem!1, s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[558, 14716, 3])).
% 2.03/2.20 tff(14718,plain,
% 2.03/2.20 (~r(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2499, 568, 408])).
% 2.03/2.20 tff(14719,plain,
% 2.03/2.20 (b(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[289, 14718, 511])).
% 2.03/2.20 tff(14720,plain,
% 2.03/2.20 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7790, 86])).
% 2.03/2.20 tff(14721,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(symmetry,[status(thm)],[10384])).
% 2.03/2.20 tff(14722,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[1787, 14721])).
% 2.03/2.20 tff(14723,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1916, 112, 545, 1798])).
% 2.03/2.20 tff(14724,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14723, 14722])).
% 2.03/2.20 tff(14725,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(14726,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14725, 1798, 545, 86])).
% 2.03/2.20 tff(14727,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1883, 14726, 10383])).
% 2.03/2.20 tff(14728,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14727, 10378])).
% 2.03/2.20 tff(14729,plain,
% 2.03/2.20 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14730,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[14729])).
% 2.03/2.20 tff(14731,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[14730, 1392])).
% 2.03/2.20 tff(14732,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(14733,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14732, 14731])).
% 2.03/2.20 tff(14734,plain,
% 2.03/2.20 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14733, 224, 1391, 1390, 14728])).
% 2.03/2.20 tff(14735,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1345, 10339, 14734, 14720])).
% 2.03/2.20 tff(14736,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(14737,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14736, 14715, 1391, 408, 86, 14717])).
% 2.03/2.20 tff(14738,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1294, 14737, 10386])).
% 2.03/2.20 tff(14739,plain,
% 2.03/2.20 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.03/2.20 inference(monotonicity,[status(thm)],[86])).
% 2.03/2.20 tff(14740,plain,
% 2.03/2.20 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.03/2.20 inference(symmetry,[status(thm)],[14739])).
% 2.03/2.20 tff(14741,plain,
% 2.03/2.20 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[14740])).
% 2.03/2.20 tff(14742,plain,
% 2.03/2.20 (~b(s(s(elem!1)), s(z))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[354, 14741])).
% 2.03/2.20 tff(14743,plain,
% 2.03/2.20 (r(s(s(elem!1)), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[901, 14742])).
% 2.03/2.20 tff(14744,plain,
% 2.03/2.20 (b(s(z), z) <=> b(elem!1, z)),
% 2.03/2.20 inference(monotonicity,[status(thm)],[86])).
% 2.03/2.20 tff(14745,plain,
% 2.03/2.20 (~r(s(z), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[895, 102, 887])).
% 2.03/2.20 tff(14746,plain,
% 2.03/2.20 (b(s(z), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[194, 14745])).
% 2.03/2.20 tff(14747,plain,
% 2.03/2.20 (b(elem!1, z)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14746, 14744])).
% 2.03/2.20 tff(14748,plain,
% 2.03/2.20 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1324, 224, 3919, 14747, 344])).
% 2.03/2.20 tff(14749,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1338, 14748])).
% 2.03/2.20 tff(14750,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14230, 112, 1181, 102, 14749])).
% 2.03/2.20 tff(14751,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14750, 10385])).
% 2.03/2.20 tff(14752,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1883, 14751, 10383])).
% 2.03/2.20 tff(14753,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14752, 10378])).
% 2.03/2.20 tff(14754,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14755,plain,
% 2.03/2.20 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14756,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[14755])).
% 2.03/2.20 tff(14757,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[14756, 14754])).
% 2.03/2.20 tff(14758,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(14759,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[14758, 14757])).
% 2.03/2.20 tff(14760,plain,
% 2.03/2.20 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14759, 224, 501, 3919, 1390, 14753])).
% 2.03/2.20 tff(14761,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1345, 14760, 14720])).
% 2.03/2.20 tff(14762,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1331, 112, 568, 14761, 14749])).
% 2.03/2.20 tff(14763,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(14764,plain,
% 2.03/2.20 (~r(s(s(elem!1)), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[14763, 14738, 501, 568, 14715, 86, 14713, 14719, 14743])).
% 2.03/2.20 tff(14765,plain,
% 2.03/2.20 (b(s(s(elem!1)), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[593, 14764])).
% 2.03/2.20 tff(14766,plain,
% 2.03/2.20 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[10377])).
% 2.03/2.20 tff(14767,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 2.03/2.20 tff(14768,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14769,plain,
% 2.03/2.20 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(14770,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[14769])).
% 2.03/2.20 tff(14771,plain,
% 2.03/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[14770, 14768])).
% 2.03/2.20 tff(14772,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(14773,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14772, 14771])).
% 2.03/2.21 tff(14774,plain,
% 2.03/2.21 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14773, 224, 3919, 1240, 344])).
% 2.03/2.21 tff(14775,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14774, 14767])).
% 2.03/2.21 tff(14776,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1338, 14775])).
% 2.03/2.21 tff(14777,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14759, 224, 501, 3919, 1390, 14767])).
% 2.03/2.21 tff(14778,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1345, 14777, 1286])).
% 2.03/2.21 tff(14779,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1331, 112, 568, 14778, 14776])).
% 2.03/2.21 tff(14780,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14781,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14780, 1240, 14720, 3919, 568, 344, 501, 1390])).
% 2.03/2.21 tff(14782,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14781, 14766])).
% 2.03/2.21 tff(14783,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1883, 14782, 10383])).
% 2.03/2.21 tff(14784,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14783, 14721])).
% 2.03/2.21 tff(14785,plain,
% 2.03/2.21 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1407, 10386])).
% 2.03/2.21 tff(14786,plain,
% 2.03/2.21 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1908, 112, 545])).
% 2.03/2.21 tff(14787,plain,
% 2.03/2.21 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14786, 14784])).
% 2.03/2.21 tff(14788,plain,
% 2.03/2.21 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1439, 14787, 14785])).
% 2.03/2.21 tff(14789,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14790,plain,
% 2.03/2.21 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14791,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14790])).
% 2.03/2.21 tff(14792,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[14791, 14789])).
% 2.03/2.21 tff(14793,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(14794,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14793, 14792])).
% 2.03/2.21 tff(14795,plain,
% 2.03/2.21 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14794, 224, 3919, 344, 14788])).
% 2.03/2.21 tff(14796,plain,
% 2.03/2.21 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4412, 14795])).
% 2.03/2.21 tff(14797,plain,
% 2.03/2.21 (~b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4154, 1240, 1390, 500])).
% 2.03/2.21 tff(14798,plain,
% 2.03/2.21 (~b(z, s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14797, 10303])).
% 2.03/2.21 tff(14799,plain,
% 2.03/2.21 (r(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[100, 14798])).
% 2.03/2.21 tff(14800,plain,
% 2.03/2.21 (r(z, s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14799, 10300])).
% 2.03/2.21 tff(14801,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10372, 112, 14800, 14796, 14784])).
% 2.03/2.21 tff(14802,plain,((~b(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14803,plain,
% 2.03/2.21 (~b(s(elem!1), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14802, 14765, 14715, 86, 14738, 14719, 14717, 568, 501])).
% 2.03/2.21 tff(14804,plain,
% 2.03/2.21 (r(s(elem!1), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[498, 14803])).
% 2.03/2.21 tff(14805,plain,
% 2.03/2.21 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[10221])).
% 2.03/2.21 tff(14806,plain,
% 2.03/2.21 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10403, 112, 467, 8086])).
% 2.03/2.21 tff(14807,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1869, 14806, 10397])).
% 2.03/2.21 tff(14808,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14809,plain,
% 2.03/2.21 (((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14810,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14809])).
% 2.03/2.21 tff(14811,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[14810, 14808])).
% 2.03/2.21 tff(14812,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(14813,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14812, 14811])).
% 2.03/2.21 tff(14814,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14813, 112, 408, 467, 8086])).
% 2.03/2.21 tff(14815,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1345, 14814, 14720])).
% 2.03/2.21 tff(14816,plain,
% 2.03/2.21 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11211, 224, 1391, 14815, 14807])).
% 2.03/2.21 tff(14817,plain,
% 2.03/2.21 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14816, 14805])).
% 2.03/2.21 tff(14818,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[5425, 14817, 10223])).
% 2.03/2.21 tff(14819,plain,
% 2.03/2.21 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14818, 10237])).
% 2.03/2.21 tff(14820,plain,
% 2.03/2.21 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[13174, 224, 501, 14815, 14807])).
% 2.03/2.21 tff(14821,plain,
% 2.03/2.21 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1439, 14820, 14785])).
% 2.03/2.21 tff(14822,plain,
% 2.03/2.21 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7427, 112, 545, 14821])).
% 2.03/2.21 tff(14823,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14822, 14819])).
% 2.03/2.21 tff(14824,plain,((~r(s(s(s(s(elem!1)))), z)) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14825,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14824, 14804, 14717, 1391, 501, 408, 86])).
% 2.03/2.21 tff(14826,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1338, 14825])).
% 2.03/2.21 tff(14827,plain,
% 2.03/2.21 (~r(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2694, 14804, 408])).
% 2.03/2.21 tff(14828,plain,
% 2.03/2.21 (b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[403, 14827, 157])).
% 2.03/2.21 tff(14829,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1324, 224, 14738, 14828, 14719, 14826])).
% 2.03/2.21 tff(14830,plain,(b(s(s(elem!1)), elem!1) | (elem!1 = z) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(z, s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14831,plain,
% 2.03/2.21 (b(s(s(elem!1)), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14830, 501, 10123, 157, 408, 14712, 10438, 3])).
% 2.03/2.21 tff(14832,plain,
% 2.03/2.21 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10462, 224, 501, 10123, 10440])).
% 2.03/2.21 tff(14833,plain,
% 2.03/2.21 (~b(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14832, 14831])).
% 2.03/2.21 tff(14834,plain,
% 2.03/2.21 (r(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[593, 14833])).
% 2.03/2.21 tff(14835,plain,
% 2.03/2.21 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7751, 14712])).
% 2.03/2.21 tff(14836,plain,
% 2.03/2.21 (~b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[743, 682, 344, 390])).
% 2.03/2.21 tff(14837,plain,
% 2.03/2.21 (~b(z, s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14836, 10303])).
% 2.03/2.21 tff(14838,plain,
% 2.03/2.21 (r(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[100, 14837])).
% 2.03/2.21 tff(14839,plain,
% 2.03/2.21 (r(z, s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14838, 10300])).
% 2.03/2.21 tff(14840,plain,
% 2.03/2.21 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3570, 682, 1391, 501])).
% 2.03/2.21 tff(14841,plain,
% 2.03/2.21 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1521, 14840, 523])).
% 2.03/2.21 tff(14842,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10730, 112, 14841, 568, 14839])).
% 2.03/2.21 tff(14843,plain,((~b(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14844,plain,
% 2.03/2.21 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14843, 14831, 14712, 319, 10440, 10438, 10123, 501])).
% 2.03/2.21 tff(14845,plain,
% 2.03/2.21 (r(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[558, 14844, 3])).
% 2.03/2.21 tff(14846,plain,
% 2.03/2.21 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4010, 14845, 408])).
% 2.03/2.21 tff(14847,plain,
% 2.03/2.21 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1521, 14846, 319])).
% 2.03/2.21 tff(14848,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14736, 14847, 10123, 408, 14712, 14845])).
% 2.03/2.21 tff(14849,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1294, 14848, 14835])).
% 2.03/2.21 tff(14850,plain,
% 2.03/2.21 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10291, 224, 501, 3919, 1391, 390])).
% 2.03/2.21 tff(14851,plain,
% 2.03/2.21 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14850, 14805])).
% 2.03/2.21 tff(14852,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[5425, 14851, 10223])).
% 2.03/2.21 tff(14853,plain,
% 2.03/2.21 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14852, 10237])).
% 2.03/2.21 tff(14854,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1324, 224, 3919, 405, 344])).
% 2.03/2.21 tff(14855,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1338, 14854])).
% 2.03/2.21 tff(14856,plain,
% 2.03/2.21 (~b(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10463, 390])).
% 2.03/2.21 tff(14857,plain,
% 2.03/2.21 (r(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[593, 14856])).
% 2.03/2.21 tff(14858,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14859,plain,
% 2.03/2.21 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14860,plain,
% 2.03/2.21 (((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14859])).
% 2.03/2.21 tff(14861,plain,
% 2.03/2.21 (((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[14860, 14858])).
% 2.03/2.21 tff(14862,plain,
% 2.03/2.21 ((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(14863,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14862, 14861])).
% 2.03/2.21 tff(14864,plain,
% 2.03/2.21 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14863, 112, 14857, 14855])).
% 2.03/2.21 tff(14865,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14864, 14853])).
% 2.03/2.21 tff(14866,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14867,plain,
% 2.03/2.21 (~b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14866, 14849, 14712, 10440, 501, 10123, 14831])).
% 2.03/2.21 tff(14868,plain,
% 2.03/2.21 (r(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[403, 14867, 157])).
% 2.03/2.21 tff(14869,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10002, 112, 14845, 14868, 14834])).
% 2.03/2.21 tff(14870,plain,((~b(elem!1, s(elem!1))) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14871,plain,
% 2.03/2.21 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14870, 14711, 3, 157, 408, 14497])).
% 2.03/2.21 tff(14872,plain,
% 2.03/2.21 (~b(s(z), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14012, 224, 14711, 14495, 14703, 14707])).
% 2.03/2.21 tff(14873,plain,
% 2.03/2.21 (r(s(z), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[670, 14872, 561])).
% 2.03/2.21 tff(14874,plain,
% 2.03/2.21 (~r(s(z), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[664, 14873, 14871])).
% 2.03/2.21 tff(14875,plain,
% 2.03/2.21 (b(s(z), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[653, 14874])).
% 2.03/2.21 tff(14876,plain,
% 2.03/2.21 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[11913, 14875, 2, 3, 7672, 74])).
% 2.03/2.21 tff(14877,plain,
% 2.03/2.21 (~b(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14514, 14876])).
% 2.03/2.21 tff(14878,plain,
% 2.03/2.21 (r(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[593, 14877])).
% 2.03/2.21 tff(14879,plain,
% 2.03/2.21 (r(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3687, 14875, 3, 328, 14707])).
% 2.03/2.21 tff(14880,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10002, 112, 14879, 14502, 14878])).
% 2.03/2.21 tff(14881,plain,(b(z, s(s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14882,plain,
% 2.03/2.21 (b(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14881, 10081, 7672, 2, 3, 328, 157, 390, 176])).
% 2.03/2.21 tff(14883,plain,
% 2.03/2.21 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14021, 224, 13893, 6255, 7672])).
% 2.03/2.21 tff(14884,plain,
% 2.03/2.21 (b(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[454, 2931, 149])).
% 2.03/2.21 tff(14885,plain,
% 2.03/2.21 (r(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3687, 14884, 3, 328, 13881])).
% 2.03/2.21 tff(14886,plain,
% 2.03/2.21 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4010, 14885, 408])).
% 2.03/2.21 tff(14887,plain,
% 2.03/2.21 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1521, 14886, 319])).
% 2.03/2.21 tff(14888,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14889,plain,
% 2.03/2.21 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(14890,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14889])).
% 2.03/2.21 tff(14891,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[14890, 14888])).
% 2.03/2.21 tff(14892,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(14893,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14892, 14891])).
% 2.03/2.21 tff(14894,plain,
% 2.03/2.21 (~b(s(z), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14893, 224, 14887, 13881, 14884, 390])).
% 2.03/2.21 tff(14895,plain,
% 2.03/2.21 (r(s(z), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[670, 14894, 561])).
% 2.03/2.21 tff(14896,plain,
% 2.03/2.21 (~r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4231, 14895, 179])).
% 2.03/2.21 tff(14897,plain,
% 2.03/2.21 (b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[625, 14896])).
% 2.03/2.21 tff(14898,plain,
% 2.03/2.21 (~b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10644, 14897, 157, 102, 14885, 327, 408, 319, 13893])).
% 2.03/2.21 tff(14899,plain,
% 2.03/2.21 (r(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[752, 14898])).
% 2.03/2.21 tff(14900,plain,
% 2.03/2.21 (~r(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[13974, 112, 14885, 14899])).
% 2.03/2.21 tff(14901,plain,
% 2.03/2.21 (b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[403, 14900, 157])).
% 2.03/2.21 tff(14902,plain,
% 2.03/2.21 (~b(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[509, 14901, 14897, 13893])).
% 2.03/2.21 tff(14903,plain,
% 2.03/2.21 (r(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[515, 14902, 327])).
% 2.03/2.21 tff(14904,plain,
% 2.03/2.21 (~(elem!1 = s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2477, 14884, 170])).
% 2.03/2.21 tff(14905,plain,
% 2.03/2.21 (~b(elem!1, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9576, 224, 14901, 6255, 7672])).
% 2.03/2.21 tff(14906,plain,
% 2.03/2.21 (r(elem!1, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[388, 14905, 14904])).
% 2.03/2.21 tff(14907,plain,
% 2.03/2.21 (~r(s(elem!1), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7891, 14906, 14903])).
% 2.03/2.21 tff(14908,plain,
% 2.03/2.21 (s(elem!1) = s(s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1534, 14907, 14883])).
% 2.03/2.21 tff(14909,plain,
% 2.03/2.21 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14908])).
% 2.03/2.21 tff(14910,plain,
% 2.03/2.21 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[14909])).
% 2.03/2.21 tff(14911,plain,
% 2.03/2.21 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14910])).
% 2.03/2.21 tff(14912,plain,
% 2.03/2.21 (~b(s(elem!1), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1554, 224, 14887, 13881, 13879])).
% 2.03/2.21 tff(14913,plain,
% 2.03/2.21 (r(s(elem!1), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1476, 14912, 409])).
% 2.03/2.21 tff(14914,plain,
% 2.03/2.21 (~r(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1604, 14903, 14913])).
% 2.03/2.21 tff(14915,plain,
% 2.03/2.21 (b(elem!1, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1277, 14914, 88])).
% 2.03/2.21 tff(14916,plain,
% 2.03/2.21 (~b(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2904, 14915, 344, 14884])).
% 2.03/2.21 tff(14917,plain,
% 2.03/2.21 (r(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[5459, 14916])).
% 2.03/2.21 tff(14918,plain,
% 2.03/2.21 (b(s(s(s(z))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8189, 14905, 170, 390, 2931, 14917])).
% 2.03/2.21 tff(14919,plain,
% 2.03/2.21 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6853, 14918, 13881, 13879])).
% 2.03/2.21 tff(14920,plain,
% 2.03/2.21 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14919, 14911])).
% 2.03/2.21 tff(14921,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14887, 14920])).
% 2.03/2.21 tff(14922,plain,(r(s(z), elem!1) | b(s(z), s(s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (elem!1 = s(z)) | (elem!1 = z) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14923,plain,
% 2.03/2.21 (r(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14922, 102, 390, 14882, 7672, 13708, 83, 157, 170, 10081, 179, 3, 328])).
% 2.03/2.21 tff(14924,plain,
% 2.03/2.21 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1485, 14923, 409, 10081, 13879])).
% 2.03/2.21 tff(14925,plain,
% 2.03/2.21 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[530, 14924, 526])).
% 2.03/2.21 tff(14926,plain,
% 2.03/2.21 (~r(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2374, 14923, 176])).
% 2.03/2.21 tff(14927,plain,
% 2.03/2.21 (~r(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2841, 14923, 179])).
% 2.03/2.21 tff(14928,plain,
% 2.03/2.21 (b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[403, 14927, 157])).
% 2.03/2.21 tff(14929,plain,
% 2.03/2.21 (~b(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9448, 224, 14928, 13708, 7672])).
% 2.03/2.21 tff(14930,plain,
% 2.03/2.21 (s(s(s(z))) = elem!1),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[374, 14929, 14926])).
% 2.03/2.21 tff(14931,plain,
% 2.03/2.21 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14930])).
% 2.03/2.21 tff(14932,plain,
% 2.03/2.21 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14931])).
% 2.03/2.21 tff(14933,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14931, 14932])).
% 2.03/2.21 tff(14934,plain,
% 2.03/2.21 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[14933])).
% 2.03/2.21 tff(14935,plain,
% 2.03/2.21 (b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4511, 14930, 13881])).
% 2.03/2.21 tff(14936,plain,
% 2.03/2.21 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10038, 14930, 13879])).
% 2.03/2.21 tff(14937,plain,
% 2.03/2.21 (~r(s(elem!1), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[436, 14923, 10081])).
% 2.03/2.21 tff(14938,plain,
% 2.03/2.21 (b(s(elem!1), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1476, 14937, 409])).
% 2.03/2.21 tff(14939,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4136, 14930, 14938])).
% 2.03/2.21 tff(14940,plain,
% 2.03/2.21 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14659, 14939, 14936, 14935])).
% 2.03/2.21 tff(14941,plain,
% 2.03/2.21 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[14940, 14934])).
% 2.03/2.21 tff(14942,plain,
% 2.03/2.21 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[743, 2589, 344, 1180])).
% 2.03/2.21 tff(14943,plain,
% 2.03/2.21 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1521, 319, 1515])).
% 2.03/2.21 tff(14944,plain,
% 2.03/2.21 (r(s(elem!1), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[939, 303, 1287])).
% 2.03/2.21 tff(14945,plain,
% 2.03/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4010, 14944, 14943])).
% 2.03/2.21 tff(14946,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[558, 14945, 14942, 3])).
% 2.03/2.21 tff(14947,plain,((elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | b(s(elem!1), elem!1) | b(s(elem!1), s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(14948,plain,
% 2.03/2.21 (~b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[14947, 14941, 3, 13708, 1287, 328])).
% 2.03/2.21 tff(14949,plain,
% 2.03/2.21 (r(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[752, 14948])).
% 2.03/2.21 tff(14950,plain,
% 2.03/2.21 (~r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[576, 14949, 14925])).
% 2.03/2.21 tff(14951,plain,
% 2.03/2.21 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1521, 14941, 319])).
% 2.03/2.21 tff(14952,plain,
% 2.03/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4010, 14951, 10081])).
% 2.03/2.21 tff(14953,plain,
% 2.03/2.21 (~b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[10673, 14952, 102, 3, 10081, 13881, 2, 328, 170, 157])).
% 2.03/2.21 tff(14954,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[625, 14953, 14950])).
% 2.03/2.21 tff(14955,plain,((~r(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), elem!1) | b(s(z), s(s(s(z)))) | (elem!1 = z) | b(s(elem!1), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(14956,plain,
% 2.03/2.22 (~r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14955, 179, 2, 328, 170, 157, 1287, 7672, 3, 390])).
% 2.03/2.22 tff(14957,plain,
% 2.03/2.22 (b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[593, 14956])).
% 2.03/2.22 tff(14958,plain,
% 2.03/2.22 (~b(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3407, 14957, 13708, 390])).
% 2.03/2.22 tff(14959,plain,
% 2.03/2.22 (r(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[403, 14958, 157])).
% 2.03/2.22 tff(14960,plain,
% 2.03/2.22 (~r(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1259, 14959, 179])).
% 2.03/2.22 tff(14961,plain,
% 2.03/2.22 (b(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1277, 14960, 83])).
% 2.03/2.22 tff(14962,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10929, 14957, 7672, 14882])).
% 2.03/2.22 tff(14963,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[147, 14962, 2])).
% 2.03/2.22 tff(14964,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4039, 14963, 176])).
% 2.03/2.22 tff(14965,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[901, 14964])).
% 2.03/2.22 tff(14966,plain,
% 2.03/2.22 (~r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2841, 14959, 179])).
% 2.03/2.22 tff(14967,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[454, 14966, 91])).
% 2.03/2.22 tff(14968,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5674, 224, 14967, 14965, 14961, 390])).
% 2.03/2.22 tff(14969,plain,((~r(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1) | b(s(z), s(s(s(z)))) | b(s(elem!1), elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(14970,plain,
% 2.03/2.22 (~r(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14969, 1287, 157, 2, 7672, 328, 170, 390, 3])).
% 2.03/2.22 tff(14971,plain,
% 2.03/2.22 (b(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[194, 14970])).
% 2.03/2.22 tff(14972,plain,
% 2.03/2.22 (~b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14578, 14971, 2, 176, 13708, 390, 7672, 14882])).
% 2.03/2.22 tff(14973,plain,
% 2.03/2.22 (r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[593, 14972])).
% 2.03/2.22 tff(14974,plain,
% 2.03/2.22 (~b(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6730, 684, 13708, 1])).
% 2.03/2.22 tff(14975,plain,
% 2.03/2.22 (r(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[403, 14974, 157])).
% 2.03/2.22 tff(14976,plain,
% 2.03/2.22 (~r(s(elem!1), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2694, 14975, 408])).
% 2.03/2.22 tff(14977,plain,
% 2.03/2.22 (b(s(elem!1), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[498, 14976])).
% 2.03/2.22 tff(14978,plain,
% 2.03/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10002, 112, 14975, 102])).
% 2.03/2.22 tff(14979,plain,
% 2.03/2.22 (b(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10079, 14978, 2, 157, 170, 102, 3])).
% 2.03/2.22 tff(14980,plain,
% 2.03/2.22 (~b(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6470, 14979, 1, 14977])).
% 2.03/2.22 tff(14981,plain,
% 2.03/2.22 (r(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1476, 14980, 409])).
% 2.03/2.22 tff(14982,plain,
% 2.03/2.22 (~b(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2904, 14979, 13708, 684])).
% 2.03/2.22 tff(14983,plain,
% 2.03/2.22 (r(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1277, 14982, 83])).
% 2.03/2.22 tff(14984,plain,
% 2.03/2.22 (~r(elem!1, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1604, 14983, 14981])).
% 2.03/2.22 tff(14985,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(14986,plain,
% 2.03/2.22 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(14987,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[14986])).
% 2.03/2.22 tff(14988,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)))),
% 2.03/2.22 inference(transitivity,[status(thm)],[14987, 14985])).
% 2.03/2.22 tff(14989,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(14990,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[14989, 14988])).
% 2.03/2.22 tff(14991,plain,
% 2.03/2.22 (~b(s(z), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14990, 224, 1, 14977, 684, 13708])).
% 2.03/2.22 tff(14992,plain,
% 2.03/2.22 (r(s(z), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[670, 14991, 561])).
% 2.03/2.22 tff(14993,plain,
% 2.03/2.22 (~b(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3687, 14978, 3, 328, 684])).
% 2.03/2.22 tff(14994,plain,
% 2.03/2.22 (r(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[653, 14993])).
% 2.03/2.22 tff(14995,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[664, 14994, 14992])).
% 2.03/2.22 tff(14996,plain,
% 2.03/2.22 (~b(elem!1, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10588, 14995, 91, 3, 157, 408, 14979])).
% 2.03/2.22 tff(14997,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[515, 14996, 14984, 327])).
% 2.03/2.22 tff(14998,plain,((~r(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(14999,plain,
% 2.03/2.22 (~b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14998, 14973, 157, 10081, 3, 14971, 328, 2, 170])).
% 2.03/2.22 tff(15000,plain,
% 2.03/2.22 (r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[454, 14999, 91])).
% 2.03/2.22 tff(15001,plain,
% 2.03/2.22 (~r(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[436, 15000, 10081])).
% 2.03/2.22 tff(15002,plain,
% 2.03/2.22 (b(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1476, 15001, 409])).
% 2.03/2.22 tff(15003,plain,
% 2.03/2.22 (~b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14578, 1, 2, 176, 13708, 390, 7672, 6255])).
% 2.03/2.22 tff(15004,plain,
% 2.03/2.22 (r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[593, 15003])).
% 2.03/2.22 tff(15005,plain,
% 2.03/2.22 (s(s(s(z))) = elem!1),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[13863, 405, 7672, 1, 176, 91, 13708])).
% 2.03/2.22 tff(15006,plain,
% 2.03/2.22 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15005])).
% 2.03/2.22 tff(15007,plain,
% 2.03/2.22 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[15006])).
% 2.03/2.22 tff(15008,plain,
% 2.03/2.22 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15005])).
% 2.03/2.22 tff(15009,plain,
% 2.03/2.22 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15008])).
% 2.03/2.22 tff(15010,plain,
% 2.03/2.22 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.22 inference(symmetry,[status(thm)],[15009])).
% 2.03/2.22 tff(15011,plain,
% 2.03/2.22 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[15010, 15007])).
% 2.03/2.22 tff(15012,plain,
% 2.03/2.22 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[408, 15011])).
% 2.03/2.22 tff(15013,plain,
% 2.03/2.22 (b(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1476, 437, 409])).
% 2.03/2.22 tff(15014,plain,
% 2.03/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4136, 15005, 15013])).
% 2.03/2.22 tff(15015,plain,
% 2.03/2.22 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11263, 196, 3318])).
% 2.03/2.22 tff(15016,plain,
% 2.03/2.22 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6185, 15015])).
% 2.03/2.22 tff(15017,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5196, 15016, 14147, 1570, 6298])).
% 2.03/2.22 tff(15018,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15019,plain,
% 2.03/2.22 (~r(s(s(z)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15018, 15014, 15012, 176])).
% 2.03/2.22 tff(15020,plain,
% 2.03/2.22 (b(s(s(z)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[249, 15019])).
% 2.03/2.22 tff(15021,plain,
% 2.03/2.22 (b(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9984, 15020, 157, 170, 15004, 3, 6255, 2])).
% 2.03/2.22 tff(15022,plain,
% 2.03/2.22 (~b(z, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[449, 15021, 409, 408, 416])).
% 2.03/2.22 tff(15023,plain,
% 2.03/2.22 (r(z, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[625, 15022])).
% 2.03/2.22 tff(15024,plain,
% 2.03/2.22 (~b(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10882, 15021, 1, 405])).
% 2.03/2.22 tff(15025,plain,
% 2.03/2.22 (r(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1277, 15024, 83])).
% 2.03/2.22 tff(15026,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15005])).
% 2.03/2.22 tff(15027,plain,
% 2.03/2.22 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[15026])).
% 2.03/2.22 tff(15028,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[390, 15027])).
% 2.03/2.22 tff(15029,plain,
% 2.03/2.22 (~b(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9201, 15020, 7672, 6255])).
% 2.03/2.22 tff(15030,plain,
% 2.03/2.22 (r(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[281, 15029])).
% 2.03/2.22 tff(15031,plain,
% 2.03/2.22 (~r(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[276, 15030, 15004])).
% 2.03/2.22 tff(15032,plain,
% 2.03/2.22 (b(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[265, 15031, 1108])).
% 2.03/2.22 tff(15033,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6362, 15032, 15020, 15028])).
% 2.03/2.22 tff(15034,plain,
% 2.03/2.22 (r(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9594, 15033, 15005])).
% 2.03/2.22 tff(15035,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1001, 15034, 15025])).
% 2.03/2.22 tff(15036,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[901, 15035])).
% 2.03/2.22 tff(15037,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1485, 15036, 409, 408, 416])).
% 2.03/2.22 tff(15038,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[530, 15037, 526])).
% 2.03/2.22 tff(15039,plain,
% 2.03/2.22 (~r(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10872, 15034, 157, 390, 15021, 1, 15004, 83])).
% 2.03/2.22 tff(15040,plain,
% 2.03/2.22 (b(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[653, 15039])).
% 2.03/2.22 tff(15041,plain,
% 2.03/2.22 (~b(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10876, 15036, 15021, 15040])).
% 2.03/2.22 tff(15042,plain,
% 2.03/2.22 (r(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[752, 15041])).
% 2.03/2.22 tff(15043,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[576, 15042, 15038, 15023])).
% 2.03/2.22 tff(15044,plain,((~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15045,plain,
% 2.03/2.22 (~b(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15044, 10081, 15000, 157, 390, 14971, 170, 3, 14882, 2, 7672])).
% 2.03/2.22 tff(15046,plain,
% 2.03/2.22 (r(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[403, 15045, 157])).
% 2.03/2.22 tff(15047,plain,
% 2.03/2.22 (~r(s(elem!1), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2694, 15046, 10081])).
% 2.03/2.22 tff(15048,plain,
% 2.03/2.22 (b(s(elem!1), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[498, 15047])).
% 2.03/2.22 tff(15049,plain,
% 2.03/2.22 (~b(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6470, 15048, 14971, 15002])).
% 2.03/2.22 tff(15050,plain,
% 2.03/2.22 (r(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5459, 15049])).
% 2.03/2.22 tff(15051,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5928, 15050, 14973])).
% 2.03/2.22 tff(15052,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[901, 15051])).
% 2.03/2.22 tff(15053,plain,
% 2.03/2.22 (r(elem!1, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10075, 15049, 157, 2, 170, 14973, 14882, 3])).
% 2.03/2.22 tff(15054,plain,
% 2.03/2.22 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4010, 15053, 10081])).
% 2.03/2.22 tff(15055,plain,
% 2.03/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1521, 15054, 319])).
% 2.03/2.22 tff(15056,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(15057,plain,
% 2.03/2.22 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(15058,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15057])).
% 2.03/2.22 tff(15059,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[15058, 15056])).
% 2.03/2.22 tff(15060,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(15061,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(z)))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[15060, 15059])).
% 2.03/2.22 tff(15062,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15061, 224, 15055, 14971, 15048, 15052, 15002])).
% 2.03/2.22 tff(15063,plain,(b(s(elem!1), elem!1) | (elem!1 = z) | (s(s(elem!1)) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15064,plain,
% 2.03/2.22 (r(s(s(elem!1)), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15063, 14701, 2, 170, 3, 14493, 7066, 11])).
% 2.03/2.22 tff(15065,plain,
% 2.03/2.22 (r(s(elem!1), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[939, 14701, 303])).
% 2.03/2.22 tff(15066,plain,
% 2.03/2.22 (b(z, s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14045, 1181, 83, 157, 7672, 344, 178])).
% 2.03/2.22 tff(15067,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[10929, 1240, 7672, 15066])).
% 2.03/2.22 tff(15068,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14286, 1240, 178, 91, 408, 15066, 7672, 2506, 1181, 157, 344, 523])).
% 2.03/2.22 tff(15069,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[147, 15068, 15067, 2])).
% 2.03/2.22 tff(15070,plain,((~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), z)) | (elem!1 = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~b(z, elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15071,plain,
% 2.03/2.22 (~b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15070, 176, 2, 15065, 7066, 327, 15064, 11, 13708, 319])).
% 2.03/2.22 tff(15072,plain,
% 2.03/2.22 (r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[593, 15071])).
% 2.03/2.22 tff(15073,plain,
% 2.03/2.22 (~r(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2076, 15072, 15064])).
% 2.03/2.22 tff(15074,plain,
% 2.03/2.22 (b(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[403, 15073, 11])).
% 2.03/2.22 tff(15075,plain,
% 2.03/2.22 (~b(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9448, 224, 15074, 13708, 7066])).
% 2.03/2.22 tff(15076,plain,
% 2.03/2.22 (b(z, s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14045, 15064, 83, 11, 7066, 13708, 176])).
% 2.03/2.22 tff(15077,plain,
% 2.03/2.22 (~b(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14215, 15064, 15065, 170, 11, 7066, 13708, 83, 3])).
% 2.03/2.22 tff(15078,plain,
% 2.03/2.22 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9984, 15072, 11, 170, 15077, 3, 15076, 2])).
% 2.03/2.22 tff(15079,plain,
% 2.03/2.22 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[249, 15078])).
% 2.03/2.22 tff(15080,plain,
% 2.03/2.22 (~r(s(s(z)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6257, 15079, 176])).
% 2.03/2.22 tff(15081,plain,
% 2.03/2.22 (b(s(s(z)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2726, 15080])).
% 2.03/2.22 tff(15082,plain,
% 2.03/2.22 (~r(s(z), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6296, 15079, 176])).
% 2.03/2.22 tff(15083,plain,
% 2.03/2.22 (b(s(z), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1071, 15082])).
% 2.03/2.22 tff(15084,plain,
% 2.03/2.22 (r(z, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5459, 15077])).
% 2.03/2.22 tff(15085,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5928, 15072, 15084])).
% 2.03/2.22 tff(15086,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[901, 15085])).
% 2.03/2.22 tff(15087,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9810, 224, 15086, 15083, 15081])).
% 2.03/2.22 tff(15088,plain,
% 2.03/2.22 (~(s(s(z)) = elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2402, 15087, 14493])).
% 2.03/2.22 tff(15089,plain,
% 2.03/2.22 (~(elem!1 = s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14085, 15088])).
% 2.03/2.22 tff(15090,plain,
% 2.03/2.22 (elem!1 = s(s(z))),
% 2.03/2.22 inference(transitivity,[status(thm)],[155, 2266, 31])).
% 2.03/2.22 tff(15091,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2786, 15090])).
% 2.03/2.22 tff(15092,plain,((~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15093,plain,
% 2.03/2.22 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15092, 15089])).
% 2.03/2.22 tff(15094,plain,
% 2.03/2.22 (~b(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6730, 684, 13708, 13787])).
% 2.03/2.22 tff(15095,plain,
% 2.03/2.22 (b(z, s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[14045, 1181, 83, 157, 7672, 13708, 176])).
% 2.03/2.22 tff(15096,plain,
% 2.03/2.22 (~r(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[13915, 14552, 1181, 7672, 15095, 2, 102, 157, 9138, 170, 7733, 3])).
% 2.03/2.22 tff(15097,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[194, 15096, 15094])).
% 2.03/2.22 tff(15098,plain,((~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | b(z, s(z)) | b(s(z), s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15099,plain,
% 2.03/2.22 (~b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15098, 15064, 7066, 2, 15072, 11, 15077, 170, 15093, 3])).
% 2.03/2.22 tff(15100,plain,
% 2.03/2.22 (r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[454, 15099, 91])).
% 2.03/2.22 tff(15101,plain,
% 2.03/2.22 (~r(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2374, 15100, 176])).
% 2.03/2.22 tff(15102,plain,
% 2.03/2.22 (s(s(s(z))) = elem!1),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[374, 15101, 15075])).
% 2.03/2.22 tff(15103,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15102])).
% 2.03/2.22 tff(15104,plain,
% 2.03/2.22 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[15103])).
% 2.03/2.22 tff(15105,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[15064, 15104])).
% 2.03/2.22 tff(15106,plain,
% 2.03/2.22 (~r(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6496, 15100, 15064])).
% 2.03/2.22 tff(15107,plain,
% 2.03/2.22 (b(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[653, 15106])).
% 2.03/2.22 tff(15108,plain,
% 2.03/2.22 (~b(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9920, 15107, 15081, 15086])).
% 2.03/2.22 tff(15109,plain,
% 2.03/2.22 (r(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[265, 15108, 169])).
% 2.03/2.22 tff(15110,plain,
% 2.03/2.22 (~r(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[276, 15109, 15072])).
% 2.03/2.22 tff(15111,plain,
% 2.03/2.22 (b(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[281, 15110])).
% 2.03/2.22 tff(15112,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8623, 15111, 7066, 15076, 15109])).
% 2.03/2.22 tff(15113,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15112, 15105])).
% 2.03/2.22 tff(15114,plain,(b(s(z), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(15115,plain,
% 2.03/2.22 (b(s(z), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15114, 4, 3, 2])).
% 2.03/2.22 tff(15116,plain,
% 2.03/2.22 (~(elem!1 = s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3418, 14500])).
% 2.03/2.22 tff(15117,plain,
% 2.03/2.22 (~r(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5767, 4569, 83, 101, 15116])).
% 2.03/2.22 tff(15118,plain,
% 2.03/2.22 (b(elem!1, z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[403, 15117, 157])).
% 2.03/2.22 tff(15119,plain,
% 2.03/2.22 (~b(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9448, 224, 15118, 13708, 7672])).
% 2.03/2.22 tff(15120,plain,
% 2.03/2.22 (r(s(s(s(z))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[374, 15119, 14500])).
% 2.03/2.22 tff(15121,plain,
% 2.03/2.22 (~b(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5988, 15120, 2, 1090, 3340])).
% 2.03/2.22 tff(15122,plain,
% 2.03/2.22 (r(s(z), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[653, 15121])).
% 2.03/2.22 tff(15123,plain,
% 2.03/2.22 (~r(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6325, 15122, 4569])).
% 2.03/2.22 tff(15124,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5814, 15119, 2, 13708, 74, 3340, 4569])).
% 2.03/2.22 tff(15125,plain,
% 2.03/2.22 (r(s(s(elem!1)), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[901, 15124])).
% 2.03/2.22 tff(15126,plain,
% 2.03/2.22 (~r(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5928, 15125, 4569])).
% 2.03/2.22 tff(15127,plain,
% 2.03/2.22 (b(s(s(elem!1)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[593, 15126])).
% 2.03/2.22 tff(15128,plain,
% 2.03/2.22 (~r(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4065, 15125, 3340])).
% 2.03/2.22 tff(15129,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[454, 15128, 91])).
% 2.03/2.22 tff(15130,plain,
% 2.03/2.22 (~b(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6730, 15129, 13708, 15118])).
% 2.03/2.22 tff(15131,plain,
% 2.03/2.22 (r(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[194, 15130])).
% 2.03/2.22 tff(15132,plain,
% 2.03/2.22 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[11714, 15131, 7672, 101, 4569, 15127, 15123])).
% 2.03/2.22 tff(15133,plain,
% 2.03/2.22 (b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[135, 68, 132, 15132])).
% 2.03/2.22 tff(15134,plain,
% 2.03/2.22 (~r(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3588, 15125, 3340])).
% 2.03/2.22 tff(15135,plain,
% 2.03/2.22 (b(elem!1, s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1277, 15134, 83])).
% 2.03/2.22 tff(15136,plain,
% 2.03/2.22 (~b(s(elem!1), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6548, 15127, 3, 13708, 354, 4569, 409, 15135, 15129])).
% 2.03/2.22 tff(15137,plain,
% 2.03/2.22 (r(s(elem!1), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[939, 15136, 303])).
% 2.03/2.22 tff(15138,plain,
% 2.03/2.22 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6557, 15137, 3340])).
% 2.03/2.22 tff(15139,plain,
% 2.03/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1521, 15138, 319])).
% 2.03/2.22 tff(15140,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(15141,plain,
% 2.03/2.22 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), 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(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(15142,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15141])).
% 2.03/2.22 tff(15143,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[15142, 15140])).
% 2.03/2.22 tff(15144,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(15145,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[15144, 15143])).
% 2.03/2.22 tff(15146,plain,
% 2.03/2.22 ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15145, 224, 15139, 15127, 7672])).
% 2.03/2.22 tff(15147,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15146, 15133])).
% 2.03/2.22 tff(15148,plain,
% 2.03/2.22 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[812, 112, 15137, 15120])).
% 2.03/2.22 tff(15149,plain,
% 2.03/2.22 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[816, 68, 15148])).
% 2.03/2.22 tff(15150,plain,
% 2.03/2.22 (s(s(s(z))) = s(elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[15149, 15147])).
% 2.03/2.22 tff(15151,plain,
% 2.03/2.22 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[15150])).
% 2.03/2.22 tff(15152,plain,
% 2.03/2.22 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.03/2.22 inference(transitivity,[status(thm)],[15151, 1143])).
% 2.03/2.22 tff(15153,plain,
% 2.03/2.22 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[15152])).
% 2.03/2.22 tff(15154,plain,
% 2.03/2.22 (b(z, s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[752, 15123])).
% 2.03/2.22 tff(15155,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4112, 112, 15137, 3340])).
% 2.03/2.22 tff(15156,plain,
% 2.03/2.22 (b(s(s(elem!1)), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[530, 15155, 526])).
% 2.03/2.22 tff(15157,plain,
% 2.03/2.22 (~b(z, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4124, 15156, 15154, 15139])).
% 2.03/2.22 tff(15158,plain,
% 2.03/2.22 (r(z, s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[625, 15157])).
% 2.03/2.22 tff(15159,plain,
% 2.03/2.22 (~r(s(elem!1), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5576, 15125, 319, 4569])).
% 2.03/2.22 tff(15160,plain,
% 2.03/2.23 (b(s(elem!1), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1476, 15159, 409])).
% 2.03/2.23 tff(15161,plain,
% 2.03/2.23 (~b(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4154, 15139, 15127, 15154])).
% 2.03/2.23 tff(15162,plain,
% 2.03/2.23 (r(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[498, 15161])).
% 2.03/2.23 tff(15163,plain,
% 2.03/2.23 (~r(s(z), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[473, 112, 15137, 15131, 15162])).
% 2.03/2.23 tff(15164,plain,
% 2.03/2.23 (b(s(z), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[670, 15163, 561])).
% 2.03/2.23 tff(15165,plain,
% 2.03/2.23 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9074, 15150])).
% 2.03/2.23 tff(15166,plain,
% 2.03/2.23 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6022, 15165, 15122, 15131, 15164, 15139, 15160, 15156, 15118, 13708, 15136, 15158])).
% 2.03/2.23 tff(15167,plain,
% 2.03/2.23 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[15166, 15153])).
% 2.03/2.23 tff(15168,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1165, 15167])).
% 2.03/2.23 tff(15169,plain,((~r(z, s(z))) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | b(z, s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15170,plain,
% 2.03/2.23 (~r(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15169, 354, 3, 7672, 2, 1090, 74, 157])).
% 2.03/2.23 tff(15171,plain,
% 2.03/2.23 (b(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5459, 15170])).
% 2.03/2.23 tff(15172,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15173,plain,
% 2.03/2.23 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15174,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[15173])).
% 2.03/2.23 tff(15175,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[15174, 15172])).
% 2.03/2.23 tff(15176,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(15177,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[15176, 15175])).
% 2.03/2.23 tff(15178,plain,
% 2.03/2.23 (~b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15177, 224, 684, 344, 1090, 7672])).
% 2.03/2.23 tff(15179,plain,
% 2.03/2.23 (r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15178])).
% 2.03/2.23 tff(15180,plain,
% 2.03/2.23 (~b(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2904, 684, 344, 77])).
% 2.03/2.23 tff(15181,plain,
% 2.03/2.23 (r(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1277, 15180, 83])).
% 2.03/2.23 tff(15182,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3588, 15181, 1181])).
% 2.03/2.23 tff(15183,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[901, 15182])).
% 2.03/2.23 tff(15184,plain,
% 2.03/2.23 (~b(z, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11740, 224, 77, 684, 15183, 344])).
% 2.03/2.23 tff(15185,plain,
% 2.03/2.23 (r(z, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[752, 15184])).
% 2.03/2.23 tff(15186,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3074, 15185, 689])).
% 2.03/2.23 tff(15187,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[147, 15186, 2])).
% 2.03/2.23 tff(15188,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15189,plain,
% 2.03/2.23 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15190,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[15189])).
% 2.03/2.23 tff(15191,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[15190, 15188])).
% 2.03/2.23 tff(15192,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(15193,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[15192, 15191])).
% 2.03/2.23 tff(15194,plain,
% 2.03/2.23 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15193, 224, 77, 15183, 7672])).
% 2.03/2.23 tff(15195,plain,
% 2.03/2.23 (~b(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15194, 15187])).
% 2.03/2.23 tff(15196,plain,
% 2.03/2.23 (r(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[593, 15195])).
% 2.03/2.23 tff(15197,plain,
% 2.03/2.23 (~r(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[10648, 15196, 15179])).
% 2.03/2.23 tff(15198,plain,
% 2.03/2.23 (b(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 15197])).
% 2.03/2.23 tff(15199,plain,
% 2.03/2.23 (~r(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5988, 15198, 2, 1090, 1181])).
% 2.03/2.23 tff(15200,plain,
% 2.03/2.23 (b(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[374, 15199, 362])).
% 2.03/2.23 tff(15201,plain,
% 2.03/2.23 (~r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1259, 15179, 15181])).
% 2.03/2.23 tff(15202,plain,
% 2.03/2.23 (b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[403, 15201, 157])).
% 2.03/2.23 tff(15203,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[13861, 224, 15202, 344, 15200, 7672])).
% 2.03/2.23 tff(15204,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15205,plain,
% 2.03/2.23 (~b(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15204, 3340, 7672, 14500, 2, 1090, 13708, 15171, 157, 101])).
% 2.03/2.23 tff(15206,plain,
% 2.03/2.23 (r(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[454, 15205, 91])).
% 2.03/2.23 tff(15207,plain,
% 2.03/2.23 (~r(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6496, 15206, 3340])).
% 2.03/2.23 tff(15208,plain,
% 2.03/2.23 (b(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 15207])).
% 2.03/2.23 tff(15209,plain,
% 2.03/2.23 (~r(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5988, 15208, 2, 1090, 3340])).
% 2.03/2.23 tff(15210,plain,
% 2.03/2.23 (b(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[374, 15209, 14500])).
% 2.03/2.23 tff(15211,plain,
% 2.03/2.23 (~b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[12100, 15208, 7672, 1090, 2, 3])).
% 2.03/2.23 tff(15212,plain,
% 2.03/2.23 (r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15211])).
% 2.03/2.23 tff(15213,plain,
% 2.03/2.23 (~r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2841, 15212, 15206])).
% 2.03/2.23 tff(15214,plain,
% 2.03/2.23 (b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[403, 15213, 157])).
% 2.03/2.23 tff(15215,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[13861, 224, 15214, 13708, 15210, 7672])).
% 2.03/2.23 tff(15216,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (elem!1 = s(s(elem!1))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15217,plain,
% 2.03/2.23 (b(s(s(elem!1)), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15216, 74, 157, 1090, 2, 3, 7672])).
% 2.03/2.23 tff(15218,plain,
% 2.03/2.23 (~r(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5767, 363, 83, 689, 680])).
% 2.03/2.23 tff(15219,plain,
% 2.03/2.23 (b(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5459, 15218])).
% 2.03/2.23 tff(15220,plain,
% 2.03/2.23 (~r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2841, 416, 363])).
% 2.03/2.23 tff(15221,plain,
% 2.03/2.23 (b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15220])).
% 2.03/2.23 tff(15222,plain,
% 2.03/2.23 (~b(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[12100, 15221, 7672, 1090, 2, 3])).
% 2.03/2.23 tff(15223,plain,
% 2.03/2.23 (r(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 15222])).
% 2.03/2.23 tff(15224,plain,
% 2.03/2.23 (~b(z, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9952, 15223, 3, 13708, 416])).
% 2.03/2.23 tff(15225,plain,
% 2.03/2.23 (r(z, s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[752, 15224])).
% 2.03/2.23 tff(15226,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3074, 15225, 689])).
% 2.03/2.23 tff(15227,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[147, 15226, 2])).
% 2.03/2.23 tff(15228,plain,
% 2.03/2.23 (~b(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[14514, 15227])).
% 2.03/2.23 tff(15229,plain,
% 2.03/2.23 (r(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[593, 15228])).
% 2.03/2.23 tff(15230,plain,
% 2.03/2.23 (~b(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[12427, 15229, 157, 390, 15221, 77, 3, 15223, 83])).
% 2.03/2.23 tff(15231,plain,
% 2.03/2.23 (r(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[939, 15230, 303])).
% 2.03/2.23 tff(15232,plain,
% 2.03/2.23 (~r(s(elem!1), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[436, 15231, 416])).
% 2.03/2.23 tff(15233,plain,
% 2.03/2.23 (b(s(elem!1), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1476, 15232, 409])).
% 2.03/2.23 tff(15234,plain,
% 2.03/2.23 (~r(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2694, 15231, 363])).
% 2.03/2.23 tff(15235,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[498, 15234])).
% 2.03/2.23 tff(15236,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6470, 15235, 15233, 77, 15221])).
% 2.03/2.23 tff(15237,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(elem!1, z)) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15238,plain,
% 2.03/2.23 (~r(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15237, 15219, 363, 157, 390, 3, 7672, 2, 689, 1090])).
% 2.03/2.23 tff(15239,plain,
% 2.03/2.23 (b(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[454, 15238, 91])).
% 2.03/2.23 tff(15240,plain,
% 2.03/2.23 (~b(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2904, 15239, 13708, 15219])).
% 2.03/2.23 tff(15241,plain,
% 2.03/2.23 (r(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1277, 15240, 83])).
% 2.03/2.23 tff(15242,plain,
% 2.03/2.23 (~r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1259, 15241, 363])).
% 2.03/2.23 tff(15243,plain,
% 2.03/2.23 (b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15242])).
% 2.03/2.23 tff(15244,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15177, 224, 15243, 15239, 13708, 1090, 7672])).
% 2.03/2.23 tff(15245,plain,((~r(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15246,plain,
% 2.03/2.23 (~r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15245, 15217, 7672, 157, 1090, 3, 2, 101, 15116])).
% 2.03/2.23 tff(15247,plain,
% 2.03/2.23 (b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[403, 15246, 157])).
% 2.03/2.23 tff(15248,plain,
% 2.03/2.23 (~b(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3407, 15247, 13708, 15217])).
% 2.03/2.23 tff(15249,plain,
% 2.03/2.23 (r(s(s(elem!1)), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[593, 15248])).
% 2.03/2.23 tff(15250,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[11579, 15248, 7672, 101])).
% 2.03/2.23 tff(15251,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3206, 10010, 11596, 1090, 152])).
% 2.03/2.23 tff(15252,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15253,plain,
% 2.03/2.23 (~r(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15252, 15250, 1090, 15249, 101])).
% 2.03/2.23 tff(15254,plain,
% 2.03/2.23 (b(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5459, 15253])).
% 2.03/2.23 tff(15255,plain,
% 2.03/2.23 (~b(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9448, 224, 15247, 13708, 7672])).
% 2.03/2.23 tff(15256,plain,
% 2.03/2.23 (r(s(s(s(z))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[374, 15255, 14500])).
% 2.03/2.23 tff(15257,plain,
% 2.03/2.23 (~b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6730, 684, 344, 405])).
% 2.03/2.23 tff(15258,plain,
% 2.03/2.23 (r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15257])).
% 2.03/2.23 tff(15259,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[895, 15258, 102])).
% 2.03/2.23 tff(15260,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[901, 15259])).
% 2.03/2.23 tff(15261,plain,
% 2.03/2.23 (~b(s(s(s(z))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3206, 15260, 1090, 152])).
% 2.03/2.23 tff(15262,plain,
% 2.03/2.23 (r(s(s(s(z))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[925, 15261])).
% 2.03/2.23 tff(15263,plain,
% 2.03/2.23 (r(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1277, 15180, 88])).
% 2.03/2.23 tff(15264,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2168, 112, 690, 15263, 15262])).
% 2.03/2.23 tff(15265,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15266,plain,
% 2.03/2.23 (~b(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15265, 15256, 1090, 15250, 15249, 83, 13708, 15247, 15254])).
% 2.03/2.23 tff(15267,plain,
% 2.03/2.23 (r(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[454, 15266, 91])).
% 2.03/2.23 tff(15268,plain,
% 2.03/2.23 (~r(s(s(s(z))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1044, 112, 15267, 15256])).
% 2.03/2.23 tff(15269,plain,
% 2.03/2.23 (b(s(s(s(z))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[925, 15268])).
% 2.03/2.23 tff(15270,plain,
% 2.03/2.23 (~b(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3206, 15269, 1090, 15250])).
% 2.03/2.23 tff(15271,plain,
% 2.03/2.23 (r(s(s(elem!1)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[901, 15270])).
% 2.03/2.23 tff(15272,plain,
% 2.03/2.23 (~r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[895, 15271, 15249])).
% 2.03/2.23 tff(15273,plain,
% 2.03/2.23 (b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[194, 15272])).
% 2.03/2.23 tff(15274,plain,
% 2.03/2.23 (~b(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[12100, 15273, 7672, 1090, 2, 3])).
% 2.03/2.23 tff(15275,plain,
% 2.03/2.23 (r(s(z), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 15274])).
% 2.03/2.23 tff(15276,plain,
% 2.03/2.23 (~b(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[12427, 15275, 157, 15217, 15249, 15254, 3, 15273, 83])).
% 2.03/2.23 tff(15277,plain,
% 2.03/2.23 (r(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[939, 15276, 303])).
% 2.03/2.23 tff(15278,plain,
% 2.03/2.23 (~b(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[449, 416, 408, 166, 77])).
% 2.03/2.23 tff(15279,plain,
% 2.03/2.23 (r(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[625, 15278])).
% 2.03/2.23 tff(15280,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15281,plain,
% 2.03/2.23 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15282,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[15281])).
% 2.03/2.23 tff(15283,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[15282, 15280])).
% 2.03/2.23 tff(15284,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(15285,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[15284, 15283])).
% 2.03/2.23 tff(15286,plain,
% 2.03/2.23 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15285, 224, 1090, 441, 560])).
% 2.03/2.23 tff(15287,plain,
% 2.03/2.23 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1534, 15286, 7733])).
% 2.03/2.23 tff(15288,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15289,plain,
% 2.03/2.23 (((~r(s(elem!1), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(15290,plain,
% 2.03/2.23 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[15289])).
% 2.03/2.23 tff(15291,plain,
% 2.03/2.23 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[15290, 15288])).
% 2.03/2.23 tff(15292,plain,
% 2.03/2.23 ((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(15293,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[15292, 15291])).
% 2.03/2.23 tff(15294,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15293, 112, 689, 15287, 15279])).
% 2.03/2.23 tff(15295,plain,((~r(s(z), elem!1)) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15296,plain,
% 2.03/2.23 (s(elem!1) = s(s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15295, 15277, 409, 101, 15267, 15269, 15254, 1090])).
% 2.03/2.23 tff(15297,plain,
% 2.03/2.23 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[15296])).
% 2.03/2.23 tff(15298,plain,
% 2.03/2.23 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.03/2.23 inference(symmetry,[status(thm)],[15297])).
% 2.03/2.23 tff(15299,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[7672, 15298])).
% 2.03/2.23 tff(15300,plain,
% 2.03/2.23 (~r(s(elem!1), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[436, 15277, 15267])).
% 2.03/2.23 tff(15301,plain,
% 2.03/2.23 (b(s(elem!1), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1476, 15300, 409])).
% 2.03/2.23 tff(15302,plain,
% 2.03/2.23 (~b(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6470, 15301, 15254, 15273])).
% 2.03/2.23 tff(15303,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15302, 15299])).
% 2.03/2.23 tff(15304,plain,(b(z, s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(15305,plain,
% 2.03/2.23 (b(z, s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[15304, 7066, 15115, 11, 3, 2])).
% 2.03/2.23 tff(15306,plain,
% 2.03/2.24 (~b(s(z), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9179, 15305, 7066, 15115])).
% 2.03/2.24 tff(15307,plain,
% 2.03/2.24 (r(s(z), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[194, 15306])).
% 2.03/2.24 tff(15308,plain,
% 2.03/2.24 (~b(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9448, 224, 405, 13708, 7066])).
% 2.03/2.24 tff(15309,plain,
% 2.03/2.24 (~b(elem!1, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9576, 224, 405, 15305, 7066])).
% 2.03/2.24 tff(15310,plain,
% 2.03/2.24 (r(s(z), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[454, 2337, 91])).
% 2.03/2.24 tff(15311,plain,
% 2.03/2.24 (~r(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[14653, 15310, 3, 13708, 4569])).
% 2.03/2.24 tff(15312,plain,
% 2.03/2.24 (b(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[653, 15311])).
% 2.03/2.24 tff(15313,plain,
% 2.03/2.24 (~r(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5988, 15312, 2, 1090, 1181])).
% 2.03/2.24 tff(15314,plain,
% 2.03/2.24 (b(z, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15304, 7672, 1090, 157, 3, 2])).
% 2.03/2.24 tff(15315,plain,
% 2.03/2.24 (~b(s(z), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9179, 15314, 7672, 1090])).
% 2.03/2.24 tff(15316,plain,
% 2.03/2.24 (r(s(z), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[194, 15315])).
% 2.03/2.24 tff(15317,plain,
% 2.03/2.24 (~r(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2841, 15310, 15316])).
% 2.03/2.24 tff(15318,plain,
% 2.03/2.24 (b(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[403, 15317, 157])).
% 2.03/2.24 tff(15319,plain,
% 2.03/2.24 (~b(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9448, 224, 15318, 13708, 7672])).
% 2.03/2.24 tff(15320,plain,
% 2.03/2.24 (s(s(s(z))) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[374, 15319, 15313])).
% 2.03/2.24 tff(15321,plain,
% 2.03/2.24 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15320])).
% 2.03/2.24 tff(15322,plain,
% 2.03/2.24 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15321])).
% 2.03/2.24 tff(15323,plain,
% 2.03/2.24 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15322])).
% 2.03/2.24 tff(15324,plain,
% 2.03/2.24 (~b(s(z), s(s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[2337, 15323])).
% 2.03/2.24 tff(15325,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1090, 15324])).
% 2.03/2.24 tff(15326,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(15327,plain,
% 2.03/2.24 (b(s(z), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15326, 3340, 7066, 2, 15115, 11, 3, 9147])).
% 2.03/2.24 tff(15328,plain,
% 2.03/2.24 (b(z, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[752, 14651])).
% 2.03/2.24 tff(15329,plain,
% 2.03/2.24 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[613, 15328, 405, 1240])).
% 2.03/2.24 tff(15330,plain,
% 2.03/2.24 (r(elem!1, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[558, 15329, 3])).
% 2.03/2.24 tff(15331,plain,
% 2.03/2.24 (~r(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9964, 112, 15330, 656])).
% 2.03/2.24 tff(15332,plain,
% 2.03/2.24 (b(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1277, 15331, 88])).
% 2.03/2.24 tff(15333,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6548, 15332, 3, 344, 354, 4569, 166, 684, 1240])).
% 2.03/2.24 tff(15334,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[939, 15333, 303])).
% 2.03/2.24 tff(15335,plain,
% 2.03/2.24 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6557, 15334, 3340])).
% 2.03/2.24 tff(15336,plain,
% 2.03/2.24 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1521, 15335, 319])).
% 2.03/2.24 tff(15337,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4112, 112, 15334, 3340])).
% 2.03/2.24 tff(15338,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[530, 15337, 526])).
% 2.03/2.24 tff(15339,plain,
% 2.03/2.24 (~b(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4124, 15338, 15328, 15336])).
% 2.03/2.24 tff(15340,plain,
% 2.03/2.24 (r(z, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[625, 15339])).
% 2.03/2.24 tff(15341,plain,
% 2.03/2.24 (~b(s(elem!1), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4154, 15336, 1240, 15328])).
% 2.03/2.24 tff(15342,plain,
% 2.03/2.24 (r(s(elem!1), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[498, 15341])).
% 2.03/2.24 tff(15343,plain,
% 2.03/2.24 (~r(s(elem!1), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[482, 112, 179, 15342])).
% 2.03/2.24 tff(15344,plain,
% 2.03/2.24 (b(s(elem!1), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1476, 15343, 166])).
% 2.03/2.24 tff(15345,plain,
% 2.03/2.24 (~r(s(z), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[473, 112, 15334, 179, 15342])).
% 2.03/2.24 tff(15346,plain,
% 2.03/2.24 (b(s(z), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[670, 15345, 415])).
% 2.03/2.24 tff(15347,plain,
% 2.03/2.24 (~b(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5970, 224, 15332, 15344, 15346])).
% 2.03/2.24 tff(15348,plain,
% 2.03/2.24 (r(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[515, 15347, 327])).
% 2.03/2.24 tff(15349,plain,
% 2.03/2.24 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[7654, 224, 1240, 15328, 7672])).
% 2.03/2.24 tff(15350,plain,
% 2.03/2.24 (r(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[135, 68, 150, 15349])).
% 2.03/2.24 tff(15351,plain,
% 2.03/2.24 (~r(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9107, 15350, 656])).
% 2.03/2.24 tff(15352,plain,
% 2.03/2.24 (b(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[925, 15351])).
% 2.03/2.24 tff(15353,plain,
% 2.03/2.24 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[7013, 224, 15344, 15346, 15352])).
% 2.03/2.24 tff(15354,plain,
% 2.03/2.24 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12135, 15353, 1090, 15348, 684])).
% 2.03/2.24 tff(15355,plain,
% 2.03/2.24 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6022, 15354, 179, 656, 15346, 15336, 15344, 15338, 405, 344, 15333, 15340])).
% 2.03/2.24 tff(15356,plain,
% 2.03/2.24 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15355])).
% 2.03/2.24 tff(15357,plain,
% 2.03/2.24 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15356])).
% 2.03/2.24 tff(15358,plain,
% 2.03/2.24 (((~![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(elem!1)))) | (~r(s(s(s(z))), s(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(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(15359,plain,
% 2.03/2.24 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(15360,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(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(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15359])).
% 2.03/2.24 tff(15361,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(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(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15360, 15358])).
% 2.03/2.24 tff(15362,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(15363,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15362, 15361])).
% 2.03/2.24 tff(15364,plain,
% 2.03/2.24 (~r(elem!1, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15363, 112, 15330, 15350])).
% 2.03/2.24 tff(15365,plain,
% 2.03/2.24 (elem!1 = s(s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[388, 15364, 7732])).
% 2.03/2.24 tff(15366,plain,
% 2.03/2.24 (s(s(s(z))) = elem!1),
% 2.03/2.24 inference(symmetry,[status(thm)],[15365])).
% 2.03/2.24 tff(15367,plain,
% 2.03/2.24 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15366, 155, 15357, 989])).
% 2.03/2.24 tff(15368,plain,
% 2.03/2.24 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15367])).
% 2.03/2.24 tff(15369,plain,
% 2.03/2.24 (s(s(z)) = s(s(elem!1))),
% 2.03/2.24 inference(transitivity,[status(thm)],[32, 15368, 1156])).
% 2.03/2.24 tff(15370,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2579, 15369])).
% 2.03/2.24 tff(15371,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | b(elem!1, s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (~r(z, s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(15372,plain,
% 2.03/2.24 (~r(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15371, 1240, 405, 13708, 15115, 15327, 15309, 15307, 7066, 160, 3, 354, 9147, 83])).
% 2.03/2.24 tff(15373,plain,
% 2.03/2.24 (b(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[653, 15372])).
% 2.03/2.24 tff(15374,plain,
% 2.03/2.24 (~r(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5988, 15373, 2, 15115, 3340])).
% 2.03/2.24 tff(15375,plain,
% 2.03/2.24 (s(s(s(z))) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[374, 15374, 15308])).
% 2.03/2.24 tff(15376,plain,
% 2.03/2.24 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15375])).
% 2.03/2.24 tff(15377,plain,
% 2.03/2.24 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15376])).
% 2.03/2.24 tff(15378,plain,
% 2.03/2.24 (~r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[13937, 15373, 1240, 4204, 3340, 15307, 319])).
% 2.03/2.24 tff(15379,plain,
% 2.03/2.24 (b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[939, 15378, 303])).
% 2.03/2.24 tff(15380,plain,
% 2.03/2.24 (~b(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6548, 15379, 3, 13708, 354, 9147, 160, 15327, 1240])).
% 2.03/2.24 tff(15381,plain,
% 2.03/2.24 (r(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1277, 15380, 83])).
% 2.03/2.24 tff(15382,plain,
% 2.03/2.24 (r(s(s(s(z))), s(z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15381, 15377])).
% 2.03/2.24 tff(15383,plain,
% 2.03/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8902, 15382, 7066, 15305, 9147])).
% 2.03/2.24 tff(15384,plain,
% 2.03/2.24 (b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4511, 15375, 15373])).
% 2.03/2.24 tff(15385,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3588, 15381, 3340])).
% 2.03/2.24 tff(15386,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[901, 15385])).
% 2.03/2.24 tff(15387,plain,
% 2.03/2.24 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10038, 15386, 15375])).
% 2.03/2.24 tff(15388,plain,
% 2.03/2.24 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15375])).
% 2.03/2.24 tff(15389,plain,
% 2.03/2.24 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15388])).
% 2.03/2.24 tff(15390,plain,
% 2.03/2.24 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15388, 15389])).
% 2.03/2.24 tff(15391,plain,
% 2.03/2.24 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15390, 519])).
% 2.03/2.24 tff(15392,plain,
% 2.03/2.24 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15391])).
% 2.03/2.24 tff(15393,plain,
% 2.03/2.24 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15392])).
% 2.03/2.24 tff(15394,plain,
% 2.03/2.24 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[526, 15393])).
% 2.03/2.24 tff(15395,plain,
% 2.03/2.24 (b(s(s(z)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[14396, 1240, 7066, 15305, 9138, 4, 354])).
% 2.03/2.24 tff(15396,plain,
% 2.03/2.24 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10929, 1240, 7066, 15305])).
% 2.03/2.24 tff(15397,plain,
% 2.03/2.24 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[147, 15396, 2])).
% 2.03/2.24 tff(15398,plain,
% 2.03/2.24 (~b(s(s(z)), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9920, 15386, 15395, 15373])).
% 2.03/2.24 tff(15399,plain,
% 2.03/2.24 (r(s(s(z)), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[265, 15398, 169])).
% 2.03/2.24 tff(15400,plain,
% 2.03/2.24 (~b(s(s(z)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8623, 15399, 7066, 15305, 15397])).
% 2.03/2.24 tff(15401,plain,
% 2.03/2.24 (r(s(s(z)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[281, 15400])).
% 2.03/2.24 tff(15402,plain,
% 2.03/2.24 (~r(s(z), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9974, 15401, 15307])).
% 2.03/2.24 tff(15403,plain,
% 2.03/2.24 (b(s(z), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1071, 15402])).
% 2.03/2.24 tff(15404,plain,
% 2.03/2.24 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15389])).
% 2.03/2.24 tff(15405,plain,
% 2.03/2.24 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15404])).
% 2.03/2.24 tff(15406,plain,
% 2.03/2.24 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15399, 15405])).
% 2.03/2.24 tff(15407,plain,
% 2.03/2.24 (~b(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8879, 15406, 15403, 15395, 15394, 15387, 15384])).
% 2.03/2.24 tff(15408,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3168, 15407, 15383])).
% 2.03/2.24 tff(15409,plain,((~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(s(z)))) | (~b(elem!1, z)) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(15410,plain,
% 2.03/2.24 (~b(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15409, 405, 354, 2, 3, 9138, 4])).
% 2.03/2.24 tff(15411,plain,
% 2.03/2.24 (r(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[593, 15410])).
% 2.03/2.24 tff(15412,plain,
% 2.03/2.24 (~r(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10648, 15411, 15307])).
% 2.03/2.24 tff(15413,plain,
% 2.03/2.24 (b(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[653, 15412])).
% 2.03/2.24 tff(15414,plain,
% 2.03/2.24 (~r(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5988, 15413, 2, 15115, 3340])).
% 2.03/2.24 tff(15415,plain,
% 2.03/2.24 (s(s(s(z))) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[374, 15414, 15308])).
% 2.03/2.24 tff(15416,plain,
% 2.03/2.24 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15415])).
% 2.03/2.24 tff(15417,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15415])).
% 2.03/2.24 tff(15418,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15417])).
% 2.03/2.24 tff(15419,plain,
% 2.03/2.24 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15415])).
% 2.03/2.24 tff(15420,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15419])).
% 2.03/2.24 tff(15421,plain,
% 2.03/2.24 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[15420])).
% 2.03/2.24 tff(15422,plain,
% 2.03/2.24 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15421, 15418])).
% 2.03/2.24 tff(15423,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[13789, 15411, 13708, 11, 319, 3340, 15307])).
% 2.03/2.24 tff(15424,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[939, 15423, 303])).
% 2.03/2.24 tff(15425,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15424, 15422])).
% 2.03/2.24 tff(15426,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[895, 15411, 15307])).
% 2.03/2.24 tff(15427,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[901, 15426])).
% 2.03/2.24 tff(15428,plain,
% 2.03/2.24 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10038, 15415, 15427])).
% 2.03/2.24 tff(15429,plain,
% 2.03/2.24 (b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4511, 15415, 15413])).
% 2.03/2.24 tff(15430,plain,
% 2.03/2.24 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15419])).
% 2.03/2.24 tff(15431,plain,
% 2.03/2.24 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15419, 15430])).
% 2.03/2.24 tff(15432,plain,
% 2.03/2.24 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15431])).
% 2.03/2.24 tff(15433,plain,
% 2.03/2.24 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6557, 15424, 3340])).
% 2.03/2.24 tff(15434,plain,
% 2.03/2.24 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1521, 15433, 319])).
% 2.03/2.24 tff(15435,plain,
% 2.03/2.24 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15434, 15432])).
% 2.03/2.24 tff(15436,plain,
% 2.03/2.24 (~b(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[14659, 15435, 15429, 15428])).
% 2.03/2.24 tff(15437,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3168, 15436])).
% 2.03/2.24 tff(15438,plain,
% 2.03/2.24 (~r(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3326, 15437, 15425])).
% 2.03/2.24 tff(15439,plain,
% 2.03/2.24 (b(s(s(s(z))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[925, 15438])).
% 2.03/2.24 tff(15440,plain,
% 2.03/2.24 (b(elem!1, s(z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15439, 15416])).
% 2.03/2.24 tff(15441,plain,
% 2.03/2.24 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15430])).
% 2.03/2.24 tff(15442,plain,
% 2.03/2.24 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15441])).
% 2.03/2.24 tff(15443,plain,
% 2.03/2.24 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15442])).
% 2.03/2.24 tff(15444,plain,
% 2.03/2.24 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15442])).
% 2.03/2.24 tff(15445,plain,
% 2.03/2.24 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[15444])).
% 2.03/2.24 tff(15446,plain,
% 2.03/2.24 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15445])).
% 2.03/2.24 tff(15447,plain,
% 2.03/2.24 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15415])).
% 2.03/2.24 tff(15448,plain,
% 2.03/2.24 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.24 inference(transitivity,[status(thm)],[15447, 1403])).
% 2.03/2.24 tff(15449,plain,
% 2.03/2.24 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15448])).
% 2.03/2.24 tff(15450,plain,
% 2.03/2.24 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1165, 15449])).
% 2.03/2.24 tff(15451,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15450, 15446])).
% 2.03/2.24 tff(15452,plain,
% 2.03/2.24 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15442])).
% 2.03/2.24 tff(15453,plain,
% 2.03/2.24 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.03/2.24 inference(symmetry,[status(thm)],[15452])).
% 2.03/2.24 tff(15454,plain,
% 2.03/2.24 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15453])).
% 2.03/2.24 tff(15455,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[7240, 15454])).
% 2.03/2.24 tff(15456,plain,
% 2.03/2.24 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15419])).
% 2.03/2.24 tff(15457,plain,
% 2.03/2.24 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15456, 11069])).
% 2.03/2.24 tff(15458,plain,
% 2.03/2.24 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15457])).
% 2.03/2.24 tff(15459,plain,
% 2.03/2.24 (elem!1 = s(s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2487, 15415])).
% 2.03/2.24 tff(15460,plain,
% 2.03/2.24 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[14250, 15459, 169])).
% 2.03/2.24 tff(15461,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15460, 15458])).
% 2.03/2.24 tff(15462,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4112, 112, 15424, 3340])).
% 2.03/2.24 tff(15463,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[530, 15462, 526])).
% 2.03/2.24 tff(15464,plain,
% 2.03/2.24 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[11016, 15463, 15424, 3340, 15461, 15455, 15434])).
% 2.03/2.24 tff(15465,plain,
% 2.03/2.24 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1777, 15464, 15451])).
% 2.03/2.24 tff(15466,plain,
% 2.03/2.24 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15465, 15443])).
% 2.03/2.24 tff(15467,plain,
% 2.03/2.24 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[10602, 224, 15466, 15327, 15440])).
% 2.03/2.24 tff(15468,plain,
% 2.03/2.24 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1369, 68, 1366, 15467])).
% 2.03/2.24 tff(15469,plain,
% 2.03/2.24 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1324, 224, 15466, 405, 13708])).
% 2.03/2.24 tff(15470,plain,
% 2.03/2.24 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1338, 15469])).
% 2.03/2.24 tff(15471,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[14435, 112, 15307, 15470, 15468])).
% 2.03/2.24 tff(15472,plain,((~b(elem!1, z)) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(15473,plain,
% 2.03/2.24 (~b(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15472, 354, 2, 3, 9138, 4])).
% 2.03/2.24 tff(15474,plain,
% 2.03/2.24 (r(elem!1, z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[403, 15473, 11])).
% 2.03/2.24 tff(15475,plain,
% 2.03/2.24 (~r(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2076, 15474, 3340])).
% 2.03/2.24 tff(15476,plain,
% 2.03/2.24 (b(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[593, 15475])).
% 2.03/2.24 tff(15477,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[13943, 15476, 13708, 354, 3, 160, 9147, 15474, 83, 15307])).
% 2.03/2.24 tff(15478,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[939, 15477, 303])).
% 2.03/2.24 tff(15479,plain,
% 2.03/2.24 (~b(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[13937, 15478, 15476, 4204, 3340, 15307, 319])).
% 2.03/2.24 tff(15480,plain,
% 2.03/2.24 (~r(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5749, 15474, 9147])).
% 2.03/2.24 tff(15481,plain,
% 2.03/2.24 (b(elem!1, s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1277, 15480, 83])).
% 2.03/2.24 tff(15482,plain,
% 2.03/2.24 (~b(z, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6742, 15476, 13708, 354, 3, 9147, 15327, 160, 15474, 15481])).
% 2.03/2.24 tff(15483,plain,
% 2.03/2.24 (r(z, s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[752, 15482])).
% 2.03/2.24 tff(15484,plain,
% 2.03/2.24 (~r(s(z), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6325, 15483, 9147])).
% 2.03/2.24 tff(15485,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[653, 15484, 15479])).
% 2.03/2.24 tff(15486,plain,(b(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(15487,plain,
% 2.03/2.24 (b(s(s(elem!1)), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15486, 9138, 2, 3, 4])).
% 2.03/2.24 tff(15488,plain,
% 2.03/2.24 (~b(elem!1, s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9576, 224, 15318, 15314, 7672])).
% 2.03/2.24 tff(15489,plain,
% 2.03/2.24 (~b(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3407, 15318, 13708, 390])).
% 2.03/2.24 tff(15490,plain,
% 2.03/2.24 (r(s(s(elem!1)), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[593, 15489])).
% 2.03/2.24 tff(15491,plain,
% 2.03/2.24 (~r(s(elem!1), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[12361, 15490, 319, 409, 15316])).
% 2.03/2.24 tff(15492,plain,
% 2.03/2.24 (b(s(elem!1), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[498, 15491])).
% 2.03/2.24 tff(15493,plain,
% 2.03/2.24 (~r(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[895, 15490, 15316])).
% 2.03/2.24 tff(15494,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[901, 15493])).
% 2.03/2.24 tff(15495,plain,
% 2.03/2.24 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(15496,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15495])).
% 2.03/2.24 tff(15497,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[15496, 941])).
% 2.03/2.24 tff(15498,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(15499,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[15498, 15497])).
% 2.03/2.24 tff(15500,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15499, 224, 15318, 15492, 13708])).
% 2.03/2.24 tff(15501,plain,
% 2.03/2.24 (r(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[939, 15500, 303])).
% 2.03/2.24 tff(15502,plain,
% 2.03/2.24 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1485, 15501, 409, 15310, 15494])).
% 2.03/2.24 tff(15503,plain,
% 2.03/2.24 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[530, 15502, 526])).
% 2.03/2.24 tff(15504,plain,
% 2.03/2.24 (~r(s(s(elem!1)), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[15326, 2337, 7672, 2, 1090, 157, 3, 4569])).
% 2.03/2.24 tff(15505,plain,
% 2.03/2.24 (~r(s(elem!1), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[436, 15501, 15310])).
% 2.03/2.24 tff(15506,plain,
% 2.03/2.24 (b(s(elem!1), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1476, 15505, 409])).
% 2.03/2.24 tff(15507,plain,
% 2.03/2.24 (((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(15508,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[15507])).
% 2.03/2.24 tff(15509,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15508, 1549])).
% 2.03/2.25 tff(15510,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(15511,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15510, 15509])).
% 2.03/2.25 tff(15512,plain,
% 2.03/2.25 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15511, 224, 15312, 15494, 15506])).
% 2.03/2.25 tff(15513,plain,
% 2.03/2.25 (~b(z, s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[14947, 15512, 3, 13708, 15504, 15500])).
% 2.03/2.25 tff(15514,plain,
% 2.03/2.25 (r(z, s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[752, 15513])).
% 2.03/2.25 tff(15515,plain,
% 2.03/2.25 (~r(z, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[576, 15514, 15503])).
% 2.03/2.25 tff(15516,plain,
% 2.03/2.25 (b(z, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[625, 15515])).
% 2.03/2.25 tff(15517,plain,
% 2.03/2.25 (~b(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[509, 15516, 15318, 15492])).
% 2.03/2.25 tff(15518,plain,
% 2.03/2.25 (r(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[515, 15517, 327])).
% 2.03/2.25 tff(15519,plain,
% 2.03/2.25 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[14021, 224, 15492, 15314, 7672])).
% 2.03/2.25 tff(15520,plain,
% 2.03/2.25 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1521, 15512, 319])).
% 2.03/2.25 tff(15521,plain,
% 2.03/2.25 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[4010, 15520, 15501])).
% 2.03/2.25 tff(15522,plain,
% 2.03/2.25 (b(elem!1, s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[558, 15521, 3])).
% 2.03/2.25 tff(15523,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2249])).
% 2.03/2.25 tff(15524,plain,
% 2.03/2.25 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[15523])).
% 2.03/2.25 tff(15525,plain,
% 2.03/2.25 (elem!1 = s(s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15092, 777])).
% 2.03/2.25 tff(15526,plain,
% 2.03/2.25 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15525])).
% 2.03/2.25 tff(15527,plain,
% 2.03/2.25 (b(s(s(z)), s(s(elem!1)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[682, 15526])).
% 2.03/2.25 tff(15528,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15527, 15524])).
% 2.03/2.25 tff(15529,plain,
% 2.03/2.25 (s(s(z)) = elem!1),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[14085, 15525])).
% 2.03/2.25 tff(15530,plain,
% 2.03/2.25 (s(s(s(z))) = s(elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[13713, 777])).
% 2.03/2.25 tff(15531,plain,
% 2.03/2.25 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9074, 15530])).
% 2.03/2.25 tff(15532,plain,
% 2.03/2.25 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[777])).
% 2.03/2.25 tff(15533,plain,
% 2.03/2.25 (b(s(s(s(z))), s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[1347, 15532])).
% 2.03/2.25 tff(15534,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 2.03/2.25 tff(15535,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15536,plain,
% 2.03/2.25 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15537,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15536])).
% 2.03/2.25 tff(15538,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15537, 15535])).
% 2.03/2.25 tff(15539,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(15540,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15539, 15538])).
% 2.03/2.25 tff(15541,plain,
% 2.03/2.25 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15540, 224, 6255, 7672])).
% 2.03/2.25 tff(15542,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15541, 15534])).
% 2.03/2.25 tff(15543,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15542, 2189])).
% 2.03/2.25 tff(15544,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1338, 15543])).
% 2.03/2.25 tff(15545,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15544, 2187])).
% 2.03/2.25 tff(15546,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15547,plain,
% 2.03/2.25 (((~b(s(z), s(s(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(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15548,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15547])).
% 2.03/2.25 tff(15549,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15548, 15546])).
% 2.03/2.25 tff(15550,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(15551,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15550, 15549])).
% 2.03/2.25 tff(15552,plain,
% 2.03/2.25 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15551, 224, 1090, 560])).
% 2.03/2.25 tff(15553,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15552, 15534])).
% 2.03/2.25 tff(15554,plain,
% 2.03/2.25 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2314, 68, 15553])).
% 2.03/2.25 tff(15555,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15554, 2265])).
% 2.03/2.25 tff(15556,plain,
% 2.03/2.25 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15557,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15556])).
% 2.03/2.25 tff(15558,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15557, 9172])).
% 2.03/2.25 tff(15559,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(15560,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15559, 15558])).
% 2.03/2.25 tff(15561,plain,
% 2.03/2.25 (~b(s(z), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15560, 224, 1090, 6255, 7672])).
% 2.03/2.25 tff(15562,plain,
% 2.03/2.25 (r(s(z), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[194, 15561])).
% 2.03/2.25 tff(15563,plain,
% 2.03/2.25 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[14199, 112, 15562])).
% 2.03/2.25 tff(15564,plain,
% 2.03/2.25 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15563, 15555])).
% 2.03/2.25 tff(15565,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15564, 15545])).
% 2.03/2.25 tff(15566,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(15567,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15566, 15533, 1090, 7672, 6255, 777])).
% 2.03/2.25 tff(15568,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2228, 15567, 777])).
% 2.03/2.25 tff(15569,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1345, 15568, 2210])).
% 2.03/2.25 tff(15570,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1317, 15569, 15531, 1287])).
% 2.03/2.25 tff(15571,plain,
% 2.03/2.25 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5887, 15570, 15529])).
% 2.03/2.25 tff(15572,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2182])).
% 2.03/2.25 tff(15573,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2402, 15529, 390])).
% 2.03/2.25 tff(15574,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15573, 15572])).
% 2.03/2.25 tff(15575,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15576,plain,
% 2.03/2.25 (((~b(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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15577,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))), s(s(s(s(z))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15576])).
% 2.03/2.25 tff(15578,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15577, 15575])).
% 2.03/2.25 tff(15579,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(15580,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(s(z))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15579, 15578])).
% 2.03/2.25 tff(15581,plain,
% 2.03/2.25 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15580, 224, 15574, 15571])).
% 2.03/2.25 tff(15582,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[15581, 15528])).
% 2.03/2.25 tff(15583,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15569, 2205])).
% 2.03/2.25 tff(15584,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15583, 2204])).
% 2.03/2.25 tff(15585,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2249])).
% 2.03/2.25 tff(15586,plain,
% 2.03/2.25 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[15585])).
% 2.03/2.25 tff(15587,plain,
% 2.03/2.25 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[777])).
% 2.03/2.25 tff(15588,plain,
% 2.03/2.25 (r(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[544, 15587])).
% 2.03/2.25 tff(15589,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[15588, 15586])).
% 2.03/2.25 tff(15590,plain,
% 2.03/2.25 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[2182])).
% 2.03/2.25 tff(15591,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[102, 15590])).
% 2.03/2.25 tff(15592,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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(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)))), z)) | (~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(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15593,plain,
% 2.03/2.25 (((~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)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~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(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(15594,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))), z)) | (~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(s(s(z)))))), s(s(s(s(z))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[15593])).
% 2.03/2.25 tff(15595,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))), z)) | (~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(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[15594, 15592])).
% 2.03/2.25 tff(15596,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(15597,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[15596, 15595])).
% 2.03/2.26 tff(15598,plain,
% 2.03/2.26 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15597, 112, 15591, 15589])).
% 2.03/2.26 tff(15599,plain,
% 2.03/2.26 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15598, 15584])).
% 2.03/2.26 tff(15600,plain,
% 2.03/2.26 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2289, 777, 2287])).
% 2.03/2.26 tff(15601,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2293, 68, 15600, 15599, 15582])).
% 2.03/2.26 tff(15602,plain,((~(s(elem!1) = s(s(s(z))))) | b(s(elem!1), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15603,plain,
% 2.03/2.26 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15602, 15500, 1090, 7672, 15314, 15490, 15522, 15506, 15503, 390, 7240])).
% 2.03/2.26 tff(15604,plain,
% 2.03/2.26 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1534, 15603, 15519])).
% 2.03/2.26 tff(15605,plain,
% 2.03/2.26 (~r(elem!1, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7891, 15604, 15518])).
% 2.03/2.26 tff(15606,plain,
% 2.03/2.26 (elem!1 = s(s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[388, 15605, 15488])).
% 2.03/2.26 tff(15607,plain,
% 2.03/2.26 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15606])).
% 2.03/2.26 tff(15608,plain,
% 2.03/2.26 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.03/2.26 inference(symmetry,[status(thm)],[15607])).
% 2.03/2.26 tff(15609,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[1090, 15608])).
% 2.03/2.26 tff(15610,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2337, 15609])).
% 2.03/2.26 tff(15611,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15612,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15611, 15487, 7066, 15115, 3, 11, 9147, 2])).
% 2.03/2.26 tff(15613,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[14549, 13940, 166, 319, 390, 684, 344])).
% 2.03/2.26 tff(15614,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5674, 224, 684, 13940, 390])).
% 2.03/2.26 tff(15615,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[901, 15614])).
% 2.03/2.26 tff(15616,plain,
% 2.03/2.26 (r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[939, 15613, 303])).
% 2.03/2.26 tff(15617,plain,
% 2.03/2.26 (~r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2694, 15616, 363])).
% 2.03/2.26 tff(15618,plain,
% 2.03/2.26 (b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[498, 15617])).
% 2.03/2.26 tff(15619,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5928, 15615, 4569])).
% 2.03/2.26 tff(15620,plain,
% 2.03/2.26 (b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[593, 15619])).
% 2.03/2.26 tff(15621,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15622,plain,
% 2.03/2.26 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15623,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15622])).
% 2.03/2.26 tff(15624,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[15623, 15621])).
% 2.03/2.26 tff(15625,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(15626,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[15625, 15624])).
% 2.03/2.26 tff(15627,plain,
% 2.03/2.26 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15626, 224, 15618, 344, 390])).
% 2.03/2.26 tff(15628,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15627, 15620])).
% 2.03/2.26 tff(15629,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[530, 15628, 526])).
% 2.03/2.26 tff(15630,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15631,plain,
% 2.03/2.26 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15632,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15631])).
% 2.03/2.26 tff(15633,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[15632, 15630])).
% 2.03/2.26 tff(15634,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(15635,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[15634, 15633])).
% 2.03/2.26 tff(15636,plain,
% 2.03/2.26 (~r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15635, 112, 544, 4569, 887])).
% 2.03/2.26 tff(15637,plain,
% 2.03/2.26 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[580, 68, 15636])).
% 2.03/2.26 tff(15638,plain,
% 2.03/2.26 (b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15637, 567])).
% 2.03/2.26 tff(15639,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5688, 112, 4569, 887])).
% 2.03/2.26 tff(15640,plain,
% 2.03/2.26 (b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[593, 15639])).
% 2.03/2.26 tff(15641,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4152, 224, 1390, 15640, 500, 15638])).
% 2.03/2.26 tff(15642,plain,((~r(z, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15643,plain,
% 2.03/2.26 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15642, 15629, 4569, 15618, 15615])).
% 2.03/2.26 tff(15644,plain,
% 2.03/2.26 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1521, 15643, 319])).
% 2.03/2.26 tff(15645,plain,
% 2.03/2.26 (~r(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6557, 15644, 15616])).
% 2.03/2.26 tff(15646,plain,
% 2.03/2.26 (~b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[14947, 15645, 3, 344, 15643, 15613])).
% 2.03/2.26 tff(15647,plain,
% 2.03/2.26 (r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[752, 15646])).
% 2.03/2.26 tff(15648,plain,
% 2.03/2.26 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4010, 15644, 15616])).
% 2.03/2.26 tff(15649,plain,
% 2.03/2.26 (~b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3687, 15648, 3, 684, 15645])).
% 2.03/2.26 tff(15650,plain,
% 2.03/2.26 (r(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[653, 15649])).
% 2.03/2.26 tff(15651,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6325, 15650, 15647, 4569])).
% 2.03/2.26 tff(15652,plain,((~r(elem!1, z)) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15653,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15652, 9147, 3, 15612, 13708, 15487, 160, 83])).
% 2.03/2.26 tff(15654,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15653, 11])).
% 2.03/2.26 tff(15655,plain,
% 2.03/2.26 (~b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3407, 15654, 13708, 15487])).
% 2.03/2.26 tff(15656,plain,
% 2.03/2.26 (r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[593, 15655])).
% 2.03/2.26 tff(15657,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[895, 15656, 15307])).
% 2.03/2.26 tff(15658,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[901, 15657])).
% 2.03/2.26 tff(15659,plain,
% 2.03/2.26 (~r(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10648, 15656, 15307])).
% 2.03/2.26 tff(15660,plain,
% 2.03/2.26 (b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[653, 15659])).
% 2.03/2.26 tff(15661,plain,
% 2.03/2.26 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3685, 15660, 15487, 15612])).
% 2.03/2.26 tff(15662,plain,
% 2.03/2.26 (r(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[558, 15661, 3])).
% 2.03/2.26 tff(15663,plain,
% 2.03/2.26 (~r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12361, 15656, 319, 160, 15307])).
% 2.03/2.26 tff(15664,plain,
% 2.03/2.26 (b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[498, 15663])).
% 2.03/2.26 tff(15665,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15499, 224, 15654, 15664, 13708])).
% 2.03/2.26 tff(15666,plain,
% 2.03/2.26 (r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[939, 15665, 303])).
% 2.03/2.26 tff(15667,plain,
% 2.03/2.26 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4010, 15666, 15662])).
% 2.03/2.26 tff(15668,plain,
% 2.03/2.26 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1521, 15667, 319])).
% 2.03/2.26 tff(15669,plain,
% 2.03/2.26 (~b(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1554, 224, 15668, 15660, 15658])).
% 2.03/2.26 tff(15670,plain,
% 2.03/2.26 (r(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1476, 15669, 160])).
% 2.03/2.26 tff(15671,plain,
% 2.03/2.26 (~b(s(z), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[14893, 224, 15668, 15660, 15612, 15487])).
% 2.03/2.26 tff(15672,plain,
% 2.03/2.26 (r(s(z), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[670, 15671, 4204])).
% 2.03/2.26 tff(15673,plain,
% 2.03/2.26 (~r(z, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4231, 15672, 15307])).
% 2.03/2.26 tff(15674,plain,
% 2.03/2.26 (b(z, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[625, 15673])).
% 2.03/2.26 tff(15675,plain,
% 2.03/2.26 (~b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[509, 15674, 15654, 15664])).
% 2.03/2.26 tff(15676,plain,
% 2.03/2.26 (r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[515, 15675, 327])).
% 2.03/2.26 tff(15677,plain,
% 2.03/2.26 (~r(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1604, 15676, 15670])).
% 2.03/2.26 tff(15678,plain,
% 2.03/2.26 (b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1277, 15677, 83])).
% 2.03/2.26 tff(15679,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5674, 224, 15612, 15658, 15678, 15487])).
% 2.03/2.26 tff(15680,plain,(b(z, s(z)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15681,plain,
% 2.03/2.26 (b(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15680, 4, 2, 3])).
% 2.03/2.26 tff(15682,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6404, 15681, 15115, 15305])).
% 2.03/2.26 tff(15683,plain,
% 2.03/2.26 (r(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[925, 15682])).
% 2.03/2.26 tff(15684,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6404, 77, 1090, 15314])).
% 2.03/2.26 tff(15685,plain,
% 2.03/2.26 (r(s(s(s(z))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[925, 15684])).
% 2.03/2.26 tff(15686,plain,
% 2.03/2.26 (~r(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6496, 15310, 1181])).
% 2.03/2.26 tff(15687,plain,
% 2.03/2.26 (b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[653, 15686])).
% 2.03/2.26 tff(15688,plain,
% 2.03/2.26 (~r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5988, 15687, 2, 1090, 1181])).
% 2.03/2.26 tff(15689,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2841, 15310, 179])).
% 2.03/2.26 tff(15690,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15689, 157])).
% 2.03/2.26 tff(15691,plain,
% 2.03/2.26 (~b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9448, 224, 15690, 344, 7672])).
% 2.03/2.26 tff(15692,plain,
% 2.03/2.26 (s(s(s(z))) = elem!1),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[374, 15691, 15688])).
% 2.03/2.26 tff(15693,plain,
% 2.03/2.26 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15692])).
% 2.03/2.26 tff(15694,plain,
% 2.03/2.26 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.03/2.26 inference(symmetry,[status(thm)],[15693])).
% 2.03/2.26 tff(15695,plain,
% 2.03/2.26 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15694])).
% 2.03/2.26 tff(15696,plain,
% 2.03/2.26 (~b(s(z), s(s(s(z))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[2337, 15695])).
% 2.03/2.26 tff(15697,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1090, 15696])).
% 2.03/2.26 tff(15698,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15699,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15698, 1181, 13708, 7672, 2, 1090, 157, 15316])).
% 2.03/2.26 tff(15700,plain,
% 2.03/2.26 (~b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2904, 15699, 13708, 77])).
% 2.03/2.26 tff(15701,plain,
% 2.03/2.26 (r(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1277, 15700, 83])).
% 2.03/2.26 tff(15702,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3588, 15701, 1181])).
% 2.03/2.26 tff(15703,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[901, 15702])).
% 2.03/2.26 tff(15704,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1259, 15701, 15316])).
% 2.03/2.26 tff(15705,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15704, 157])).
% 2.03/2.26 tff(15706,plain,
% 2.03/2.26 (~b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9448, 224, 15705, 13708, 7672])).
% 2.03/2.26 tff(15707,plain,
% 2.03/2.26 (~r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2168, 112, 15701, 15685])).
% 2.03/2.26 tff(15708,plain,
% 2.03/2.26 (s(s(s(z))) = elem!1),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[374, 15707, 15706])).
% 2.03/2.26 tff(15709,plain,
% 2.03/2.26 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10038, 15708, 15703])).
% 2.03/2.26 tff(15710,plain,
% 2.03/2.26 (~b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[11740, 224, 77, 15699, 15703, 13708])).
% 2.03/2.26 tff(15711,plain,
% 2.03/2.26 (r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[752, 15710])).
% 2.03/2.26 tff(15712,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[761, 112, 179, 656, 293])).
% 2.03/2.26 tff(15713,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15714,plain,
% 2.03/2.26 (~r(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15713, 15711, 15316])).
% 2.03/2.26 tff(15715,plain,
% 2.03/2.26 (b(s(z), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[653, 15714])).
% 2.03/2.26 tff(15716,plain,
% 2.03/2.26 (b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4511, 15715, 15708])).
% 2.03/2.26 tff(15717,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[4131, 4505])).
% 2.03/2.26 tff(15718,plain,
% 2.03/2.26 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.26 inference(symmetry,[status(thm)],[15717])).
% 2.03/2.26 tff(15719,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[13923, 15718])).
% 2.03/2.26 tff(15720,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3326, 6621, 3188])).
% 2.03/2.26 tff(15721,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3168, 15720])).
% 2.03/2.26 tff(15722,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[14659, 15721, 4494, 4495])).
% 2.03/2.26 tff(15723,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15722, 15719])).
% 2.03/2.26 tff(15724,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15725,plain,
% 2.03/2.26 (~r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15724, 15708, 15716, 15709, 15685, 319, 1181])).
% 2.03/2.26 tff(15726,plain,
% 2.03/2.26 (b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[939, 15725, 303])).
% 2.03/2.26 tff(15727,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[13789, 15726, 13708, 157, 319, 1181, 15316])).
% 2.03/2.26 tff(15728,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1259, 993, 179])).
% 2.03/2.26 tff(15729,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15728, 157])).
% 2.03/2.26 tff(15730,plain,
% 2.03/2.26 (~b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[946, 224, 1488, 15729, 344])).
% 2.03/2.26 tff(15731,plain,
% 2.03/2.26 (r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[498, 15730])).
% 2.03/2.26 tff(15732,plain,
% 2.03/2.26 (~r(s(z), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12351, 112, 179, 15731])).
% 2.03/2.26 tff(15733,plain,
% 2.03/2.26 (b(s(z), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[670, 15732, 561])).
% 2.03/2.26 tff(15734,plain,
% 2.03/2.26 (~r(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[482, 112, 179, 15731])).
% 2.03/2.26 tff(15735,plain,
% 2.03/2.26 (b(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1476, 15734, 409])).
% 2.03/2.26 tff(15736,plain,
% 2.03/2.26 (~b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4221, 15733, 1488, 684])).
% 2.03/2.26 tff(15737,plain,
% 2.03/2.26 (r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[515, 15736, 327])).
% 2.03/2.26 tff(15738,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[539, 15737, 1181])).
% 2.03/2.26 tff(15739,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15740,plain,
% 2.03/2.26 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(15741,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[15740])).
% 2.03/2.26 tff(15742,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[15741, 15739])).
% 2.03/2.26 tff(15743,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(15744,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[15743, 15742])).
% 2.03/2.26 tff(15745,plain,
% 2.03/2.26 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15744, 224, 1488, 684, 4450])).
% 2.03/2.26 tff(15746,plain,
% 2.03/2.26 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15745, 15735])).
% 2.03/2.26 tff(15747,plain,
% 2.03/2.26 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1521, 15746, 319])).
% 2.03/2.26 tff(15748,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4310, 467, 543])).
% 2.03/2.26 tff(15749,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15748, 157])).
% 2.03/2.26 tff(15750,plain,
% 2.03/2.26 (~b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[613, 15749, 682, 1240])).
% 2.03/2.26 tff(15751,plain,
% 2.03/2.26 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[580, 68, 15750])).
% 2.03/2.26 tff(15752,plain,
% 2.03/2.26 (r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15751, 567])).
% 2.03/2.26 tff(15753,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10321, 112, 1700, 467, 15752])).
% 2.03/2.26 tff(15754,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15755,plain,
% 2.03/2.26 (~b(elem!1, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15754, 15747, 157, 1240, 15731, 15737])).
% 2.03/2.26 tff(15756,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10522, 15755, 15738, 3, 993, 15735, 15733])).
% 2.03/2.26 tff(15757,plain,((~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (elem!1 = z) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15758,plain,
% 2.03/2.26 (~b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15757, 15726, 15701, 157, 3, 1181, 15699, 15316, 13708])).
% 2.03/2.26 tff(15759,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[593, 15758, 15727])).
% 2.03/2.26 tff(15760,plain,((~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15761,plain,
% 2.03/2.26 (~r(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15760, 11, 3, 7066, 15681, 2, 15115])).
% 2.03/2.26 tff(15762,plain,
% 2.03/2.26 (b(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[360, 15761, 353])).
% 2.03/2.26 tff(15763,plain,
% 2.03/2.26 (~r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2841, 416, 179])).
% 2.03/2.26 tff(15764,plain,
% 2.03/2.26 (b(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[403, 15763, 157])).
% 2.03/2.26 tff(15765,plain,
% 2.03/2.26 (~b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3407, 15764, 344, 390])).
% 2.03/2.26 tff(15766,plain,
% 2.03/2.26 (r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[593, 15765])).
% 2.03/2.26 tff(15767,plain,
% 2.03/2.26 (~b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10849, 15766, 179, 77])).
% 2.03/2.26 tff(15768,plain,
% 2.03/2.26 (r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[752, 15767])).
% 2.03/2.26 tff(15769,plain,
% 2.03/2.26 (~r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[12361, 15766, 523, 409, 179])).
% 2.03/2.26 tff(15770,plain,
% 2.03/2.26 (b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[498, 15769])).
% 2.03/2.26 tff(15771,plain,
% 2.03/2.26 (~b(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15499, 224, 15764, 15770, 344])).
% 2.03/2.26 tff(15772,plain,
% 2.03/2.26 (r(s(elem!1), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[939, 15771, 324])).
% 2.03/2.26 tff(15773,plain,
% 2.03/2.26 (~b(z, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[449, 15772, 409, 77, 416])).
% 2.03/2.26 tff(15774,plain,
% 2.03/2.26 (r(z, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[625, 15773])).
% 2.03/2.26 tff(15775,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[895, 15766, 179])).
% 2.03/2.26 tff(15776,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[901, 15775])).
% 2.03/2.26 tff(15777,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1485, 15772, 409, 416, 15776])).
% 2.03/2.26 tff(15778,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[530, 15777, 1923])).
% 2.03/2.26 tff(15779,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[576, 15778, 15774, 15768])).
% 2.03/2.26 tff(15780,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (s(elem!1) = elem!1) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(15781,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[15780, 15681, 303, 13708, 15307, 319, 15762, 11])).
% 2.03/2.26 tff(15782,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[454, 15781, 91])).
% 2.03/2.26 tff(15783,plain,
% 2.03/2.26 (~b(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2904, 15782, 13708, 15681])).
% 2.03/2.26 tff(15784,plain,
% 2.03/2.26 (r(elem!1, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1277, 15783, 83])).
% 2.03/2.27 tff(15785,plain,
% 2.03/2.27 (~r(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1259, 15784, 15307])).
% 2.03/2.27 tff(15786,plain,
% 2.03/2.27 (b(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[403, 15785, 11])).
% 2.03/2.27 tff(15787,plain,
% 2.03/2.27 (~b(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9448, 224, 15786, 13708, 7066])).
% 2.03/2.27 tff(15788,plain,
% 2.03/2.27 (~r(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2168, 112, 15784, 15683])).
% 2.03/2.27 tff(15789,plain,
% 2.03/2.27 (s(s(s(z))) = elem!1),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[374, 15788, 15787])).
% 2.03/2.27 tff(15790,plain,
% 2.03/2.27 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15789])).
% 2.03/2.27 tff(15791,plain,
% 2.03/2.27 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15790])).
% 2.03/2.27 tff(15792,plain,
% 2.03/2.27 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15789])).
% 2.03/2.27 tff(15793,plain,
% 2.03/2.27 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15792])).
% 2.03/2.27 tff(15794,plain,
% 2.03/2.27 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15793])).
% 2.03/2.27 tff(15795,plain,
% 2.03/2.27 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[15794, 15791])).
% 2.03/2.27 tff(15796,plain,
% 2.03/2.27 (~b(s(s(elem!1)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3407, 15786, 13708, 15762])).
% 2.03/2.27 tff(15797,plain,
% 2.03/2.27 (r(s(s(elem!1)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[593, 15796])).
% 2.03/2.27 tff(15798,plain,
% 2.03/2.27 (~r(s(elem!1), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[12361, 15797, 319, 160, 15307])).
% 2.03/2.27 tff(15799,plain,
% 2.03/2.27 (b(s(elem!1), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[498, 15798])).
% 2.03/2.27 tff(15800,plain,
% 2.03/2.27 (~b(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15499, 224, 15786, 15799, 13708])).
% 2.03/2.27 tff(15801,plain,
% 2.03/2.27 (r(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[939, 15800, 303])).
% 2.03/2.27 tff(15802,plain,
% 2.03/2.27 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15801, 15795])).
% 2.03/2.27 tff(15803,plain,
% 2.03/2.27 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3326, 15802, 15683])).
% 2.03/2.27 tff(15804,plain,
% 2.03/2.27 (~r(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[895, 15797, 15307])).
% 2.03/2.27 tff(15805,plain,
% 2.03/2.27 (b(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[901, 15804])).
% 2.03/2.27 tff(15806,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10038, 15789, 15805])).
% 2.03/2.27 tff(15807,plain,
% 2.03/2.27 (~r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10648, 15797, 15307])).
% 2.03/2.27 tff(15808,plain,
% 2.03/2.27 (b(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[653, 15807])).
% 2.03/2.27 tff(15809,plain,
% 2.03/2.27 (b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4511, 15789, 15808])).
% 2.03/2.27 tff(15810,plain,
% 2.03/2.27 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15792])).
% 2.03/2.27 tff(15811,plain,
% 2.03/2.27 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15792, 15810])).
% 2.03/2.27 tff(15812,plain,
% 2.03/2.27 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15811])).
% 2.03/2.27 tff(15813,plain,
% 2.03/2.27 (r(elem!1, s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3687, 15808, 3, 15761, 15782])).
% 2.03/2.27 tff(15814,plain,
% 2.03/2.27 (~r(s(elem!1), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4010, 15801, 15813])).
% 2.03/2.27 tff(15815,plain,
% 2.03/2.27 (b(s(elem!1), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1521, 15814, 319])).
% 2.03/2.27 tff(15816,plain,
% 2.03/2.27 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15815, 15812])).
% 2.03/2.27 tff(15817,plain,
% 2.03/2.27 (~b(s(s(s(s(z)))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[14659, 15816, 15809, 15806])).
% 2.03/2.27 tff(15818,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3168, 15817, 15803])).
% 2.03/2.27 tff(15819,plain,((z = elem!1) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15820,plain,
% 2.03/2.27 (z = elem!1),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15819, 3, 2])).
% 2.03/2.27 tff(15821,plain,
% 2.03/2.27 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15820])).
% 2.03/2.27 tff(15822,plain,
% 2.03/2.27 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15821])).
% 2.03/2.27 tff(15823,plain,
% 2.03/2.27 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15822])).
% 2.03/2.27 tff(15824,plain,
% 2.03/2.27 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(15825,plain,
% 2.03/2.27 (~b(elem!1, elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15824, 2927])).
% 2.03/2.27 tff(15826,plain,
% 2.03/2.27 (~b(z, elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15825, 15823])).
% 2.03/2.27 tff(15827,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[13708, 15826])).
% 2.03/2.27 tff(15828,plain,((elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15829,plain,
% 2.03/2.27 (elem!1 = s(s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15828, 2])).
% 2.03/2.27 tff(15830,plain,
% 2.03/2.27 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15829])).
% 2.03/2.27 tff(15831,plain,
% 2.03/2.27 (s(s(elem!1)) = s(s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[13707, 3, 4538])).
% 2.03/2.27 tff(15832,plain,
% 2.03/2.27 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.27 tff(15833,plain,
% 2.03/2.27 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15832])).
% 2.03/2.27 tff(15834,plain,
% 2.03/2.27 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.27 tff(15835,plain,
% 2.03/2.27 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.27 inference(transitivity,[status(thm)],[15834, 284])).
% 2.03/2.27 tff(15836,plain,
% 2.03/2.27 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15835])).
% 2.03/2.27 tff(15837,plain,
% 2.03/2.27 (~(s(s(s(z))) = elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[3, 15836])).
% 2.03/2.27 tff(15838,plain,
% 2.03/2.27 (s(s(s(z))) = s(s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[310, 15831])).
% 2.03/2.27 tff(15839,plain,
% 2.03/2.27 (s(z) = elem!1),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[131, 15838])).
% 2.03/2.27 tff(15840,plain,
% 2.03/2.27 (elem!1 = s(z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[90, 15839])).
% 2.03/2.27 tff(15841,plain,
% 2.03/2.27 (~(s(s(s(s(z)))) = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8776, 15840])).
% 2.03/2.27 tff(15842,plain,
% 2.03/2.27 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[86])).
% 2.03/2.27 tff(15843,plain,
% 2.03/2.27 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15842])).
% 2.03/2.27 tff(15844,plain,
% 2.03/2.27 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9457])).
% 2.03/2.27 tff(15845,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[4538, 15844])).
% 2.03/2.27 tff(15846,plain,
% 2.03/2.27 (r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[5459, 15845])).
% 2.03/2.27 tff(15847,plain,
% 2.03/2.27 ((s(z) = z) <=> (elem!1 = z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[86])).
% 2.03/2.27 tff(15848,plain,
% 2.03/2.27 ((s(z) = z) <=> (z = elem!1)),
% 2.03/2.27 inference(transitivity,[status(thm)],[15847, 6])).
% 2.03/2.27 tff(15849,plain,
% 2.03/2.27 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15848])).
% 2.03/2.27 tff(15850,plain,
% 2.03/2.27 (~(z = elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[190, 15849])).
% 2.03/2.27 tff(15851,plain,
% 2.03/2.27 (r(z, elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[289, 15850, 4538])).
% 2.03/2.27 tff(15852,plain,
% 2.03/2.27 (b(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8971, 170, 4538, 15851, 15846])).
% 2.03/2.27 tff(15853,plain,
% 2.03/2.27 (b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15852, 15843])).
% 2.03/2.27 tff(15854,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[170, 15853])).
% 2.03/2.27 tff(15855,plain,(b(s(z), s(s(s(z)))) | (~(s(z) = elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15856,plain,
% 2.03/2.27 (b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15855, 15839, 4538])).
% 2.03/2.27 tff(15857,plain,
% 2.03/2.27 ((elem!1 = z) <=> (s(s(elem!1)) = z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15829])).
% 2.03/2.27 tff(15858,plain,
% 2.03/2.27 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15857])).
% 2.03/2.27 tff(15859,plain,
% 2.03/2.27 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.03/2.27 inference(transitivity,[status(thm)],[15858, 6])).
% 2.03/2.27 tff(15860,plain,
% 2.03/2.27 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15859])).
% 2.03/2.27 tff(15861,plain,
% 2.03/2.27 (~(z = elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[566, 15860])).
% 2.03/2.27 tff(15862,plain,
% 2.03/2.27 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.27 tff(15863,plain,
% 2.03/2.27 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[15862, 774])).
% 2.03/2.27 tff(15864,plain,
% 2.03/2.27 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15863])).
% 2.03/2.27 tff(15865,plain,
% 2.03/2.27 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[526, 15864])).
% 2.03/2.27 tff(15866,plain,
% 2.03/2.27 (b(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8581, 170, 15851, 15846, 1, 7733, 4538])).
% 2.03/2.27 tff(15867,plain,
% 2.03/2.27 (b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15866, 15843])).
% 2.03/2.27 tff(15868,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[170, 15867])).
% 2.03/2.27 tff(15869,plain,(b(s(z), s(s(s(z)))) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15870,plain,
% 2.03/2.27 (b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15869, 15839, 1, 15865, 4538])).
% 2.03/2.27 tff(15871,plain,
% 2.03/2.27 (b(z, s(z)) <=> b(z, elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15839])).
% 2.03/2.27 tff(15872,plain,
% 2.03/2.27 (b(z, elem!1) <=> b(z, s(z))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15871])).
% 2.03/2.27 tff(15873,plain,
% 2.03/2.27 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15872])).
% 2.03/2.27 tff(15874,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[4538, 15873])).
% 2.03/2.27 tff(15875,plain,
% 2.03/2.27 (r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[5459, 15874])).
% 2.03/2.27 tff(15876,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4608, 15875, 177])).
% 2.03/2.27 tff(15877,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[925, 15876])).
% 2.03/2.27 tff(15878,plain,
% 2.03/2.27 ((s(z) = z) <=> (elem!1 = z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15839])).
% 2.03/2.27 tff(15879,plain,
% 2.03/2.27 ((s(z) = z) <=> (z = elem!1)),
% 2.03/2.27 inference(transitivity,[status(thm)],[15878, 6])).
% 2.03/2.27 tff(15880,plain,
% 2.03/2.27 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15879])).
% 2.03/2.27 tff(15881,plain,
% 2.03/2.27 (~(z = elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[190, 15880])).
% 2.03/2.27 tff(15882,plain,
% 2.03/2.27 (r(z, elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[289, 15881, 4538])).
% 2.03/2.27 tff(15883,plain,
% 2.03/2.27 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.27 tff(15884,plain,
% 2.03/2.27 (s(elem!1) = s(s(z))),
% 2.03/2.27 inference(transitivity,[status(thm)],[164, 15883, 31])).
% 2.03/2.27 tff(15885,plain,
% 2.03/2.27 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15884])).
% 2.03/2.27 tff(15886,plain,
% 2.03/2.27 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.27 tff(15887,plain,
% 2.03/2.27 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15886])).
% 2.03/2.27 tff(15888,plain,
% 2.03/2.27 (r(s(s(elem!1)), z)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[177, 15887])).
% 2.03/2.27 tff(15889,plain,
% 2.03/2.27 (~r(s(s(elem!1)), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2346, 15882, 15888])).
% 2.03/2.27 tff(15890,plain,
% 2.03/2.27 (b(s(s(elem!1)), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[360, 15889, 353])).
% 2.03/2.27 tff(15891,plain,
% 2.03/2.27 (b(s(z), z) <=> b(elem!1, z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15839])).
% 2.03/2.27 tff(15892,plain,
% 2.03/2.27 (b(elem!1, z)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[1, 15891])).
% 2.03/2.27 tff(15893,plain,
% 2.03/2.27 (~r(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2431, 15882, 177])).
% 2.03/2.27 tff(15894,plain,
% 2.03/2.27 (b(s(s(s(z))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[374, 15893, 15837])).
% 2.03/2.27 tff(15895,plain,
% 2.03/2.27 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.03/2.27 inference(commutativity,[status(thm)],[])).
% 2.03/2.27 tff(15896,plain,
% 2.03/2.27 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15895])).
% 2.03/2.27 tff(15897,plain,
% 2.03/2.27 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15896])).
% 2.03/2.27 tff(15898,plain,
% 2.03/2.27 (s(s(s(z))) = s(s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[310, 306])).
% 2.03/2.27 tff(15899,plain,
% 2.03/2.27 (s(z) = elem!1),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[131, 15898])).
% 2.03/2.27 tff(15900,plain,
% 2.03/2.27 (elem!1 = s(z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[90, 15899])).
% 2.03/2.27 tff(15901,plain,
% 2.03/2.27 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8833, 15900])).
% 2.03/2.27 tff(15902,plain,
% 2.03/2.27 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15901, 15897])).
% 2.03/2.27 tff(15903,plain,
% 2.03/2.27 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[306])).
% 2.03/2.27 tff(15904,plain,
% 2.03/2.27 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15903])).
% 2.03/2.27 tff(15905,plain,
% 2.03/2.27 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15904])).
% 2.03/2.27 tff(15906,plain,
% 2.03/2.27 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15905])).
% 2.03/2.27 tff(15907,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[15906])).
% 2.03/2.27 tff(15908,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15905])).
% 2.03/2.27 tff(15909,plain,
% 2.03/2.27 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15908])).
% 2.03/2.27 tff(15910,plain,
% 2.03/2.27 (elem!1 = s(z)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15899])).
% 2.03/2.27 tff(15911,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15910])).
% 2.03/2.27 tff(15912,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.27 inference(symmetry,[status(thm)],[15911])).
% 2.03/2.27 tff(15913,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15904, 15910])).
% 2.03/2.27 tff(15914,plain,
% 2.03/2.27 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[306])).
% 2.03/2.27 tff(15915,plain,
% 2.03/2.27 (s(elem!1) = s(s(z))),
% 2.03/2.27 inference(transitivity,[status(thm)],[164, 15914, 31])).
% 2.03/2.27 tff(15916,plain,
% 2.03/2.27 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15915])).
% 2.03/2.27 tff(15917,plain,
% 2.03/2.27 (r(s(elem!1), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[939, 1287, 324])).
% 2.03/2.27 tff(15918,plain,
% 2.03/2.27 (r(s(s(z)), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15917, 15916])).
% 2.03/2.27 tff(15919,plain,
% 2.03/2.27 (~r(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2456, 112, 688, 15918])).
% 2.03/2.27 tff(15920,plain,
% 2.03/2.27 (b(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[281, 15919])).
% 2.03/2.27 tff(15921,plain,
% 2.03/2.27 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15915])).
% 2.03/2.27 tff(15922,plain,
% 2.03/2.27 (~r(z, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2499, 15917, 688])).
% 2.03/2.27 tff(15923,plain,
% 2.03/2.27 (b(z, s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[625, 15922])).
% 2.03/2.27 tff(15924,plain,
% 2.03/2.27 (b(z, s(s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15923, 15921])).
% 2.03/2.27 tff(15925,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15904])).
% 2.03/2.27 tff(15926,plain,
% 2.03/2.27 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7751, 15899])).
% 2.03/2.27 tff(15927,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1294, 1290, 15926])).
% 2.03/2.27 tff(15928,plain,
% 2.03/2.27 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15927, 15925])).
% 2.03/2.27 tff(15929,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), 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(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15930,plain,
% 2.03/2.27 (((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15931,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15930])).
% 2.03/2.27 tff(15932,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.27 inference(transitivity,[status(thm)],[15931, 15929])).
% 2.03/2.27 tff(15933,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(15934,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15933, 15932])).
% 2.03/2.27 tff(15935,plain,
% 2.03/2.27 (~r(s(s(s(s(s(z))))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15934, 112, 688, 15928])).
% 2.03/2.27 tff(15936,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15904, 15915])).
% 2.03/2.27 tff(15937,plain,
% 2.03/2.27 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7790, 15899])).
% 2.03/2.27 tff(15938,plain,
% 2.03/2.27 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1317, 1290, 15926, 1287])).
% 2.03/2.27 tff(15939,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1345, 15938, 15937])).
% 2.03/2.27 tff(15940,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15939, 15936])).
% 2.03/2.27 tff(15941,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15942,plain,
% 2.03/2.27 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15943,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15942])).
% 2.03/2.27 tff(15944,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[15943, 15941])).
% 2.03/2.27 tff(15945,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(15946,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15945, 15944])).
% 2.03/2.27 tff(15947,plain,
% 2.03/2.27 (~b(s(s(s(s(s(z))))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15946, 224, 2191, 1118, 15940])).
% 2.03/2.27 tff(15948,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 15947, 15935])).
% 2.03/2.27 tff(15949,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15950,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15949, 15924, 15920, 688, 306, 1287])).
% 2.03/2.27 tff(15951,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15950, 15913])).
% 2.03/2.27 tff(15952,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[15951, 15912])).
% 2.03/2.27 tff(15953,plain,
% 2.03/2.27 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(z), s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[15843])).
% 2.03/2.27 tff(15954,plain,
% 2.03/2.27 (~b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[7732, 15953])).
% 2.03/2.27 tff(15955,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1090, 15954])).
% 2.03/2.27 tff(15956,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(15957,plain,
% 2.03/2.27 (b(elem!1, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[15956, 1090, 15899])).
% 2.03/2.27 tff(15958,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15959,plain,
% 2.03/2.27 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(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))) <=> ((~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)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(15960,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15959])).
% 2.03/2.28 tff(15961,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[15960, 15958])).
% 2.03/2.28 tff(15962,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(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)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(15963,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[15962, 15961])).
% 2.03/2.28 tff(15964,plain,
% 2.03/2.28 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15963, 224, 15957, 787])).
% 2.03/2.28 tff(15965,plain,
% 2.03/2.28 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15964, 15952])).
% 2.03/2.28 tff(15966,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[15965, 15909])).
% 2.03/2.28 tff(15967,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1884, 15966])).
% 2.03/2.28 tff(15968,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[15967, 15907])).
% 2.03/2.28 tff(15969,plain,
% 2.03/2.28 (~(s(s(s(s(z)))) = elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8776, 15900])).
% 2.03/2.28 tff(15970,plain,
% 2.03/2.28 (b(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[281, 2457])).
% 2.03/2.28 tff(15971,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), 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(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15972,plain,
% 2.03/2.28 (((~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(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15973,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15972])).
% 2.03/2.28 tff(15974,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[15973, 15971])).
% 2.03/2.28 tff(15975,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(15976,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[15975, 15974])).
% 2.03/2.28 tff(15977,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15976, 112, 1047, 2274])).
% 2.03/2.28 tff(15978,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6185, 15977])).
% 2.03/2.28 tff(15979,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12998, 15978, 15970, 2191])).
% 2.03/2.28 tff(15980,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), 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(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15981,plain,
% 2.03/2.28 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15982,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15981])).
% 2.03/2.28 tff(15983,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[15982, 15980])).
% 2.03/2.28 tff(15984,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(15985,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[15984, 15983])).
% 2.03/2.28 tff(15986,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15985, 112, 688, 2276, 2274])).
% 2.03/2.28 tff(15987,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(15988,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15987, 2274, 688])).
% 2.03/2.28 tff(15989,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 15988, 15979])).
% 2.03/2.28 tff(15990,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(15991,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15990, 15924, 15918, 688])).
% 2.03/2.28 tff(15992,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3183, 15991, 15969])).
% 2.03/2.28 tff(15993,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8884, 15992, 15900])).
% 2.03/2.28 tff(15994,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1579, 15993, 560, 1090])).
% 2.03/2.28 tff(15995,plain,
% 2.03/2.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3252, 15994])).
% 2.03/2.28 tff(15996,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15997,plain,
% 2.03/2.28 (((~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(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))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(15998,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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(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)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15997])).
% 2.03/2.28 tff(15999,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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(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))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[15998, 15996])).
% 2.03/2.28 tff(16000,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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)))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(16001,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(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)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16000, 15999])).
% 2.03/2.28 tff(16002,plain,
% 2.03/2.28 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16001, 112, 15995, 15968])).
% 2.03/2.28 tff(16003,plain,
% 2.03/2.28 (((~![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))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16004,plain,
% 2.03/2.28 ((~![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))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(16005,plain,
% 2.03/2.28 ((~![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)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16004, 16003])).
% 2.03/2.28 tff(16006,plain,
% 2.03/2.28 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16005, 68, 16002])).
% 2.03/2.28 tff(16007,plain,
% 2.03/2.28 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16006, 15902])).
% 2.03/2.28 tff(16008,plain,
% 2.03/2.28 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15904])).
% 2.03/2.28 tff(16009,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15905])).
% 2.03/2.28 tff(16010,plain,
% 2.03/2.28 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[16009])).
% 2.03/2.28 tff(16011,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.03/2.28 tff(16012,plain,
% 2.03/2.28 (((~![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))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16013,plain,
% 2.03/2.28 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16014,plain,
% 2.03/2.28 (((~![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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), 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))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[16013])).
% 2.03/2.28 tff(16015,plain,
% 2.03/2.28 (((~![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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), 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))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[16014, 16012])).
% 2.03/2.28 tff(16016,plain,
% 2.03/2.28 ((~![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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(16017,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16016, 16015])).
% 2.03/2.28 tff(16018,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16017, 112, 177, 8784, 16011])).
% 2.03/2.28 tff(16019,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(16020,plain,
% 2.03/2.28 (~r(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16019, 15968, 177])).
% 2.03/2.28 tff(16021,plain,
% 2.03/2.28 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16020, 16010])).
% 2.03/2.28 tff(16022,plain,
% 2.03/2.28 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1338, 16021])).
% 2.03/2.28 tff(16023,plain,
% 2.03/2.28 (b(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16022, 16008])).
% 2.03/2.28 tff(16024,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16025,plain,
% 2.03/2.28 (((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(elem!1, z)) | (~b(s(s(s(s(s(z))))), 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)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16026,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[16025])).
% 2.03/2.28 tff(16027,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[16026, 16024])).
% 2.03/2.28 tff(16028,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(16029,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16028, 16027])).
% 2.03/2.28 tff(16030,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16029, 224, 405, 15992, 16023, 15952, 16007])).
% 2.03/2.28 tff(16031,plain,(b(s(elem!1), elem!1) | (~b(elem!1, z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(16032,plain,
% 2.03/2.28 (b(s(elem!1), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16031, 15892, 15831, 177, 15877, 15870, 15882, 15894, 303])).
% 2.03/2.28 tff(16033,plain,
% 2.03/2.28 (~b(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8320, 16032, 177, 15840, 15892, 15890])).
% 2.03/2.28 tff(16034,plain,
% 2.03/2.28 (r(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[515, 16033, 327])).
% 2.03/2.28 tff(16035,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[4866, 112, 543, 688, 568])).
% 2.03/2.28 tff(16036,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(16037,plain,
% 2.03/2.28 (~r(z, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16036, 16034, 15882])).
% 2.03/2.28 tff(16038,plain,
% 2.03/2.28 (b(z, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[625, 16037])).
% 2.03/2.28 tff(16039,plain,
% 2.03/2.28 (b(z, s(s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16038, 15885])).
% 2.03/2.28 tff(16040,plain,
% 2.03/2.28 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15831])).
% 2.03/2.28 tff(16041,plain,
% 2.03/2.28 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.03/2.28 inference(symmetry,[status(thm)],[16040])).
% 2.03/2.28 tff(16042,plain,
% 2.03/2.28 (b(elem!1, s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[15956, 15870, 15839])).
% 2.03/2.28 tff(16043,plain,
% 2.03/2.28 (b(s(s(z)), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7872, 16032, 15839])).
% 2.03/2.28 tff(16044,plain,
% 2.03/2.28 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2412, 16043, 15894, 16042])).
% 2.03/2.28 tff(16045,plain,
% 2.03/2.28 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[249, 16044])).
% 2.03/2.28 tff(16046,plain,
% 2.03/2.28 (r(s(s(z)), s(s(elem!1)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16045, 16041])).
% 2.03/2.28 tff(16047,plain,
% 2.03/2.28 (~r(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[276, 16046, 15888])).
% 2.03/2.28 tff(16048,plain,
% 2.03/2.28 (b(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[281, 16047])).
% 2.03/2.28 tff(16049,plain,
% 2.03/2.28 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[15884])).
% 2.03/2.28 tff(16050,plain,
% 2.03/2.28 (r(elem!1, s(s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16034, 16049])).
% 2.03/2.28 tff(16051,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 15988])).
% 2.03/2.28 tff(16052,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12998, 16051, 1118, 2191])).
% 2.03/2.28 tff(16053,plain,
% 2.03/2.28 (r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6185, 16052])).
% 2.03/2.28 tff(16054,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 2.03/2.28 tff(16055,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), 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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16056,plain,
% 2.03/2.28 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(16057,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, 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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[16056])).
% 2.03/2.28 tff(16058,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, 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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[16057, 16055])).
% 2.03/2.28 tff(16059,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(16060,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[16059, 16058])).
% 2.03/2.28 tff(16061,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16060, 112, 16054, 2274, 16053])).
% 2.03/2.28 tff(16062,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(16063,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[16062, 16050, 16048, 16039, 15882])).
% 2.03/2.28 tff(16064,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3183, 16063, 15841])).
% 2.03/2.28 tff(16065,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8884, 16064, 15840])).
% 2.03/2.28 tff(16066,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1579, 16065, 15877, 15870])).
% 2.03/2.28 tff(16067,plain,
% 2.03/2.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3252, 16066])).
% 2.03/2.28 tff(16068,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[11263, 16067, 16045])).
% 2.03/2.28 tff(16069,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6185, 16068])).
% 2.03/2.28 tff(16070,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[12998, 16069, 16048, 16039])).
% 2.03/2.29 tff(16071,plain,
% 2.03/2.29 (r(s(s(s(s(z)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 16070])).
% 2.03/2.29 tff(16072,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), 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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16073,plain,
% 2.03/2.29 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16074,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), 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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16073])).
% 2.03/2.29 tff(16075,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), 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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16074, 16072])).
% 2.03/2.29 tff(16076,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(16077,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16076, 16075])).
% 2.03/2.29 tff(16078,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16077, 112, 177, 16071, 16067])).
% 2.03/2.29 tff(16079,plain,((elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16080,plain,
% 2.03/2.29 (elem!1 = s(s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16079, 73, 1, 4538])).
% 2.03/2.29 tff(16081,plain,
% 2.03/2.29 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16080])).
% 2.03/2.29 tff(16082,plain,
% 2.03/2.29 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16080])).
% 2.03/2.29 tff(16083,plain,
% 2.03/2.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.29 inference(symmetry,[status(thm)],[16082])).
% 2.03/2.29 tff(16084,plain,
% 2.03/2.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.29 inference(transitivity,[status(thm)],[16083, 284])).
% 2.03/2.29 tff(16085,plain,
% 2.03/2.29 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16084])).
% 2.03/2.29 tff(16086,plain,
% 2.03/2.29 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1306, 16080])).
% 2.03/2.29 tff(16087,plain,
% 2.03/2.29 (~(s(z) = elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7751, 16086])).
% 2.03/2.29 tff(16088,plain,
% 2.03/2.29 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[131, 16087])).
% 2.03/2.29 tff(16089,plain,
% 2.03/2.29 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[310, 16088])).
% 2.03/2.29 tff(16090,plain,
% 2.03/2.29 (~(s(s(s(z))) = elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16089, 16085])).
% 2.03/2.29 tff(16091,plain,
% 2.03/2.29 ((elem!1 = z) <=> (s(s(elem!1)) = z)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16080])).
% 2.03/2.29 tff(16092,plain,
% 2.03/2.29 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.03/2.29 inference(symmetry,[status(thm)],[16091])).
% 2.03/2.29 tff(16093,plain,
% 2.03/2.29 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.03/2.29 inference(transitivity,[status(thm)],[16092, 6])).
% 2.03/2.29 tff(16094,plain,
% 2.03/2.29 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16093])).
% 2.03/2.29 tff(16095,plain,
% 2.03/2.29 (~(z = elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[566, 16094])).
% 2.03/2.29 tff(16096,plain,
% 2.03/2.29 (r(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[289, 16095, 4538])).
% 2.03/2.29 tff(16097,plain,
% 2.03/2.29 (~r(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2431, 16096, 73])).
% 2.03/2.29 tff(16098,plain,
% 2.03/2.29 (b(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[374, 16097, 16090])).
% 2.03/2.29 tff(16099,plain,
% 2.03/2.29 (b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16098, 16081])).
% 2.03/2.29 tff(16100,plain,
% 2.03/2.29 (b(z, s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6253, 16095, 12, 16089])).
% 2.03/2.29 tff(16101,plain,
% 2.03/2.29 (~r(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5737, 16096, 73, 16089])).
% 2.03/2.29 tff(16102,plain,
% 2.03/2.29 (b(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5459, 16101])).
% 2.03/2.29 tff(16103,plain,
% 2.03/2.29 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16080])).
% 2.03/2.29 tff(16104,plain,
% 2.03/2.29 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16103, 3620])).
% 2.03/2.29 tff(16105,plain,
% 2.03/2.29 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16104, 3621])).
% 2.03/2.29 tff(16106,plain,
% 2.03/2.29 ((~(elem!1 = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16105])).
% 2.03/2.29 tff(16107,plain,
% 2.03/2.29 (~(elem!1 = s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2783, 16086, 16080])).
% 2.03/2.29 tff(16108,plain,
% 2.03/2.29 (~(s(s(elem!1)) = s(s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16107, 16106])).
% 2.03/2.29 tff(16109,plain,
% 2.03/2.29 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16104])).
% 2.03/2.29 tff(16110,plain,
% 2.03/2.29 (~(s(s(z)) = s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16107, 16109])).
% 2.03/2.29 tff(16111,plain,
% 2.03/2.29 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[1296])).
% 2.03/2.29 tff(16112,plain,
% 2.03/2.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.29 inference(symmetry,[status(thm)],[16111])).
% 2.03/2.29 tff(16113,plain,
% 2.03/2.29 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.29 inference(transitivity,[status(thm)],[16112, 284])).
% 2.03/2.29 tff(16114,plain,
% 2.03/2.29 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16113])).
% 2.03/2.29 tff(16115,plain,
% 2.03/2.29 (~(s(z) = elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7751, 2831])).
% 2.03/2.29 tff(16116,plain,
% 2.03/2.29 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[131, 16115])).
% 2.03/2.29 tff(16117,plain,
% 2.03/2.29 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[310, 16116])).
% 2.03/2.29 tff(16118,plain,
% 2.03/2.29 (~(s(s(s(z))) = elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16117, 16114])).
% 2.03/2.29 tff(16119,plain,
% 2.03/2.29 (b(s(s(s(z))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[374, 3334, 16118])).
% 2.03/2.29 tff(16120,plain,
% 2.03/2.29 (b(s(s(s(z))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16119, 2826])).
% 2.03/2.29 tff(16121,plain,
% 2.03/2.29 (~r(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5737, 688, 177, 16117])).
% 2.03/2.29 tff(16122,plain,
% 2.03/2.29 (b(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5459, 16121])).
% 2.03/2.29 tff(16123,plain,
% 2.03/2.29 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[1296])).
% 2.03/2.29 tff(16124,plain,
% 2.03/2.29 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16123, 3620])).
% 2.03/2.29 tff(16125,plain,
% 2.03/2.29 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16124])).
% 2.03/2.29 tff(16126,plain,
% 2.03/2.29 (~(s(s(z)) = s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[2832, 16125])).
% 2.03/2.29 tff(16127,plain,
% 2.03/2.29 (b(s(s(elem!1)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[147, 312, 16117])).
% 2.03/2.29 tff(16128,plain,
% 2.03/2.29 (b(elem!1, s(s(s(z))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16127, 3126])).
% 2.03/2.29 tff(16129,plain,
% 2.03/2.29 (~r(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6329, 102, 6255, 2, 177])).
% 2.03/2.29 tff(16130,plain,
% 2.03/2.29 (b(z, s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5459, 16129])).
% 2.03/2.29 tff(16131,plain,
% 2.03/2.29 (~(s(s(elem!1)) = s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3490, 259])).
% 2.03/2.29 tff(16132,plain,
% 2.03/2.29 (~b(s(s(z)), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6392, 178, 2, 1, 16131, 6255, 177])).
% 2.03/2.29 tff(16133,plain,
% 2.03/2.29 (r(s(s(z)), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[265, 16132, 259])).
% 2.03/2.29 tff(16134,plain,
% 2.03/2.29 (~r(s(s(z)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[276, 16133, 102])).
% 2.03/2.29 tff(16135,plain,
% 2.03/2.29 (b(s(s(z)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[281, 16134])).
% 2.03/2.29 tff(16136,plain,
% 2.03/2.29 (~b(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2846, 16135, 1, 16130])).
% 2.03/2.29 tff(16137,plain,
% 2.03/2.29 (r(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2726, 16136])).
% 2.03/2.29 tff(16138,plain,
% 2.03/2.29 (~r(s(z), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3706, 16133, 6317, 16130])).
% 2.03/2.29 tff(16139,plain,
% 2.03/2.29 (b(s(z), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[653, 16138])).
% 2.03/2.29 tff(16140,plain,
% 2.03/2.29 (~r(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2993, 16137, 16133])).
% 2.03/2.29 tff(16141,plain,
% 2.03/2.29 (b(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[901, 16140])).
% 2.03/2.29 tff(16142,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6853, 16141, 6260, 16139])).
% 2.03/2.29 tff(16143,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[925, 16142])).
% 2.03/2.29 tff(16144,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16145,plain,
% 2.03/2.29 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16146,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16145])).
% 2.03/2.29 tff(16147,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16146, 16144])).
% 2.03/2.29 tff(16148,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(16149,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16148, 16147])).
% 2.03/2.29 tff(16150,plain,
% 2.03/2.29 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16149, 112, 16143, 16137])).
% 2.03/2.29 tff(16151,plain,
% 2.03/2.29 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3535, 68, 16150])).
% 2.03/2.29 tff(16152,plain,
% 2.03/2.29 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16151, 56])).
% 2.03/2.29 tff(16153,plain,
% 2.03/2.29 (~r(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[243, 178, 16130, 1, 177])).
% 2.03/2.29 tff(16154,plain,
% 2.03/2.29 (b(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[249, 16153])).
% 2.03/2.29 tff(16155,plain,
% 2.03/2.29 (~b(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2412, 16154, 787, 685])).
% 2.03/2.29 tff(16156,plain,
% 2.03/2.29 (r(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1135, 16155, 2796])).
% 2.03/2.29 tff(16157,plain,
% 2.03/2.29 (~r(z, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3758, 16156, 688])).
% 2.03/2.29 tff(16158,plain,
% 2.03/2.29 (b(z, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1088, 16157])).
% 2.03/2.29 tff(16159,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6358, 224, 16154, 6255, 16158, 16152])).
% 2.03/2.29 tff(16160,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16161,plain,
% 2.03/2.29 (~r(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16160, 16128, 16117, 1, 688, 2833, 6255, 16119, 16126, 177, 102])).
% 2.03/2.29 tff(16162,plain,
% 2.03/2.29 (b(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 16161])).
% 2.03/2.29 tff(16163,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6404, 16162, 16122, 6255])).
% 2.03/2.29 tff(16164,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[925, 16163])).
% 2.03/2.29 tff(16165,plain,
% 2.03/2.29 (r(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2951, 16162, 16118, 2930, 3334, 2913])).
% 2.03/2.29 tff(16166,plain,
% 2.03/2.29 (r(s(z), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16165, 2849])).
% 2.03/2.29 tff(16167,plain,
% 2.03/2.29 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7280, 3317, 656])).
% 2.03/2.29 tff(16168,plain,
% 2.03/2.29 (~r(s(s(s(s(z)))), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16167, 5170])).
% 2.03/2.29 tff(16169,plain,
% 2.03/2.29 (b(s(s(s(s(z)))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3183, 16168, 3121])).
% 2.03/2.29 tff(16170,plain,
% 2.03/2.29 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16169, 3102])).
% 2.03/2.29 tff(16171,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3237, 224, 152, 8894, 968, 16170])).
% 2.03/2.29 tff(16172,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16173,plain,
% 2.03/2.29 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16172, 16166, 1296, 16120, 16127, 16164])).
% 2.03/2.29 tff(16174,plain,
% 2.03/2.29 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3168, 16173])).
% 2.03/2.29 tff(16175,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3175, 224, 77, 1, 1570, 12996])).
% 2.03/2.29 tff(16176,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16177,plain,
% 2.03/2.29 (~b(s(s(s(s(z)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16176, 16174, 1, 16122])).
% 2.03/2.29 tff(16178,plain,
% 2.03/2.29 (r(s(s(s(s(z)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 16177])).
% 2.03/2.29 tff(16179,plain,
% 2.03/2.29 (~r(s(s(s(s(z)))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[15987, 16178, 688])).
% 2.03/2.29 tff(16180,plain,
% 2.03/2.29 (b(s(s(s(s(z)))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3183, 16179, 3121])).
% 2.03/2.29 tff(16181,plain,
% 2.03/2.29 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[5274, 3102])).
% 2.03/2.29 tff(16182,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16183,plain,
% 2.03/2.29 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16184,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16183])).
% 2.03/2.29 tff(16185,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16184, 16182])).
% 2.03/2.29 tff(16186,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(16187,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16186, 16185])).
% 2.03/2.29 tff(16188,plain,
% 2.03/2.29 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16187, 224, 1090, 1571, 1570, 968])).
% 2.03/2.29 tff(16189,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16188, 16181])).
% 2.03/2.29 tff(16190,plain,((~b(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16191,plain,
% 2.03/2.29 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16190, 16180, 16162, 1296, 16174, 16120])).
% 2.03/2.29 tff(16192,plain,
% 2.03/2.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3252, 16191])).
% 2.03/2.29 tff(16193,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16077, 112, 177, 16178, 16192])).
% 2.03/2.29 tff(16194,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16195,plain,
% 2.03/2.29 (~r(s(s(elem!1)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16194, 73, 16080, 16096, 1, 16100])).
% 2.03/2.29 tff(16196,plain,
% 2.03/2.29 (b(s(s(elem!1)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[593, 16195])).
% 2.03/2.29 tff(16197,plain,
% 2.03/2.29 (~b(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1249, 16196, 1, 16102])).
% 2.03/2.29 tff(16198,plain,
% 2.03/2.29 (r(s(s(elem!1)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[901, 16197])).
% 2.03/2.29 tff(16199,plain,
% 2.03/2.29 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16080])).
% 2.03/2.29 tff(16200,plain,
% 2.03/2.29 ((~b(z, elem!1)) <=> (~b(z, s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16199])).
% 2.03/2.29 tff(16201,plain,
% 2.03/2.29 (~b(z, s(s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[4538, 16200])).
% 2.03/2.29 tff(16202,plain,
% 2.03/2.29 (r(z, s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[580, 68, 16201, 748])).
% 2.03/2.29 tff(16203,plain,
% 2.03/2.29 (~r(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2993, 267, 887])).
% 2.03/2.29 tff(16204,plain,
% 2.03/2.29 (b(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2726, 16203])).
% 2.03/2.29 tff(16205,plain,
% 2.03/2.29 (~b(s(s(z)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2846, 16204, 77, 1])).
% 2.03/2.29 tff(16206,plain,
% 2.03/2.29 (r(s(s(z)), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[281, 16205])).
% 2.03/2.29 tff(16207,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16208,plain,
% 2.03/2.29 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(16209,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[16208])).
% 2.03/2.29 tff(16210,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[16209, 16207])).
% 2.03/2.29 tff(16211,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(16212,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[16211, 16210])).
% 2.03/2.29 tff(16213,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16212, 112, 293, 16206, 267])).
% 2.03/2.29 tff(16214,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(16215,plain,
% 2.03/2.29 (~r(s(s(z)), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[16214, 16202, 16102, 1, 16198])).
% 2.03/2.29 tff(16216,plain,
% 2.03/2.29 (b(s(s(z)), s(s(elem!1)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[265, 16215, 16110])).
% 2.03/2.29 tff(16217,plain,
% 2.03/2.29 (~r(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6392, 16216, 16089, 16108, 73, 16100, 1])).
% 2.03/2.29 tff(16218,plain,
% 2.03/2.29 (b(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 16217])).
% 2.03/2.29 tff(16219,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6404, 16218, 16102, 16100])).
% 2.03/2.29 tff(16220,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[925, 16219])).
% 2.03/2.29 tff(16221,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16222,plain,
% 2.13/2.30 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16223,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16222])).
% 2.13/2.30 tff(16224,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[16223, 16221])).
% 2.13/2.30 tff(16225,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(16226,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16225, 16224])).
% 2.13/2.30 tff(16227,plain,
% 2.13/2.30 ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16226, 224, 16196, 1, 16099])).
% 2.13/2.30 tff(16228,plain,
% 2.13/2.30 (~b(s(z), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16227, 16218])).
% 2.13/2.30 tff(16229,plain,
% 2.13/2.30 (r(s(z), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[653, 16228])).
% 2.13/2.30 tff(16230,plain,
% 2.13/2.30 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[5342, 112, 16198, 16220])).
% 2.13/2.30 tff(16231,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[147, 16230, 16089])).
% 2.13/2.30 tff(16232,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16172, 16231, 16080, 16099, 16229, 16220])).
% 2.13/2.30 tff(16233,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3168, 16232])).
% 2.13/2.30 tff(16234,plain,
% 2.13/2.30 (s(s(elem!1)) = elem!1),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16080, 76])).
% 2.13/2.30 tff(16235,plain,
% 2.13/2.30 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3120, 16234])).
% 2.13/2.30 tff(16236,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16176, 16233, 1, 16102])).
% 2.13/2.30 tff(16237,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.13/2.30 tff(16238,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 13552, 16237])).
% 2.13/2.30 tff(16239,plain,(r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(16240,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16239, 16236])).
% 2.13/2.30 tff(16241,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[15987, 16240, 16096])).
% 2.13/2.30 tff(16242,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3183, 16241, 16235])).
% 2.13/2.30 tff(16243,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16190, 16242, 16218, 16080, 16233, 16099])).
% 2.13/2.30 tff(16244,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3252, 16243])).
% 2.13/2.30 tff(16245,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16077, 112, 73, 16240, 16244])).
% 2.13/2.30 tff(16246,plain,(b(s(s(s(z))), z) | (~b(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(16247,plain,
% 2.13/2.30 (b(s(s(s(z))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16246, 1, 4538])).
% 2.13/2.30 tff(16248,plain,
% 2.13/2.30 (r(elem!1, s(s(elem!1))) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16249,plain,
% 2.13/2.30 (r(s(s(elem!1)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[16248])).
% 2.13/2.30 tff(16250,plain,
% 2.13/2.30 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16249])).
% 2.13/2.30 tff(16251,plain,
% 2.13/2.30 (~r(elem!1, s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[5127, 16250])).
% 2.13/2.30 tff(16252,plain,
% 2.13/2.30 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16253,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.30 inference(symmetry,[status(thm)],[16252])).
% 2.13/2.30 tff(16254,plain,
% 2.13/2.30 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16253])).
% 2.13/2.30 tff(16255,plain,
% 2.13/2.30 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[2929, 16254])).
% 2.13/2.30 tff(16256,plain,
% 2.13/2.30 ((~b(z, elem!1)) <=> (~b(z, s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15830])).
% 2.13/2.30 tff(16257,plain,
% 2.13/2.30 (~b(z, s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[4538, 16256])).
% 2.13/2.30 tff(16258,plain,
% 2.13/2.30 (r(z, s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[580, 68, 16257, 748])).
% 2.13/2.30 tff(16259,plain,
% 2.13/2.30 (r(z, elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[289, 15861, 4538])).
% 2.13/2.30 tff(16260,plain,
% 2.13/2.30 (b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9882, 170, 7672, 15861, 16255, 16251])).
% 2.13/2.30 tff(16261,plain,
% 2.13/2.30 (~b(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1249, 1240, 1, 77])).
% 2.13/2.30 tff(16262,plain,
% 2.13/2.30 (r(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[901, 16261])).
% 2.13/2.30 tff(16263,plain,
% 2.13/2.30 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16264,plain,
% 2.13/2.30 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[16263])).
% 2.13/2.30 tff(16265,plain,
% 2.13/2.30 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[16264, 284])).
% 2.13/2.30 tff(16266,plain,
% 2.13/2.30 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16265])).
% 2.13/2.30 tff(16267,plain,
% 2.13/2.30 (~(s(s(s(z))) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[2, 16266])).
% 2.13/2.30 tff(16268,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = elem!1),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1306, 15829])).
% 2.13/2.30 tff(16269,plain,
% 2.13/2.30 (~(elem!1 = s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2783, 16268, 15829])).
% 2.13/2.30 tff(16270,plain,
% 2.13/2.30 (~(s(s(z)) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2788, 16269])).
% 2.13/2.30 tff(16271,plain,
% 2.13/2.30 (s(s(elem!1)) = elem!1),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[15829, 76])).
% 2.13/2.30 tff(16272,plain,
% 2.13/2.30 (~r(s(s(z)), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16214, 16262, 293, 1, 77])).
% 2.13/2.30 tff(16273,plain,
% 2.13/2.30 (~r(s(s(z)), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2801, 16272, 16271])).
% 2.13/2.30 tff(16274,plain,
% 2.13/2.30 (b(s(s(z)), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1135, 16273, 16270])).
% 2.13/2.30 tff(16275,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[5356, 16274, 15829, 16267, 10739, 2, 16262])).
% 2.13/2.30 tff(16276,plain,
% 2.13/2.30 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4039, 16262, 178])).
% 2.13/2.30 tff(16277,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[147, 16276, 2])).
% 2.13/2.30 tff(16278,plain,
% 2.13/2.30 (~b(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10929, 16277, 7672, 1240])).
% 2.13/2.30 tff(16279,plain,
% 2.13/2.30 (r(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[100, 16278])).
% 2.13/2.30 tff(16280,plain,
% 2.13/2.30 (~r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[12443, 16279, 10739, 77, 1])).
% 2.13/2.30 tff(16281,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[249, 16280, 16275])).
% 2.13/2.30 tff(16282,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(16283,plain,
% 2.13/2.30 (~b(s(s(elem!1)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16282, 16260, 1, 2, 7672, 293, 176])).
% 2.13/2.30 tff(16284,plain,
% 2.13/2.30 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16264])).
% 2.13/2.30 tff(16285,plain,
% 2.13/2.30 (~(elem!1 = s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[2, 16284])).
% 2.13/2.30 tff(16286,plain,
% 2.13/2.30 (~b(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10094, 224, 16260, 1, 7672])).
% 2.13/2.30 tff(16287,plain,
% 2.13/2.30 (r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[925, 16286])).
% 2.13/2.30 tff(16288,plain,
% 2.13/2.30 (r(s(s(elem!1)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[593, 16283])).
% 2.13/2.30 tff(16289,plain,
% 2.13/2.30 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16290,plain,
% 2.13/2.30 (s(s(elem!1)) = elem!1),
% 2.13/2.30 inference(symmetry,[status(thm)],[15829])).
% 2.13/2.30 tff(16291,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16290])).
% 2.13/2.30 tff(16292,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[16291])).
% 2.13/2.30 tff(16293,plain,
% 2.13/2.30 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3120, 16271])).
% 2.13/2.30 tff(16294,plain,
% 2.13/2.30 (~r(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[698, 690, 688])).
% 2.13/2.30 tff(16295,plain,
% 2.13/2.30 (b(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[100, 16294])).
% 2.13/2.30 tff(16296,plain,
% 2.13/2.30 (~b(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2846, 1118, 77, 1])).
% 2.13/2.30 tff(16297,plain,
% 2.13/2.30 (r(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2726, 16296])).
% 2.13/2.30 tff(16298,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3196, 9840, 16297, 10739])).
% 2.13/2.30 tff(16299,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(16300,plain,
% 2.13/2.30 (~b(s(s(z)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16299, 16295, 7672, 77, 1])).
% 2.13/2.30 tff(16301,plain,
% 2.13/2.30 (r(s(s(z)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[281, 16300])).
% 2.13/2.30 tff(16302,plain,
% 2.13/2.30 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16303,plain,
% 2.13/2.30 (~r(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2374, 690, 178])).
% 2.13/2.30 tff(16304,plain,
% 2.13/2.30 (b(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[454, 16303, 91])).
% 2.13/2.30 tff(16305,plain,
% 2.13/2.30 (b(s(z), s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16304, 16302])).
% 2.13/2.30 tff(16306,plain,
% 2.13/2.30 (~r(s(s(z)), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[276, 16301, 102])).
% 2.13/2.30 tff(16307,plain,
% 2.13/2.30 (~r(s(s(z)), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2801, 16306, 16271])).
% 2.13/2.30 tff(16308,plain,
% 2.13/2.30 (b(s(s(z)), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1135, 16307, 16270])).
% 2.13/2.30 tff(16309,plain,
% 2.13/2.30 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16310,plain,
% 2.13/2.30 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16290])).
% 2.13/2.30 tff(16311,plain,
% 2.13/2.30 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16310])).
% 2.13/2.30 tff(16312,plain,
% 2.13/2.30 (~r(s(s(elem!1)), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9513, 112, 102, 16301])).
% 2.13/2.30 tff(16313,plain,
% 2.13/2.30 (~r(elem!1, s(s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16312, 16311])).
% 2.13/2.30 tff(16314,plain,
% 2.13/2.30 (b(elem!1, s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2874, 16313, 16269])).
% 2.13/2.30 tff(16315,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16314, 16309])).
% 2.13/2.30 tff(16316,plain,
% 2.13/2.30 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[15829])).
% 2.13/2.30 tff(16317,plain,
% 2.13/2.30 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[16316, 3620])).
% 2.13/2.30 tff(16318,plain,
% 2.13/2.30 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16317])).
% 2.13/2.30 tff(16319,plain,
% 2.13/2.30 (~(s(s(z)) = s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16269, 16318])).
% 2.13/2.30 tff(16320,plain,
% 2.13/2.30 (b(s(s(z)), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[265, 16306, 16319])).
% 2.13/2.30 tff(16321,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16322,plain,
% 2.13/2.30 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16323,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16322])).
% 2.13/2.30 tff(16324,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[16323, 16321])).
% 2.13/2.30 tff(16325,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(16326,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16325, 16324])).
% 2.13/2.30 tff(16327,plain,
% 2.13/2.30 (~b(s(z), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16326, 224, 16305, 16320, 16315])).
% 2.13/2.30 tff(16328,plain,
% 2.13/2.30 (r(s(z), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1071, 16327])).
% 2.13/2.30 tff(16329,plain,
% 2.13/2.30 (~r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6296, 16328, 178])).
% 2.13/2.30 tff(16330,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[249, 16329])).
% 2.13/2.30 tff(16331,plain,
% 2.13/2.30 (~r(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[5356, 16330, 15829, 16267, 10739, 2, 16308])).
% 2.13/2.30 tff(16332,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[901, 16331])).
% 2.13/2.30 tff(16333,plain,
% 2.13/2.30 (b(s(s(z)), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[265, 2584, 16126])).
% 2.13/2.30 tff(16334,plain,
% 2.13/2.30 (~b(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9920, 16333, 1241, 2252])).
% 2.13/2.30 tff(16335,plain,
% 2.13/2.30 (r(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2726, 16334])).
% 2.13/2.30 tff(16336,plain,
% 2.13/2.30 (~r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3196, 16335, 3188])).
% 2.13/2.30 tff(16337,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[249, 16336])).
% 2.13/2.30 tff(16338,plain,
% 2.13/2.30 (((~![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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16339,plain,
% 2.13/2.30 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16340,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16339])).
% 2.13/2.30 tff(16341,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[16340, 16338])).
% 2.13/2.30 tff(16342,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(16343,plain,
% 2.13/2.30 ((~![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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16342, 16341])).
% 2.13/2.30 tff(16344,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16343, 112, 3188, 268, 16335])).
% 2.13/2.30 tff(16345,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3535, 68, 16344, 11591])).
% 2.13/2.30 tff(16346,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[13309, 16345, 8894, 16337])).
% 2.13/2.30 tff(16347,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6185, 16346])).
% 2.13/2.30 tff(16348,plain,
% 2.13/2.30 (~r(elem!1, s(s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[9514, 3187])).
% 2.13/2.30 tff(16349,plain,
% 2.13/2.30 (b(elem!1, s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2874, 16348, 2832])).
% 2.13/2.30 tff(16350,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16349, 3186])).
% 2.13/2.30 tff(16351,plain,
% 2.13/2.30 (~b(s(z), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16326, 224, 2252, 16333, 16350])).
% 2.13/2.30 tff(16352,plain,
% 2.13/2.30 (r(s(z), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1071, 16351])).
% 2.13/2.30 tff(16353,plain,
% 2.13/2.30 (((~![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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16354,plain,
% 2.13/2.30 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(16355,plain,
% 2.13/2.30 (((~![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(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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[16354])).
% 2.13/2.30 tff(16356,plain,
% 2.13/2.30 (((~![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(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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[16355, 16353])).
% 2.13/2.30 tff(16357,plain,
% 2.13/2.30 ((~![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(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(16358,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16357, 16356])).
% 2.13/2.30 tff(16359,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16358, 112, 178, 16352, 3317, 16347])).
% 2.13/2.30 tff(16360,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(16361,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16360, 16332, 178, 16305, 15829, 10739, 102, 16301])).
% 2.13/2.30 tff(16362,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3168, 16361])).
% 2.13/2.30 tff(16363,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16176, 16362, 1, 77])).
% 2.13/2.30 tff(16364,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16239, 16363])).
% 2.13/2.30 tff(16365,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[15987, 16364, 688])).
% 2.13/2.30 tff(16366,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3183, 16365, 16293])).
% 2.13/2.30 tff(16367,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[16366, 16292])).
% 2.13/2.30 tff(16368,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3310, 224, 16305, 16332, 16362])).
% 2.13/2.30 tff(16369,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[16368, 16367])).
% 2.13/2.30 tff(16370,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16371,plain,
% 2.13/2.31 (~r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16370, 16260, 1, 688, 176, 16288, 2, 7672])).
% 2.13/2.31 tff(16372,plain,
% 2.13/2.31 (b(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[374, 16371, 16267])).
% 2.13/2.31 tff(16373,plain,
% 2.13/2.31 (b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16372, 16289])).
% 2.13/2.31 tff(16374,plain,
% 2.13/2.31 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4039, 887, 178])).
% 2.13/2.31 tff(16375,plain,
% 2.13/2.31 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[147, 16374, 2])).
% 2.13/2.31 tff(16376,plain,
% 2.13/2.31 (~r(s(s(z)), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16214, 887, 293, 1, 77])).
% 2.13/2.31 tff(16377,plain,
% 2.13/2.31 (b(s(s(z)), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[265, 16376, 16319])).
% 2.13/2.31 tff(16378,plain,
% 2.13/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6362, 16377, 968, 16375])).
% 2.13/2.31 tff(16379,plain,
% 2.13/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[249, 16378])).
% 2.13/2.31 tff(16380,plain,
% 2.13/2.31 (~r(s(s(z)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3196, 16379, 3188])).
% 2.13/2.31 tff(16381,plain,
% 2.13/2.31 (b(s(s(z)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2726, 16380])).
% 2.13/2.31 tff(16382,plain,
% 2.13/2.31 (~b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2846, 16381, 77, 1])).
% 2.13/2.31 tff(16383,plain,
% 2.13/2.31 (r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[281, 16382])).
% 2.13/2.31 tff(16384,plain,
% 2.13/2.31 (~r(s(s(elem!1)), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9513, 112, 102, 16383])).
% 2.13/2.31 tff(16385,plain,
% 2.13/2.31 (~r(elem!1, s(s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16384, 16311])).
% 2.13/2.31 tff(16386,plain,
% 2.13/2.31 (b(elem!1, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2874, 16385, 16269])).
% 2.13/2.31 tff(16387,plain,
% 2.13/2.31 (b(s(s(elem!1)), s(s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16386, 16309])).
% 2.13/2.31 tff(16388,plain,
% 2.13/2.31 (~r(s(z), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6296, 16379, 178])).
% 2.13/2.31 tff(16389,plain,
% 2.13/2.31 (b(s(z), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1071, 16388])).
% 2.13/2.31 tff(16390,plain,
% 2.13/2.31 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(16391,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16390])).
% 2.13/2.31 tff(16392,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[16391, 16321])).
% 2.13/2.31 tff(16393,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(16394,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16393, 16392])).
% 2.13/2.31 tff(16395,plain,
% 2.13/2.31 (~b(s(z), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16394, 224, 16389, 16377, 16387])).
% 2.13/2.31 tff(16396,plain,
% 2.13/2.31 (r(s(z), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[653, 16395])).
% 2.13/2.31 tff(16397,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16172, 16396, 15829, 968, 16375, 3188])).
% 2.13/2.31 tff(16398,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3168, 16397])).
% 2.13/2.31 tff(16399,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16176, 16398, 1, 77])).
% 2.13/2.31 tff(16400,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16239, 16399])).
% 2.13/2.31 tff(16401,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[5196, 16398, 16389, 16381])).
% 2.13/2.31 tff(16402,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6185, 16401])).
% 2.13/2.31 tff(16403,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[5298, 112, 2276, 268, 6075])).
% 2.13/2.31 tff(16404,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16405,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16404, 16402, 16400, 16383])).
% 2.13/2.31 tff(16406,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16407,plain,
% 2.13/2.31 (~r(s(s(elem!1)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16406, 16260, 1, 16373, 16287, 16288, 176, 2, 293])).
% 2.13/2.31 tff(16408,plain,
% 2.13/2.31 (b(s(s(elem!1)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[901, 16407])).
% 2.13/2.31 tff(16409,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16172, 11375, 15829, 968, 656, 3188])).
% 2.13/2.31 tff(16410,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3168, 16409])).
% 2.13/2.31 tff(16411,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16176, 16410, 1, 77])).
% 2.13/2.31 tff(16412,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16239, 16411])).
% 2.13/2.31 tff(16413,plain,
% 2.13/2.31 (~r(s(s(z)), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3706, 656, 293, 77])).
% 2.13/2.31 tff(16414,plain,
% 2.13/2.31 (b(s(s(z)), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[265, 16413, 16319])).
% 2.13/2.31 tff(16415,plain,
% 2.13/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6362, 16414, 968, 11375])).
% 2.13/2.31 tff(16416,plain,
% 2.13/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[249, 16415])).
% 2.13/2.31 tff(16417,plain,
% 2.13/2.31 (~r(s(s(z)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3196, 16416, 3188])).
% 2.13/2.31 tff(16418,plain,
% 2.13/2.31 (b(s(s(z)), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2726, 16417])).
% 2.13/2.31 tff(16419,plain,
% 2.13/2.31 (~b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2846, 16418, 77, 1])).
% 2.13/2.31 tff(16420,plain,
% 2.13/2.31 (r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[281, 16419])).
% 2.13/2.31 tff(16421,plain,
% 2.13/2.31 (~r(s(z), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6296, 16416, 178])).
% 2.13/2.31 tff(16422,plain,
% 2.13/2.31 (b(s(z), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1071, 16421])).
% 2.13/2.31 tff(16423,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[5196, 16422, 16410, 16418])).
% 2.13/2.31 tff(16424,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6185, 16423])).
% 2.13/2.31 tff(16425,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16404, 16424, 16420, 16412])).
% 2.13/2.31 tff(16426,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16427,plain,
% 2.13/2.31 (~r(s(z), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16426, 16260, 1, 176, 16287, 16373, 2, 293])).
% 2.13/2.31 tff(16428,plain,
% 2.13/2.31 (b(s(z), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[653, 16427])).
% 2.13/2.31 tff(16429,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16176, 1570, 1, 77])).
% 2.13/2.31 tff(16430,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16239, 16429])).
% 2.13/2.31 tff(16431,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15987, 16430, 688])).
% 2.13/2.31 tff(16432,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3183, 16431, 3121])).
% 2.13/2.31 tff(16433,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16432, 3102])).
% 2.13/2.31 tff(16434,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3310, 224, 2252, 1241, 1570])).
% 2.13/2.31 tff(16435,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16434, 16433])).
% 2.13/2.31 tff(16436,plain,((~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16437,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16436, 16428, 15829, 16408, 688, 1, 16260])).
% 2.13/2.31 tff(16438,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3168, 16437])).
% 2.13/2.31 tff(16439,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3326, 16438, 16287])).
% 2.13/2.31 tff(16440,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3252, 16439])).
% 2.13/2.31 tff(16441,plain,
% 2.13/2.31 (b(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[374, 12301, 362])).
% 2.13/2.31 tff(16442,plain,
% 2.13/2.31 (b(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[388, 12302, 680])).
% 2.13/2.31 tff(16443,plain,
% 2.13/2.31 (~r(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12443, 689, 10739, 77, 1])).
% 2.13/2.31 tff(16444,plain,
% 2.13/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[249, 16443])).
% 2.13/2.31 tff(16445,plain,
% 2.13/2.31 (~b(s(s(z)), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2412, 16444, 16442, 16441])).
% 2.13/2.31 tff(16446,plain,
% 2.13/2.31 (r(s(s(z)), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1135, 16445, 2833])).
% 2.13/2.31 tff(16447,plain,
% 2.13/2.31 (~r(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3758, 16446, 688])).
% 2.13/2.31 tff(16448,plain,
% 2.13/2.31 (b(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1088, 16447])).
% 2.13/2.31 tff(16449,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15990, 16448, 16446, 688])).
% 2.13/2.31 tff(16450,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3183, 16449, 3121])).
% 2.13/2.31 tff(16451,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16450, 3102])).
% 2.13/2.31 tff(16452,plain,
% 2.13/2.31 (b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16441, 2826])).
% 2.13/2.31 tff(16453,plain,
% 2.13/2.31 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11579, 689, 7672, 9139])).
% 2.13/2.31 tff(16454,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3237, 224, 16453, 1571, 16452])).
% 2.13/2.31 tff(16455,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16454, 16451])).
% 2.13/2.31 tff(16456,plain,((~r(z, s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16457,plain,
% 2.13/2.31 (~r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16456, 16440, 15829, 688, 16267, 16285, 16260, 1, 7672, 16283])).
% 2.13/2.31 tff(16458,plain,
% 2.13/2.31 (~r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16360, 16438, 176, 16408, 15829, 16287, 16288, 16428])).
% 2.13/2.31 tff(16459,plain,
% 2.13/2.31 (b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[281, 16458])).
% 2.13/2.31 tff(16460,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16299, 16459, 7672, 16260, 1])).
% 2.13/2.31 tff(16461,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[100, 16460, 16457])).
% 2.13/2.31 tff(16462,plain,(b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16463,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16462, 16259, 1, 16247, 2, 16258])).
% 2.13/2.31 tff(16464,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9179, 16463, 1, 16247])).
% 2.13/2.31 tff(16465,plain,
% 2.13/2.31 (r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[100, 16464])).
% 2.13/2.31 tff(16466,plain,
% 2.13/2.31 (b(z, s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9717, 16465, 16255, 16251, 16247, 15861])).
% 2.13/2.31 tff(16467,plain,
% 2.13/2.31 (~r(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2420, 16465, 16259])).
% 2.13/2.31 tff(16468,plain,
% 2.13/2.31 (b(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[388, 16467, 16285])).
% 2.13/2.31 tff(16469,plain,
% 2.13/2.31 (~r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[698, 16465, 16259])).
% 2.13/2.31 tff(16470,plain,
% 2.13/2.31 (b(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[374, 16469, 16267])).
% 2.13/2.31 tff(16471,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2951, 16467, 16267, 16255, 16463, 16469])).
% 2.13/2.31 tff(16472,plain,
% 2.13/2.31 (~r(s(s(z)), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2468, 16471, 16259, 16466])).
% 2.13/2.31 tff(16473,plain,
% 2.13/2.31 (b(s(s(z)), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1135, 16472, 16270])).
% 2.13/2.31 tff(16474,plain,
% 2.13/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2412, 16473, 16470, 16468])).
% 2.13/2.31 tff(16475,plain,
% 2.13/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[249, 16474])).
% 2.13/2.31 tff(16476,plain,
% 2.13/2.31 (~r(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12443, 16475, 16465, 16466, 1])).
% 2.13/2.31 tff(16477,plain,
% 2.13/2.31 (b(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[925, 16476])).
% 2.13/2.31 tff(16478,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10094, 224, 16466, 1, 16247, 16477])).
% 2.13/2.31 tff(16479,plain,((s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16480,plain,
% 2.13/2.31 (s(s(elem!1)) = s(s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16479, 1, 4538])).
% 2.13/2.31 tff(16481,plain,
% 2.13/2.31 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16480])).
% 2.13/2.31 tff(16482,plain,
% 2.13/2.31 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16481])).
% 2.13/2.31 tff(16483,plain,
% 2.13/2.31 (s(s(s(z))) = s(s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[310, 16480])).
% 2.13/2.31 tff(16484,plain,
% 2.13/2.31 (s(z) = elem!1),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[131, 16483])).
% 2.13/2.31 tff(16485,plain,
% 2.13/2.31 (b(s(z), z) <=> b(elem!1, z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16484])).
% 2.13/2.31 tff(16486,plain,
% 2.13/2.31 (b(elem!1, z)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[1, 16485])).
% 2.13/2.31 tff(16487,plain,
% 2.13/2.31 (b(s(s(elem!1)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9144, 16480, 16247])).
% 2.13/2.31 tff(16488,plain,
% 2.13/2.31 ((s(z) = z) <=> (elem!1 = z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16484])).
% 2.13/2.31 tff(16489,plain,
% 2.13/2.31 ((s(z) = z) <=> (z = elem!1)),
% 2.13/2.31 inference(transitivity,[status(thm)],[16488, 6])).
% 2.13/2.31 tff(16490,plain,
% 2.13/2.31 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16489])).
% 2.13/2.31 tff(16491,plain,
% 2.13/2.31 (~(z = elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[190, 16490])).
% 2.13/2.31 tff(16492,plain,
% 2.13/2.31 (r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[289, 16491, 4538])).
% 2.13/2.31 tff(16493,plain,
% 2.13/2.31 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16480])).
% 2.13/2.31 tff(16494,plain,
% 2.13/2.31 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[16493, 774])).
% 2.13/2.31 tff(16495,plain,
% 2.13/2.31 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16494])).
% 2.13/2.31 tff(16496,plain,
% 2.13/2.31 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7751, 16484])).
% 2.13/2.31 tff(16497,plain,
% 2.13/2.31 (~(elem!1 = s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1306, 16496])).
% 2.13/2.31 tff(16498,plain,
% 2.13/2.31 (~(s(elem!1) = s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[318, 16497])).
% 2.13/2.31 tff(16499,plain,
% 2.13/2.31 (~(s(s(elem!1)) = s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[525, 16498])).
% 2.13/2.31 tff(16500,plain,
% 2.13/2.31 (~(s(elem!1) = s(s(s(z))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16499, 16495])).
% 2.13/2.31 tff(16501,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15869, 16500, 1, 16484, 4538])).
% 2.13/2.31 tff(16502,plain,
% 2.13/2.31 (b(elem!1, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15956, 16501, 16484])).
% 2.13/2.31 tff(16503,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9179, 16501, 1, 16247])).
% 2.13/2.31 tff(16504,plain,
% 2.13/2.31 (r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[100, 16503])).
% 2.13/2.31 tff(16505,plain,
% 2.13/2.31 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[15904])).
% 2.13/2.31 tff(16506,plain,
% 2.13/2.31 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[15904])).
% 2.13/2.31 tff(16507,plain,
% 2.13/2.31 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[16506])).
% 2.13/2.31 tff(16508,plain,
% 2.13/2.31 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16507])).
% 2.13/2.31 tff(16509,plain,
% 2.13/2.31 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.31 tff(16510,plain,
% 2.13/2.31 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.13/2.31 inference(transitivity,[status(thm)],[16509, 284])).
% 2.13/2.31 tff(16511,plain,
% 2.13/2.31 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16510])).
% 2.13/2.31 tff(16512,plain,
% 2.13/2.31 (~(s(s(s(z))) = elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[3, 16511])).
% 2.13/2.31 tff(16513,plain,
% 2.13/2.31 ((s(z) = z) <=> (elem!1 = z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.31 tff(16514,plain,
% 2.13/2.31 ((s(z) = z) <=> (z = elem!1)),
% 2.13/2.31 inference(transitivity,[status(thm)],[16513, 6])).
% 2.13/2.31 tff(16515,plain,
% 2.13/2.31 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16514])).
% 2.13/2.31 tff(16516,plain,
% 2.13/2.31 (~(z = elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[190, 16515])).
% 2.13/2.31 tff(16517,plain,
% 2.13/2.31 (b(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9704, 9138, 7672, 689, 1240, 2597, 16516, 16512])).
% 2.13/2.31 tff(16518,plain,
% 2.13/2.31 (~r(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4621, 9147, 689])).
% 2.13/2.31 tff(16519,plain,
% 2.13/2.31 (b(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[925, 16518])).
% 2.13/2.31 tff(16520,plain,
% 2.13/2.31 (~r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6173, 16519, 689, 9147])).
% 2.13/2.31 tff(16521,plain,
% 2.13/2.31 (~b(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9460, 9138, 15899])).
% 2.13/2.31 tff(16522,plain,
% 2.13/2.31 (r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[289, 16521, 16516])).
% 2.13/2.31 tff(16523,plain,
% 2.13/2.31 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.31 tff(16524,plain,
% 2.13/2.31 ((s(s(z)) = s(z)) <=> (elem!1 = s(s(z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[16523, 2587])).
% 2.13/2.31 tff(16525,plain,
% 2.13/2.31 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.13/2.31 inference(transitivity,[status(thm)],[16524, 2588])).
% 2.13/2.31 tff(16526,plain,
% 2.13/2.31 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16525])).
% 2.13/2.31 tff(16527,plain,
% 2.13/2.31 (~(s(s(z)) = elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[210, 16526])).
% 2.13/2.31 tff(16528,plain,
% 2.13/2.31 (r(s(s(z)), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1135, 5829, 16527])).
% 2.13/2.31 tff(16529,plain,
% 2.13/2.31 (~r(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3758, 16528, 688])).
% 2.13/2.31 tff(16530,plain,
% 2.13/2.31 (b(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1088, 16529])).
% 2.13/2.31 tff(16531,plain,
% 2.13/2.31 (b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[281, 279])).
% 2.13/2.31 tff(16532,plain,
% 2.13/2.31 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8776, 78])).
% 2.13/2.31 tff(16533,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1579, 1571, 1090, 560])).
% 2.13/2.31 tff(16534,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8884, 16533, 78])).
% 2.13/2.31 tff(16535,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3183, 16534, 16532])).
% 2.13/2.31 tff(16536,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15985, 112, 688, 16535])).
% 2.13/2.31 tff(16537,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 16536])).
% 2.13/2.31 tff(16538,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[15976, 112, 1047, 16535])).
% 2.13/2.31 tff(16539,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6185, 16538])).
% 2.13/2.31 tff(16540,plain,
% 2.13/2.31 (~r(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3758, 1047, 688])).
% 2.13/2.31 tff(16541,plain,
% 2.13/2.31 (b(z, s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1088, 16540])).
% 2.13/2.31 tff(16542,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(16543,plain,
% 2.13/2.31 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(16544,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16543])).
% 2.13/2.31 tff(16545,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[16544, 16542])).
% 2.13/2.31 tff(16546,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(16547,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16546, 16545])).
% 2.13/2.31 tff(16548,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16547, 224, 7672, 16541, 1571, 16539, 16537])).
% 2.13/2.31 tff(16549,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16550,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16549, 16528, 7672, 688, 15900, 1090, 560])).
% 2.13/2.31 tff(16551,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3252, 16550])).
% 2.13/2.31 tff(16552,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(16553,plain,
% 2.13/2.31 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(16554,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[16553])).
% 2.13/2.31 tff(16555,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[16554, 16552])).
% 2.13/2.31 tff(16556,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(16557,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[16556, 16555])).
% 2.13/2.31 tff(16558,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16557, 112, 688, 689, 2276, 3318])).
% 2.13/2.31 tff(16559,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(16560,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[16559, 16551, 689, 688])).
% 2.13/2.31 tff(16561,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 16560])).
% 2.13/2.31 tff(16562,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[12998, 16561, 16531, 16530])).
% 2.13/2.31 tff(16563,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6185, 16562])).
% 2.13/2.31 tff(16564,plain,
% 2.13/2.31 (~b(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7872, 5829, 15899])).
% 2.13/2.31 tff(16565,plain,
% 2.13/2.31 (r(s(elem!1), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[939, 16564, 324])).
% 2.13/2.31 tff(16566,plain,
% 2.13/2.31 (~r(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2499, 16565, 688])).
% 2.13/2.31 tff(16567,plain,
% 2.13/2.31 (b(z, s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[625, 16566])).
% 2.13/2.31 tff(16568,plain,
% 2.13/2.31 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[15915])).
% 2.13/2.31 tff(16569,plain,
% 2.13/2.31 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.13/2.31 inference(symmetry,[status(thm)],[16568])).
% 2.13/2.31 tff(16570,plain,
% 2.13/2.31 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16569])).
% 2.13/2.32 tff(16571,plain,
% 2.13/2.32 (~r(s(elem!1), z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[279, 16570])).
% 2.13/2.32 tff(16572,plain,
% 2.13/2.32 (b(s(elem!1), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[498, 16571])).
% 2.13/2.32 tff(16573,plain,
% 2.13/2.32 (~b(s(s(elem!1)), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4320, 16572, 1240, 16567])).
% 2.13/2.32 tff(16574,plain,
% 2.13/2.32 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[530, 16573, 2505])).
% 2.13/2.32 tff(16575,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8303, 16574, 15900])).
% 2.13/2.32 tff(16576,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11651, 112, 16551, 16575, 16563])).
% 2.13/2.32 tff(16577,plain,(b(s(s(z)), elem!1) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), z)) | r(s(s(z)), z) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(16578,plain,
% 2.13/2.32 (b(s(s(z)), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16577, 16522, 689, 7672, 1090, 16519, 526, 1240, 16520, 306, 303])).
% 2.13/2.32 tff(16579,plain,
% 2.13/2.32 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2412, 16578, 16517, 685])).
% 2.13/2.32 tff(16580,plain,
% 2.13/2.32 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[249, 16579])).
% 2.13/2.32 tff(16581,plain,
% 2.13/2.32 (~r(s(elem!1), z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16520, 16570])).
% 2.13/2.32 tff(16582,plain,
% 2.13/2.32 (b(s(elem!1), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[498, 16581])).
% 2.13/2.32 tff(16583,plain,
% 2.13/2.32 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[7775])).
% 2.13/2.32 tff(16584,plain,
% 2.13/2.32 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 2.13/2.32 inference(symmetry,[status(thm)],[16583])).
% 2.13/2.32 tff(16585,plain,
% 2.13/2.32 (b(s(s(s(z))), z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[1240, 16584])).
% 2.13/2.32 tff(16586,plain,
% 2.13/2.32 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[7742])).
% 2.13/2.32 tff(16587,plain,
% 2.13/2.32 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.13/2.32 inference(symmetry,[status(thm)],[16586])).
% 2.13/2.32 tff(16588,plain,
% 2.13/2.32 (b(s(s(s(z))), s(z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[787, 16587])).
% 2.13/2.32 tff(16589,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[7742])).
% 2.13/2.32 tff(16590,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.32 inference(symmetry,[status(thm)],[16589])).
% 2.13/2.32 tff(16591,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[3919, 16590])).
% 2.13/2.32 tff(16592,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16593,plain,
% 2.13/2.32 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16594,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16593])).
% 2.13/2.32 tff(16595,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[16594, 16592])).
% 2.13/2.32 tff(16596,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(16597,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16596, 16595])).
% 2.13/2.32 tff(16598,plain,
% 2.13/2.32 ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16597, 224, 1])).
% 2.13/2.32 tff(16599,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16598, 16591, 16588, 16585])).
% 2.13/2.32 tff(16600,plain,
% 2.13/2.32 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10192, 78])).
% 2.13/2.32 tff(16601,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[5424, 68, 16600, 16599])).
% 2.13/2.32 tff(16602,plain,
% 2.13/2.32 (b(s(s(z)), s(z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[1109, 7835])).
% 2.13/2.32 tff(16603,plain,
% 2.13/2.32 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[7760])).
% 2.13/2.32 tff(16604,plain,
% 2.13/2.32 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.13/2.32 inference(symmetry,[status(thm)],[16603])).
% 2.13/2.32 tff(16605,plain,
% 2.13/2.32 (b(s(s(z)), z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[500, 16604])).
% 2.13/2.32 tff(16606,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16607,plain,
% 2.13/2.32 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16608,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16607])).
% 2.13/2.32 tff(16609,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[16608, 16606])).
% 2.13/2.32 tff(16610,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(16611,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16610, 16609])).
% 2.13/2.32 tff(16612,plain,
% 2.13/2.32 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16611, 224, 1])).
% 2.13/2.32 tff(16613,plain,
% 2.13/2.32 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16612, 16591, 16605, 16602])).
% 2.13/2.32 tff(16614,plain,
% 2.13/2.32 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7787, 78])).
% 2.13/2.32 tff(16615,plain,
% 2.13/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16616,plain,
% 2.13/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(16617,plain,
% 2.13/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16616, 16615])).
% 2.13/2.32 tff(16618,plain,
% 2.13/2.32 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16617, 68, 16614, 16613])).
% 2.13/2.32 tff(16619,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[5413, 16618, 16601, 196])).
% 2.13/2.32 tff(16620,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~(elem!1 = s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(16621,plain,
% 2.13/2.32 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16620, 16582, 15900, 1, 16517, 16578, 16580, 1240])).
% 2.13/2.32 tff(16622,plain,
% 2.13/2.32 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1294, 16621, 15926])).
% 2.13/2.32 tff(16623,plain,
% 2.13/2.32 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16622, 15925])).
% 2.13/2.32 tff(16624,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(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(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16625,plain,
% 2.13/2.32 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16626,plain,
% 2.13/2.32 (((~![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(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16625])).
% 2.13/2.32 tff(16627,plain,
% 2.13/2.32 (((~![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(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(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(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[16626, 16624])).
% 2.13/2.32 tff(16628,plain,
% 2.13/2.32 ((~![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(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(16629,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16628, 16627])).
% 2.13/2.32 tff(16630,plain,
% 2.13/2.32 (~r(z, s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16629, 112, 16522, 16623])).
% 2.13/2.32 tff(16631,plain,
% 2.13/2.32 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16630, 16508])).
% 2.13/2.32 tff(16632,plain,
% 2.13/2.32 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4412, 16631])).
% 2.13/2.32 tff(16633,plain,
% 2.13/2.32 (b(z, s(s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16632, 16505])).
% 2.13/2.32 tff(16634,plain,
% 2.13/2.32 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[15915, 15904])).
% 2.13/2.32 tff(16635,plain,
% 2.13/2.32 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8842, 15899])).
% 2.13/2.32 tff(16636,plain,
% 2.13/2.32 (b(s(z), z) <=> b(elem!1, z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.32 tff(16637,plain,
% 2.13/2.32 (b(elem!1, z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[1, 16636])).
% 2.13/2.32 tff(16638,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16639,plain,
% 2.13/2.32 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16640,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16639])).
% 2.13/2.32 tff(16641,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[16640, 16638])).
% 2.13/2.32 tff(16642,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(16643,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[16642, 16641])).
% 2.13/2.32 tff(16644,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16643, 224, 16637, 16517, 16578, 7672])).
% 2.13/2.32 tff(16645,plain,
% 2.13/2.32 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[306, 15915])).
% 2.13/2.32 tff(16646,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[1391, 16645])).
% 2.13/2.32 tff(16647,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[13298, 16646])).
% 2.13/2.32 tff(16648,plain,((~b(s(s(elem!1)), s(elem!1))) | b(s(s(s(z))), s(s(z))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(16649,plain,
% 2.13/2.32 (~b(s(s(elem!1)), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16648, 16644, 306])).
% 2.13/2.32 tff(16650,plain,
% 2.13/2.32 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[530, 16649, 526])).
% 2.13/2.32 tff(16651,plain,
% 2.13/2.32 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[16513])).
% 2.13/2.32 tff(16652,plain,
% 2.13/2.32 (~(elem!1 = z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[190, 16651])).
% 2.13/2.32 tff(16653,plain,
% 2.13/2.32 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.32 tff(16654,plain,
% 2.13/2.32 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[16653])).
% 2.13/2.32 tff(16655,plain,
% 2.13/2.32 (r(z, s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[689, 16654])).
% 2.13/2.32 tff(16656,plain,
% 2.13/2.32 (~r(z, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[576, 16650, 16655])).
% 2.13/2.32 tff(16657,plain,
% 2.13/2.32 (b(z, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[625, 16656])).
% 2.13/2.32 tff(16658,plain,
% 2.13/2.32 (~b(elem!1, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[509, 16657, 16637, 16582])).
% 2.13/2.32 tff(16659,plain,
% 2.13/2.32 (r(elem!1, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[515, 2618, 517])).
% 2.13/2.32 tff(16660,plain,
% 2.13/2.32 (~r(elem!1, s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[553, 16659, 544])).
% 2.13/2.32 tff(16661,plain,
% 2.13/2.32 (b(elem!1, s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[558, 16660, 3])).
% 2.13/2.32 tff(16662,plain,
% 2.13/2.32 (b(elem!1, z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[12249, 16661, 1, 1240, 544, 16659, 500, 157])).
% 2.13/2.32 tff(16663,plain,
% 2.13/2.32 (~b(z, s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[613, 16662, 1240, 16661])).
% 2.13/2.32 tff(16664,plain,
% 2.13/2.32 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[580, 68, 16663])).
% 2.13/2.32 tff(16665,plain,
% 2.13/2.32 (r(z, s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16664, 567])).
% 2.13/2.32 tff(16666,plain,
% 2.13/2.32 (~r(z, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[576, 16665, 544])).
% 2.13/2.32 tff(16667,plain,
% 2.13/2.32 (b(z, s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[625, 16666])).
% 2.13/2.32 tff(16668,plain,
% 2.13/2.32 (~b(s(z), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10118, 224, 1, 500, 16667])).
% 2.13/2.32 tff(16669,plain,
% 2.13/2.32 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[426, 68, 16668])).
% 2.13/2.32 tff(16670,plain,
% 2.13/2.32 (r(s(z), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[16669, 12220])).
% 2.13/2.32 tff(16671,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(16672,plain,
% 2.13/2.32 (((~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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16673,plain,
% 2.13/2.33 (((~![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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16672])).
% 2.13/2.33 tff(16674,plain,
% 2.13/2.33 (((~![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(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16673, 16671])).
% 2.13/2.33 tff(16675,plain,
% 2.13/2.33 ((~![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))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16676,plain,
% 2.13/2.33 ((~![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(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16675, 16674])).
% 2.13/2.33 tff(16677,plain,
% 2.13/2.33 (~r(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16676, 112, 16659, 16670])).
% 2.13/2.33 tff(16678,plain,
% 2.13/2.33 (~r(s(z), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6325, 16665, 4569])).
% 2.13/2.33 tff(16679,plain,
% 2.13/2.33 (b(s(z), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[653, 16678])).
% 2.13/2.33 tff(16680,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16681,plain,
% 2.13/2.33 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16682,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16681])).
% 2.13/2.33 tff(16683,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16682, 16680])).
% 2.13/2.33 tff(16684,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16685,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16684, 16683])).
% 2.13/2.33 tff(16686,plain,
% 2.13/2.33 (~b(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16685, 224, 16661, 16662, 1240, 16679])).
% 2.13/2.33 tff(16687,plain,
% 2.13/2.33 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1275, 68, 16686])).
% 2.13/2.33 tff(16688,plain,
% 2.13/2.33 (elem!1 = s(z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16687, 16677])).
% 2.13/2.33 tff(16689,plain,
% 2.13/2.33 (s(elem!1) = s(s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16688])).
% 2.13/2.33 tff(16690,plain,
% 2.13/2.33 (s(s(elem!1)) = s(s(s(z)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16689])).
% 2.13/2.33 tff(16691,plain,
% 2.13/2.33 (s(s(s(z))) = s(s(elem!1))),
% 2.13/2.33 inference(symmetry,[status(thm)],[16690])).
% 2.13/2.33 tff(16692,plain,
% 2.13/2.33 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16691])).
% 2.13/2.33 tff(16693,plain,
% 2.13/2.33 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 2.13/2.33 inference(symmetry,[status(thm)],[16692])).
% 2.13/2.33 tff(16694,plain,
% 2.13/2.33 (b(s(s(s(z))), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[1240, 16693])).
% 2.13/2.33 tff(16695,plain,
% 2.13/2.33 (s(z) = elem!1),
% 2.13/2.33 inference(symmetry,[status(thm)],[16688])).
% 2.13/2.33 tff(16696,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16695])).
% 2.13/2.33 tff(16697,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(symmetry,[status(thm)],[16696])).
% 2.13/2.33 tff(16698,plain,
% 2.13/2.33 ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12240, 224, 16661, 1240, 1])).
% 2.13/2.33 tff(16699,plain,
% 2.13/2.33 (~b(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16698, 16679])).
% 2.13/2.33 tff(16700,plain,
% 2.13/2.33 (~r(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12231, 112, 16659, 16670])).
% 2.13/2.33 tff(16701,plain,
% 2.13/2.33 (s(z) = elem!1),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[454, 16700, 16699])).
% 2.13/2.33 tff(16702,plain,
% 2.13/2.33 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7751, 16701])).
% 2.13/2.33 tff(16703,plain,
% 2.13/2.33 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16691, 16688])).
% 2.13/2.33 tff(16704,plain,
% 2.13/2.33 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[16703])).
% 2.13/2.33 tff(16705,plain,
% 2.13/2.33 (~r(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9052, 112, 544, 16670])).
% 2.13/2.33 tff(16706,plain,
% 2.13/2.33 (b(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[901, 16705])).
% 2.13/2.33 tff(16707,plain,
% 2.13/2.33 (b(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16706, 16704])).
% 2.13/2.33 tff(16708,plain,
% 2.13/2.33 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16689])).
% 2.13/2.33 tff(16709,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 2.13/2.33 tff(16710,plain,
% 2.13/2.33 (b(s(elem!1), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[939, 324, 16709])).
% 2.13/2.33 tff(16711,plain,
% 2.13/2.33 (b(s(s(z)), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16710, 16708])).
% 2.13/2.33 tff(16712,plain,
% 2.13/2.33 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16689, 16690])).
% 2.13/2.33 tff(16713,plain,
% 2.13/2.33 (~b(s(elem!1), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[13567, 16661, 16710, 1240, 500])).
% 2.13/2.33 tff(16714,plain,
% 2.13/2.33 (r(s(elem!1), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1521, 16713, 319])).
% 2.13/2.33 tff(16715,plain,
% 2.13/2.33 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16714, 16712])).
% 2.13/2.33 tff(16716,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16620, 16715, 1, 16711, 16688, 500, 16707, 1240])).
% 2.13/2.33 tff(16717,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1294, 16716, 16702])).
% 2.13/2.33 tff(16718,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16717, 16697])).
% 2.13/2.33 tff(16719,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16720,plain,
% 2.13/2.33 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16721,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16720])).
% 2.13/2.33 tff(16722,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16721, 16719])).
% 2.13/2.33 tff(16723,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16724,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16723, 16722])).
% 2.13/2.33 tff(16725,plain,
% 2.13/2.33 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16724, 112, 4569])).
% 2.13/2.33 tff(16726,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16725, 16718])).
% 2.13/2.33 tff(16727,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1337, 68, 1334, 16726])).
% 2.13/2.33 tff(16728,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16729,plain,
% 2.13/2.33 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16730,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16729])).
% 2.13/2.33 tff(16731,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16730, 16728])).
% 2.13/2.33 tff(16732,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16733,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16732, 16731])).
% 2.13/2.33 tff(16734,plain,
% 2.13/2.33 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16733, 112, 4569])).
% 2.13/2.33 tff(16735,plain,
% 2.13/2.33 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16734, 16718])).
% 2.13/2.33 tff(16736,plain,
% 2.13/2.33 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4410, 68, 16735])).
% 2.13/2.33 tff(16737,plain,
% 2.13/2.33 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16736, 4407])).
% 2.13/2.33 tff(16738,plain,
% 2.13/2.33 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[12167, 224, 16737, 16727])).
% 2.13/2.33 tff(16739,plain,
% 2.13/2.33 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16738, 16694])).
% 2.13/2.33 tff(16740,plain,
% 2.13/2.33 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10192, 16688])).
% 2.13/2.33 tff(16741,plain,
% 2.13/2.33 (s(s(z)) = s(elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[16689])).
% 2.13/2.33 tff(16742,plain,
% 2.13/2.33 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16741])).
% 2.13/2.33 tff(16743,plain,
% 2.13/2.33 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.13/2.33 inference(symmetry,[status(thm)],[16742])).
% 2.13/2.33 tff(16744,plain,
% 2.13/2.33 (b(s(s(z)), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[500, 16743])).
% 2.13/2.33 tff(16745,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16746,plain,
% 2.13/2.33 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16747,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16746])).
% 2.13/2.33 tff(16748,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16747, 16745])).
% 2.13/2.33 tff(16749,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16750,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16749, 16748])).
% 2.13/2.33 tff(16751,plain,
% 2.13/2.33 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16750, 224, 16737, 16727, 16744])).
% 2.13/2.33 tff(16752,plain,
% 2.13/2.33 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7787, 16688])).
% 2.13/2.33 tff(16753,plain,
% 2.13/2.33 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16617, 68, 16752, 16751])).
% 2.13/2.33 tff(16754,plain,
% 2.13/2.33 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5413, 16753, 16715])).
% 2.13/2.33 tff(16755,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5424, 68, 16754, 16740, 16739])).
% 2.13/2.33 tff(16756,plain,((s(elem!1) = elem!1) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | b(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(16757,plain,
% 2.13/2.33 (r(s(elem!1), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16756, 16658, 9147, 1, 303, 16652, 1240, 3, 16650, 16582])).
% 2.13/2.33 tff(16758,plain,
% 2.13/2.33 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10270, 16757, 16622])).
% 2.13/2.33 tff(16759,plain,
% 2.13/2.33 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1869, 16758, 16635])).
% 2.13/2.33 tff(16760,plain,
% 2.13/2.33 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16759, 16634])).
% 2.13/2.33 tff(16761,plain,
% 2.13/2.33 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[15934, 112, 16522, 16623])).
% 2.13/2.33 tff(16762,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16761, 16010])).
% 2.13/2.33 tff(16763,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1338, 16762])).
% 2.13/2.33 tff(16764,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16763, 16008])).
% 2.13/2.33 tff(16765,plain,
% 2.13/2.33 (b(s(s(z)), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[281, 16520])).
% 2.13/2.33 tff(16766,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3480, 224, 16765, 16764, 16760, 16633])).
% 2.13/2.33 tff(16767,plain,(b(z, s(z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(16768,plain,
% 2.13/2.33 (b(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16767, 1, 306, 1240, 3, 7672, 685, 689, 1090, 2597])).
% 2.13/2.33 tff(16769,plain,
% 2.13/2.33 (b(z, s(z)) <=> b(z, elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.33 tff(16770,plain,
% 2.13/2.33 (b(z, elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16768, 16769])).
% 2.13/2.33 tff(16771,plain,
% 2.13/2.33 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3407, 16770, 16637, 1240])).
% 2.13/2.33 tff(16772,plain,
% 2.13/2.33 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.33 tff(16773,plain,
% 2.13/2.33 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[16772])).
% 2.13/2.33 tff(16774,plain,
% 2.13/2.33 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.33 tff(16775,plain,
% 2.13/2.33 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.33 tff(16776,plain,
% 2.13/2.33 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.33 inference(transitivity,[status(thm)],[16775, 16774, 16773])).
% 2.13/2.33 tff(16777,plain,
% 2.13/2.33 (~b(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1249, 16768, 1240, 1])).
% 2.13/2.33 tff(16778,plain,
% 2.13/2.33 (r(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[901, 16777])).
% 2.13/2.33 tff(16779,plain,
% 2.13/2.33 (r(s(s(elem!1)), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16778, 16776])).
% 2.13/2.33 tff(16780,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.33 tff(16781,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16780, 15909])).
% 2.13/2.33 tff(16782,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1884, 16781])).
% 2.13/2.33 tff(16783,plain,
% 2.13/2.33 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16782, 15907])).
% 2.13/2.33 tff(16784,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16785,plain,
% 2.13/2.33 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(16786,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16785])).
% 2.13/2.33 tff(16787,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[16786, 16784])).
% 2.13/2.33 tff(16788,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(16789,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16788, 16787])).
% 2.13/2.33 tff(16790,plain,
% 2.13/2.33 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[16789, 112, 689, 16783])).
% 2.13/2.33 tff(16791,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16790, 16010])).
% 2.13/2.33 tff(16792,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1338, 16791])).
% 2.13/2.33 tff(16793,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16792, 16008])).
% 2.13/2.33 tff(16794,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.33 tff(16795,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.33 inference(symmetry,[status(thm)],[16794])).
% 2.13/2.33 tff(16796,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[15908, 16795])).
% 2.13/2.33 tff(16797,plain,
% 2.13/2.33 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[16796])).
% 2.13/2.33 tff(16798,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[16780, 16797])).
% 2.13/2.33 tff(16799,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4920, 16798, 1181, 15926])).
% 2.13/2.34 tff(16800,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16799, 15913])).
% 2.13/2.34 tff(16801,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16800, 15912])).
% 2.13/2.34 tff(16802,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16803,plain,
% 2.13/2.34 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16804,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16803])).
% 2.13/2.34 tff(16805,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16804, 16802])).
% 2.13/2.34 tff(16806,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(16807,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16806, 16805])).
% 2.13/2.34 tff(16808,plain,
% 2.13/2.34 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16807, 224, 405, 344])).
% 2.13/2.34 tff(16809,plain,
% 2.13/2.34 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16808, 16801])).
% 2.13/2.34 tff(16810,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16809, 16793])).
% 2.13/2.34 tff(16811,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16812,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16811, 16637, 306, 16770, 689, 16779])).
% 2.13/2.34 tff(16813,plain,
% 2.13/2.34 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15910])).
% 2.13/2.34 tff(16814,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[16813])).
% 2.13/2.34 tff(16815,plain,
% 2.13/2.34 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1407, 15926])).
% 2.13/2.34 tff(16816,plain,
% 2.13/2.34 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15910, 15904])).
% 2.13/2.34 tff(16817,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[16816])).
% 2.13/2.34 tff(16818,plain,
% 2.13/2.34 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15910])).
% 2.13/2.34 tff(16819,plain,
% 2.13/2.34 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16818, 16817])).
% 2.13/2.34 tff(16820,plain,
% 2.13/2.34 ((~b(elem!1, s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16819])).
% 2.13/2.34 tff(16821,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.34 tff(16822,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, 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))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16823,plain,
% 2.13/2.34 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, 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))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16824,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, 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)))))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16823])).
% 2.13/2.34 tff(16825,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, 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))))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16824, 16822])).
% 2.13/2.34 tff(16826,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(16827,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, 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)))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16826, 16825])).
% 2.13/2.34 tff(16828,plain,
% 2.13/2.34 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16827, 224, 405, 685, 7672, 16821])).
% 2.13/2.34 tff(16829,plain,
% 2.13/2.34 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16828, 16820])).
% 2.13/2.34 tff(16830,plain,
% 2.13/2.34 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1439, 16829, 16815])).
% 2.13/2.34 tff(16831,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[8812, 16830, 15900])).
% 2.13/2.34 tff(16832,plain,
% 2.13/2.34 (r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16831, 16814])).
% 2.13/2.34 tff(16833,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.34 inference(symmetry,[status(thm)],[15936])).
% 2.13/2.34 tff(16834,plain,
% 2.13/2.34 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16833])).
% 2.13/2.34 tff(16835,plain,
% 2.13/2.34 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15915])).
% 2.13/2.34 tff(16836,plain,
% 2.13/2.34 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.13/2.34 inference(symmetry,[status(thm)],[16835])).
% 2.13/2.34 tff(16837,plain,
% 2.13/2.34 ((~b(elem!1, s(s(z)))) <=> (~b(elem!1, s(elem!1)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16836])).
% 2.13/2.34 tff(16838,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16839,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(16840,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16839, 16838])).
% 2.13/2.34 tff(16841,plain,
% 2.13/2.34 (~b(elem!1, s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16840, 224, 405, 2212, 685, 7672])).
% 2.13/2.34 tff(16842,plain,
% 2.13/2.34 (~b(elem!1, s(elem!1))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16841, 16837])).
% 2.13/2.34 tff(16843,plain,
% 2.13/2.34 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[541, 16842, 3, 354])).
% 2.13/2.34 tff(16844,plain,
% 2.13/2.34 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16648, 16843, 306])).
% 2.13/2.34 tff(16845,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16846,plain,
% 2.13/2.34 (((~b(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(z)))) | (~b(s(s(s(s(s(z))))), 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(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16847,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16846])).
% 2.13/2.34 tff(16848,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16847, 16845])).
% 2.13/2.34 tff(16849,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(16850,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16849, 16848])).
% 2.13/2.34 tff(16851,plain,
% 2.13/2.34 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16850, 224, 2212, 16821, 16844])).
% 2.13/2.34 tff(16852,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16851, 16834])).
% 2.13/2.34 tff(16853,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1345, 16852, 15937])).
% 2.13/2.34 tff(16854,plain,
% 2.13/2.34 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[8351, 16853, 15900])).
% 2.13/2.34 tff(16855,plain,
% 2.13/2.34 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(s(z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16524])).
% 2.13/2.34 tff(16856,plain,
% 2.13/2.34 (~(elem!1 = s(s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[210, 16855])).
% 2.13/2.34 tff(16857,plain,
% 2.13/2.34 (r(elem!1, s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2874, 16841, 16856])).
% 2.13/2.34 tff(16858,plain,
% 2.13/2.34 (((~![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(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16859,plain,
% 2.13/2.34 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(16860,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16859])).
% 2.13/2.34 tff(16861,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16860, 16858])).
% 2.13/2.34 tff(16862,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(16863,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16862, 16861])).
% 2.13/2.34 tff(16864,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16863, 112, 16857, 16854, 16832])).
% 2.13/2.34 tff(16865,plain,((~b(s(s(z)), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16866,plain,
% 2.13/2.34 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16865, 16812, 306, 3, 16771, 16637, 685, 7672])).
% 2.13/2.34 tff(16867,plain,
% 2.13/2.34 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[249, 16866])).
% 2.13/2.34 tff(16868,plain,
% 2.13/2.34 (~r(s(s(z)), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3455, 16867, 689])).
% 2.13/2.34 tff(16869,plain,
% 2.13/2.34 (b(s(s(z)), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[281, 16868])).
% 2.13/2.34 tff(16870,plain,
% 2.13/2.34 (r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16778, 16775])).
% 2.13/2.34 tff(16871,plain,
% 2.13/2.34 (~r(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3196, 16867, 16870])).
% 2.13/2.34 tff(16872,plain,
% 2.13/2.34 (b(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2726, 16871])).
% 2.13/2.34 tff(16873,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2846, 16872, 16869, 1, 16768])).
% 2.13/2.34 tff(16874,plain,((~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16875,plain,
% 2.13/2.34 (r(elem!1, s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16874, 16504, 1, 16247, 16480, 16497, 16487, 16501, 16502])).
% 2.13/2.34 tff(16876,plain,
% 2.13/2.34 (~r(z, s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3631, 16875, 16492])).
% 2.13/2.34 tff(16877,plain,
% 2.13/2.34 (b(z, s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[752, 16876])).
% 2.13/2.34 tff(16878,plain,
% 2.13/2.34 (~b(elem!1, s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[613, 16877, 16487, 16486])).
% 2.13/2.34 tff(16879,plain,
% 2.13/2.34 (~b(elem!1, s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16878, 16482])).
% 2.13/2.34 tff(16880,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16502, 16879])).
% 2.13/2.34 tff(16881,plain,((~b(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16882,plain,
% 2.13/2.34 (~b(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16881, 4538])).
% 2.13/2.34 tff(16883,plain,
% 2.13/2.34 (r(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[194, 16882])).
% 2.13/2.34 tff(16884,plain,
% 2.13/2.34 (r(s(s(z)), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[281, 278])).
% 2.13/2.34 tff(16885,plain,
% 2.13/2.34 (~b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3472, 689, 179, 268, 1090])).
% 2.13/2.34 tff(16886,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[925, 5753, 16885])).
% 2.13/2.34 tff(16887,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16888,plain,
% 2.13/2.34 (~r(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16887, 16884, 179, 4569, 1090])).
% 2.13/2.34 tff(16889,plain,
% 2.13/2.34 (b(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[100, 16888])).
% 2.13/2.34 tff(16890,plain,
% 2.13/2.34 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.34 tff(16891,plain,
% 2.13/2.34 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 2.13/2.34 inference(transitivity,[status(thm)],[16890, 320])).
% 2.13/2.34 tff(16892,plain,
% 2.13/2.34 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 2.13/2.34 inference(symmetry,[status(thm)],[16891])).
% 2.13/2.34 tff(16893,plain,
% 2.13/2.34 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16892])).
% 2.13/2.34 tff(16894,plain,
% 2.13/2.34 (~(s(elem!1) = s(z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[2618, 16893])).
% 2.13/2.34 tff(16895,plain,
% 2.13/2.34 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[79])).
% 2.13/2.34 tff(16896,plain,
% 2.13/2.34 (b(s(s(z)), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[500, 16895])).
% 2.13/2.34 tff(16897,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[278, 16896])).
% 2.13/2.34 tff(16898,plain,((~b(s(elem!1), z)) | b(s(s(z)), z) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16899,plain,
% 2.13/2.34 (~b(s(elem!1), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16898, 278, 15900])).
% 2.13/2.34 tff(16900,plain,
% 2.13/2.34 (r(s(elem!1), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[498, 16899])).
% 2.13/2.34 tff(16901,plain,
% 2.13/2.34 (~r(s(s(elem!1)), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[12361, 16900, 179, 523, 16894])).
% 2.13/2.34 tff(16902,plain,
% 2.13/2.34 (b(s(s(elem!1)), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[593, 16901])).
% 2.13/2.34 tff(16903,plain,
% 2.13/2.34 (b(s(s(s(z))), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16902, 9140])).
% 2.13/2.34 tff(16904,plain,
% 2.13/2.34 (r(s(z), z) <=> r(elem!1, z)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.34 tff(16905,plain,
% 2.13/2.34 (r(elem!1, z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[179, 16904])).
% 2.13/2.34 tff(16906,plain,
% 2.13/2.34 (~r(elem!1, s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[4310, 16900, 16905])).
% 2.13/2.34 tff(16907,plain,
% 2.13/2.34 (b(elem!1, s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[515, 16906, 2618])).
% 2.13/2.34 tff(16908,plain,
% 2.13/2.34 (~r(s(elem!1), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2694, 16900, 16905])).
% 2.13/2.34 tff(16909,plain,
% 2.13/2.34 (b(s(elem!1), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[939, 16908, 324])).
% 2.13/2.34 tff(16910,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 2.13/2.34 tff(16911,plain,
% 2.13/2.34 (s(s(s(s(z)))) = elem!1),
% 2.13/2.34 inference(symmetry,[status(thm)],[16910])).
% 2.13/2.34 tff(16912,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9205, 16911])).
% 2.13/2.34 tff(16913,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16914,plain,
% 2.13/2.34 (~(elem!1 = s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16913, 15969])).
% 2.13/2.34 tff(16915,plain,
% 2.13/2.34 (~r(s(z), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9974, 16884, 179])).
% 2.13/2.34 tff(16916,plain,
% 2.13/2.34 (b(s(z), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1071, 16915])).
% 2.13/2.34 tff(16917,plain,
% 2.13/2.34 (~r(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6167, 16884, 4569])).
% 2.13/2.34 tff(16918,plain,
% 2.13/2.34 (b(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2726, 16917])).
% 2.13/2.34 tff(16919,plain,
% 2.13/2.34 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.34 tff(16920,plain,
% 2.13/2.34 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.34 inference(symmetry,[status(thm)],[16919])).
% 2.13/2.34 tff(16921,plain,
% 2.13/2.34 (b(elem!1, s(s(elem!1)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[15957, 16920])).
% 2.13/2.34 tff(16922,plain,
% 2.13/2.34 (~r(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9251, 2274, 688, 7672, 4569, 6255])).
% 2.13/2.34 tff(16923,plain,
% 2.13/2.34 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[16773])).
% 2.13/2.34 tff(16924,plain,
% 2.13/2.34 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[2932, 16923])).
% 2.13/2.34 tff(16925,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1181, 16924])).
% 2.13/2.34 tff(16926,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(16927,plain,
% 2.13/2.34 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16926, 16922, 306])).
% 2.13/2.34 tff(16928,plain,
% 2.13/2.34 (b(s(s(elem!1)), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[360, 16927, 355])).
% 2.13/2.34 tff(16929,plain,
% 2.13/2.34 (~b(s(s(elem!1)), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1496, 16928, 1488, 501])).
% 2.13/2.34 tff(16930,plain,
% 2.13/2.34 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[530, 16929, 2505])).
% 2.13/2.34 tff(16931,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7481, 16930, 2287, 682, 1488, 15937, 16928, 501])).
% 2.13/2.34 tff(16932,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1294, 16931, 15926])).
% 2.13/2.34 tff(16933,plain,
% 2.13/2.34 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[16932, 15925])).
% 2.13/2.34 tff(16934,plain,
% 2.13/2.34 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[15934, 112, 688, 16933])).
% 2.13/2.34 tff(16935,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[16239, 15988])).
% 2.13/2.34 tff(16936,plain,
% 2.13/2.35 (~r(z, s(s(s(s(s(z))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16629, 112, 688, 16933])).
% 2.13/2.35 tff(16937,plain,
% 2.13/2.35 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16936, 16508])).
% 2.13/2.35 tff(16938,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(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(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16939,plain,
% 2.13/2.35 (((~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(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16940,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16939])).
% 2.13/2.35 tff(16941,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[16940, 16938])).
% 2.13/2.35 tff(16942,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16943,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16942, 16941])).
% 2.13/2.35 tff(16944,plain,
% 2.13/2.35 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16943, 112, 2274, 16933])).
% 2.13/2.35 tff(16945,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8869, 68, 15901, 16944])).
% 2.13/2.35 tff(16946,assumption,(~r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.13/2.35 tff(16947,plain,
% 2.13/2.35 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4412, 16946])).
% 2.13/2.35 tff(16948,plain,
% 2.13/2.35 (b(z, s(s(s(s(s(z))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16947, 16505])).
% 2.13/2.35 tff(16949,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.13/2.35 tff(16950,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 16949])).
% 2.13/2.35 tff(16951,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16952,plain,
% 2.13/2.35 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16953,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16952])).
% 2.13/2.35 tff(16954,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[16953, 16951])).
% 2.13/2.35 tff(16955,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16956,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16955, 16954])).
% 2.13/2.35 tff(16957,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16956, 224, 16950, 14657, 16948, 12996])).
% 2.13/2.35 tff(16958,plain,(r(z, s(s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~(s(s(elem!1)) = s(s(s(z))))) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(16959,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16958, 16945, 16937, 16935, 306, 16934])).
% 2.13/2.35 tff(16960,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(16961,plain,
% 2.13/2.35 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16960, 16909, 688, 2287, 16921, 306, 16907, 1923, 355, 16903, 4569, 16889])).
% 2.13/2.35 tff(16962,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3183, 16961, 15969])).
% 2.13/2.35 tff(16963,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8884, 16962, 15900])).
% 2.13/2.35 tff(16964,plain,
% 2.13/2.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[5196, 16963, 16918, 16916])).
% 2.13/2.35 tff(16965,plain,
% 2.13/2.35 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[6185, 16964])).
% 2.13/2.35 tff(16966,plain,
% 2.13/2.35 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11651, 112, 3523, 6075])).
% 2.13/2.35 tff(16967,plain,
% 2.13/2.35 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3252, 16966])).
% 2.13/2.35 tff(16968,plain,
% 2.13/2.35 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16969,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16968])).
% 2.13/2.35 tff(16970,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[16969, 8895])).
% 2.13/2.35 tff(16971,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16972,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16971, 16970])).
% 2.13/2.35 tff(16973,plain,
% 2.13/2.35 (~b(s(s(s(s(z)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16972, 224, 6255, 7672, 16967])).
% 2.13/2.35 tff(16974,plain,
% 2.13/2.35 (r(s(s(s(s(z)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 16973])).
% 2.13/2.35 tff(16975,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16976,plain,
% 2.13/2.35 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16977,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16976])).
% 2.13/2.35 tff(16978,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[16977, 16975])).
% 2.13/2.35 tff(16979,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16980,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16979, 16978])).
% 2.13/2.35 tff(16981,plain,
% 2.13/2.35 (~r(elem!1, s(s(s(s(z)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16980, 112, 363, 16974])).
% 2.13/2.35 tff(16982,plain,
% 2.13/2.35 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.13/2.35 inference(commutativity,[status(thm)],[])).
% 2.13/2.35 tff(16983,plain,
% 2.13/2.35 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.13/2.35 inference(symmetry,[status(thm)],[16982])).
% 2.13/2.35 tff(16984,plain,
% 2.13/2.35 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16983])).
% 2.13/2.35 tff(16985,plain,
% 2.13/2.35 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[3246, 16984])).
% 2.13/2.35 tff(16986,plain,
% 2.13/2.35 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11674, 112, 3523, 6075])).
% 2.13/2.35 tff(16987,plain,
% 2.13/2.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16988,plain,
% 2.13/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16989,plain,
% 2.13/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16988, 16987])).
% 2.13/2.35 tff(16990,plain,
% 2.13/2.35 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16989, 68, 16986])).
% 2.13/2.35 tff(16991,plain,
% 2.13/2.35 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16990, 16985])).
% 2.13/2.35 tff(16992,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16993,plain,
% 2.13/2.35 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(16994,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[16993])).
% 2.13/2.35 tff(16995,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[16994, 16992])).
% 2.13/2.35 tff(16996,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(16997,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[16996, 16995])).
% 2.13/2.35 tff(16998,plain,
% 2.13/2.35 (~b(elem!1, s(s(s(s(z)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16997, 224, 685, 16967, 16991])).
% 2.13/2.35 tff(16999,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 2.13/2.35 tff(17000,plain,
% 2.13/2.35 (((~![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))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(17001,plain,
% 2.13/2.35 ((~![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))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(17002,plain,
% 2.13/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[17001, 17000])).
% 2.13/2.35 tff(17003,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[17002, 68, 16999, 16998, 16981])).
% 2.13/2.35 tff(17004,plain,((~r(s(s(s(z))), s(s(z)))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(17005,plain,
% 2.13/2.35 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[17004, 16965, 16903, 16914, 16905, 16889, 15957])).
% 2.13/2.35 tff(17006,plain,
% 2.13/2.35 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8303, 17005, 15900])).
% 2.13/2.35 tff(17007,plain,
% 2.13/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[530, 17006, 1923])).
% 2.13/2.35 tff(17008,plain,
% 2.13/2.35 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1496, 17007, 16909, 16907])).
% 2.13/2.35 tff(17009,plain,
% 2.13/2.35 (r(s(s(elem!1)), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[360, 17008, 355])).
% 2.13/2.35 tff(17010,plain,
% 2.13/2.35 (r(s(s(s(z))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[16926, 17009, 306])).
% 2.13/2.35 tff(17011,plain,
% 2.13/2.35 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.35 inference(symmetry,[status(thm)],[15908])).
% 2.13/2.35 tff(17012,plain,
% 2.13/2.35 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[15906])).
% 2.13/2.35 tff(17013,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.13/2.35 tff(17014,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), 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(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(17015,plain,
% 2.13/2.35 (((~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(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(17016,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[17015])).
% 2.13/2.35 tff(17017,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17016, 17014])).
% 2.13/2.36 tff(17018,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(17019,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17018, 17017])).
% 2.13/2.36 tff(17020,plain,
% 2.13/2.36 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17019, 112, 690])).
% 2.13/2.36 tff(17021,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17020, 17013])).
% 2.13/2.36 tff(17022,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17021, 17012])).
% 2.13/2.36 tff(17023,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1884, 17022])).
% 2.13/2.36 tff(17024,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17023, 17011])).
% 2.13/2.36 tff(17025,plain,
% 2.13/2.36 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15934, 112, 688])).
% 2.13/2.36 tff(17026,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17025, 17013])).
% 2.13/2.36 tff(17027,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17026, 16010])).
% 2.13/2.36 tff(17028,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1338, 17027])).
% 2.13/2.36 tff(17029,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17028, 16008])).
% 2.13/2.36 tff(17030,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8104, 224, 6255, 7672, 17029, 17024])).
% 2.13/2.36 tff(17031,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(17032,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17031, 17010, 16903, 306, 688, 16889])).
% 2.13/2.36 tff(17033,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[1798, 15925])).
% 2.13/2.36 tff(17034,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.13/2.36 tff(17035,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17034, 17033])).
% 2.13/2.36 tff(17036,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(s(s(s(s(z))))), elem!1) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(17037,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17036, 17032, 306])).
% 2.13/2.36 tff(17038,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1294, 17037, 15926])).
% 2.13/2.36 tff(17039,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17038, 15913])).
% 2.13/2.36 tff(17040,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17039, 15912])).
% 2.13/2.36 tff(17041,plain,
% 2.13/2.36 (b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7872, 16909, 15899])).
% 2.13/2.36 tff(17042,plain,
% 2.13/2.36 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.36 tff(17043,plain,
% 2.13/2.36 (b(elem!1, s(s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[16916, 17042])).
% 2.13/2.36 tff(17044,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17045,plain,
% 2.13/2.36 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17046,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[17045])).
% 2.13/2.36 tff(17047,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17046, 17044])).
% 2.13/2.36 tff(17048,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(17049,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17048, 17047])).
% 2.13/2.36 tff(17050,plain,
% 2.13/2.36 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17049, 224, 17043, 17041])).
% 2.13/2.36 tff(17051,plain,
% 2.13/2.36 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17050, 17040])).
% 2.13/2.36 tff(17052,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17051, 16834])).
% 2.13/2.36 tff(17053,plain,
% 2.13/2.36 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1345, 17052, 15937])).
% 2.13/2.36 tff(17054,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8351, 17053, 15900])).
% 2.13/2.36 tff(17055,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8096, 17054, 15900, 16884])).
% 2.13/2.36 tff(17056,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1338, 17055])).
% 2.13/2.36 tff(17057,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17056, 16008])).
% 2.13/2.36 tff(17058,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17059,plain,
% 2.13/2.36 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~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))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17060,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[17059])).
% 2.13/2.36 tff(17061,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17060, 17058])).
% 2.13/2.36 tff(17062,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(17063,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17062, 17061])).
% 2.13/2.36 tff(17064,plain,
% 2.13/2.36 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17063, 224, 15957, 16903, 17057, 17040])).
% 2.13/2.36 tff(17065,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17064, 15909])).
% 2.13/2.36 tff(17066,plain,
% 2.13/2.36 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1884, 17065])).
% 2.13/2.36 tff(17067,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17066, 15907])).
% 2.13/2.36 tff(17068,plain,
% 2.13/2.36 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[15915])).
% 2.13/2.36 tff(17069,plain,
% 2.13/2.36 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.36 tff(17070,plain,
% 2.13/2.36 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17069, 17068])).
% 2.13/2.36 tff(17071,plain,
% 2.13/2.36 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[17070])).
% 2.13/2.36 tff(17072,plain,
% 2.13/2.36 (~b(s(elem!1), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3570, 17007, 16921, 16907])).
% 2.13/2.36 tff(17073,plain,
% 2.13/2.36 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17072, 17071])).
% 2.13/2.36 tff(17074,plain,
% 2.13/2.36 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[249, 17073])).
% 2.13/2.36 tff(17075,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(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(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))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17076,plain,
% 2.13/2.36 (((~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(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))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17077,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(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(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)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[17076])).
% 2.13/2.36 tff(17078,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(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(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))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17077, 17075])).
% 2.13/2.36 tff(17079,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(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)))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(17080,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17079, 17078])).
% 2.13/2.36 tff(17081,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17080, 112, 17074, 17054, 17067])).
% 2.13/2.36 tff(17082,plain,(b(s(s(z)), z) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (s(elem!1) = elem!1) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(17083,plain,
% 2.13/2.36 (b(s(s(z)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17082, 15831, 15882, 353, 7240, 15875, 16883, 15856, 303, 319])).
% 2.13/2.36 tff(17084,plain,
% 2.13/2.36 (~r(s(z), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[187, 177, 179])).
% 2.13/2.36 tff(17085,plain,
% 2.13/2.36 (b(s(z), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[175, 17084])).
% 2.13/2.36 tff(17086,plain,
% 2.13/2.36 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.36 tff(17087,plain,
% 2.13/2.36 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.13/2.36 inference(symmetry,[status(thm)],[17086])).
% 2.13/2.36 tff(17088,plain,
% 2.13/2.36 (r(s(s(elem!1)), z)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[177, 17087])).
% 2.13/2.36 tff(17089,plain,
% 2.13/2.36 (~r(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[12361, 17088, 179, 523, 16894])).
% 2.13/2.36 tff(17090,plain,
% 2.13/2.36 (b(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[498, 17089])).
% 2.13/2.36 tff(17091,plain,
% 2.13/2.36 (b(s(s(z)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[16898, 17090, 15900])).
% 2.13/2.36 tff(17092,plain,
% 2.13/2.36 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.36 tff(17093,plain,
% 2.13/2.36 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.36 inference(symmetry,[status(thm)],[17092])).
% 2.13/2.36 tff(17094,plain,
% 2.13/2.36 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[15899])).
% 2.13/2.36 tff(17095,plain,
% 2.13/2.36 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.36 inference(transitivity,[status(thm)],[17094, 17093])).
% 2.13/2.36 tff(17096,plain,
% 2.13/2.36 (b(s(s(elem!1)), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[560, 17095])).
% 2.13/2.36 tff(17097,plain,
% 2.13/2.36 (~r(z, s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2621, 17088, 688, 16905, 17096, 1923, 324])).
% 2.13/2.36 tff(17098,plain,
% 2.13/2.36 (b(z, s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[625, 17097])).
% 2.13/2.36 tff(17099,plain,
% 2.13/2.36 (b(z, s(s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17098, 15921])).
% 2.13/2.36 tff(17100,plain,
% 2.13/2.36 (b(elem!1, s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15956, 17085, 15899])).
% 2.13/2.36 tff(17101,plain,
% 2.13/2.36 (b(elem!1, s(s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17100, 16920])).
% 2.13/2.36 tff(17102,plain,
% 2.13/2.36 (~r(elem!1, s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[16062, 2274, 1118, 2191, 688])).
% 2.13/2.36 tff(17103,plain,
% 2.13/2.36 (b(elem!1, s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2874, 17102, 16856])).
% 2.13/2.36 tff(17104,plain,
% 2.13/2.36 (b(elem!1, s(elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17103, 16836])).
% 2.13/2.36 tff(17105,plain,
% 2.13/2.36 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[15915])).
% 2.13/2.36 tff(17106,plain,
% 2.13/2.36 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.13/2.36 inference(symmetry,[status(thm)],[17105])).
% 2.13/2.36 tff(17107,plain,
% 2.13/2.36 (~r(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15990, 2274, 2191, 688])).
% 2.13/2.36 tff(17108,plain,
% 2.13/2.36 (b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1135, 17107, 16527])).
% 2.13/2.36 tff(17109,plain,
% 2.13/2.36 (b(s(elem!1), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17108, 17106])).
% 2.13/2.36 tff(17110,plain,
% 2.13/2.36 (~b(s(s(elem!1)), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1496, 17104, 390, 17109])).
% 2.13/2.36 tff(17111,plain,
% 2.13/2.36 (r(s(s(elem!1)), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[530, 17110, 2505])).
% 2.13/2.36 tff(17112,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7481, 17111, 2287, 390, 682, 15937, 17109, 17104])).
% 2.13/2.36 tff(17113,plain,
% 2.13/2.36 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1294, 17112, 15926])).
% 2.13/2.36 tff(17114,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17113, 15925])).
% 2.13/2.36 tff(17115,plain,
% 2.13/2.36 (~r(z, s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[16629, 112, 688, 17114])).
% 2.13/2.36 tff(17116,plain,
% 2.13/2.36 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17115, 16508])).
% 2.13/2.36 tff(17117,plain,
% 2.13/2.36 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[4412, 17116])).
% 2.13/2.36 tff(17118,plain,
% 2.13/2.36 (b(z, s(s(s(s(s(z))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17117, 16505])).
% 2.13/2.36 tff(17119,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[16943, 112, 2274, 17114])).
% 2.13/2.36 tff(17120,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8869, 68, 15901, 17119])).
% 2.13/2.36 tff(17121,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15934, 112, 688, 17114])).
% 2.13/2.36 tff(17122,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 17121])).
% 2.13/2.36 tff(17123,plain,
% 2.13/2.36 (((~b(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))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(17124,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[17123])).
% 2.13/2.36 tff(17125,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[17124, 16951])).
% 2.13/2.36 tff(17126,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(17127,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17126, 17125])).
% 2.13/2.36 tff(17128,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17127, 224, 17122, 17120, 17118, 16935])).
% 2.13/2.36 tff(17129,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(17130,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17129, 17101, 688, 2287, 17096, 306, 1923, 17099, 17091])).
% 2.13/2.36 tff(17131,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3183, 17130, 15969])).
% 2.13/2.36 tff(17132,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8884, 17131, 15900])).
% 2.13/2.36 tff(17133,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1579, 17132, 560, 17085])).
% 2.13/2.36 tff(17134,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3252, 17133])).
% 2.13/2.36 tff(17135,plain,
% 2.13/2.36 (b(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[560, 17094])).
% 2.13/2.36 tff(17136,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[12998, 12996, 1118, 2191])).
% 2.13/2.36 tff(17137,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[6185, 17136])).
% 2.13/2.36 tff(17138,plain,
% 2.13/2.36 (~r(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11263, 17137, 3318])).
% 2.13/2.36 tff(17139,plain,
% 2.13/2.36 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[249, 17138])).
% 2.13/2.36 tff(17140,plain,
% 2.13/2.36 (~b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2412, 17139, 787, 685])).
% 2.13/2.36 tff(17141,plain,
% 2.13/2.36 (~b(s(elem!1), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7872, 17140, 15899])).
% 2.13/2.36 tff(17142,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15949, 17141, 306, 688, 2191, 1118])).
% 2.13/2.36 tff(17143,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17142, 15913])).
% 2.13/2.36 tff(17144,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17143, 15912])).
% 2.13/2.36 tff(17145,plain,
% 2.13/2.36 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[15963, 224, 685, 787])).
% 2.13/2.36 tff(17146,plain,
% 2.13/2.36 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[17145, 17144])).
% 2.13/2.36 tff(17147,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17146, 15909])).
% 2.13/2.36 tff(17148,plain,
% 2.13/2.36 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1884, 17147])).
% 2.13/2.36 tff(17149,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[17148, 15907])).
% 2.13/2.36 tff(17150,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[16019, 17149, 177])).
% 2.13/2.36 tff(17151,plain,
% 2.13/2.36 (((~![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(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(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))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17152,plain,
% 2.13/2.37 (((~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(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))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17153,plain,
% 2.13/2.37 (((~![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(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(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)))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[17152])).
% 2.13/2.37 tff(17154,plain,
% 2.13/2.37 (((~![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(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(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))))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[17153, 17151])).
% 2.13/2.37 tff(17155,plain,
% 2.13/2.37 ((~![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(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))))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(17156,plain,
% 2.13/2.37 ((~![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(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)))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17155, 17154])).
% 2.13/2.37 tff(17157,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17156, 112, 3318, 17149])).
% 2.13/2.37 tff(17158,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8869, 68, 15901, 17157])).
% 2.13/2.37 tff(17159,plain,
% 2.13/2.37 (r(z, s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16958, 17158, 12996, 306, 17150])).
% 2.13/2.37 tff(17160,plain,
% 2.13/2.37 (r(z, s(s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17159, 16506])).
% 2.13/2.37 tff(17161,plain,
% 2.13/2.37 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 17150])).
% 2.13/2.37 tff(17162,plain,
% 2.13/2.37 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17163,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[17162])).
% 2.13/2.37 tff(17164,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[17163, 15941])).
% 2.13/2.37 tff(17165,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(17166,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17165, 17164])).
% 2.13/2.37 tff(17167,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17166, 224, 2191, 1118, 17161])).
% 2.13/2.37 tff(17168,plain,
% 2.13/2.37 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17167, 16834])).
% 2.13/2.37 tff(17169,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1345, 17168, 15937])).
% 2.13/2.37 tff(17170,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8351, 17169, 15900])).
% 2.13/2.37 tff(17171,plain,
% 2.13/2.37 (((~![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(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(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(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17172,plain,
% 2.13/2.37 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17173,plain,
% 2.13/2.37 (((~![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(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[17172])).
% 2.13/2.37 tff(17174,plain,
% 2.13/2.37 (((~![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(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[17173, 17171])).
% 2.13/2.37 tff(17175,plain,
% 2.13/2.37 ((~![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(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(17176,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17175, 17174])).
% 2.13/2.37 tff(17177,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17176, 112, 177, 8010, 3523, 8784])).
% 2.13/2.37 tff(17178,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17179,plain,
% 2.13/2.37 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17178, 17170, 177, 17149])).
% 2.13/2.37 tff(17180,plain,
% 2.13/2.37 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8303, 17179, 15900])).
% 2.13/2.37 tff(17181,plain,
% 2.13/2.37 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[530, 17180, 2505])).
% 2.13/2.37 tff(17182,plain,
% 2.13/2.37 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16648, 17181, 306])).
% 2.13/2.37 tff(17183,plain,
% 2.13/2.37 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17184,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[17183])).
% 2.13/2.37 tff(17185,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[17184, 6353])).
% 2.13/2.37 tff(17186,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(17187,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17186, 17185])).
% 2.13/2.37 tff(17188,plain,
% 2.13/2.37 (~b(z, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17187, 224, 17139, 2191, 17182])).
% 2.13/2.37 tff(17189,plain,
% 2.13/2.37 (r(z, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[100, 17188])).
% 2.13/2.37 tff(17190,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(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(z, s(s(s(s(s(z))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17191,plain,
% 2.13/2.37 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(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(z, s(s(s(s(s(z))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(17192,plain,
% 2.13/2.37 (((~![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(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(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(z, s(s(s(s(s(z)))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[17191])).
% 2.13/2.37 tff(17193,plain,
% 2.13/2.37 (((~![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(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(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(z, s(s(s(s(s(z))))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[17192, 17190])).
% 2.13/2.37 tff(17194,plain,
% 2.13/2.37 ((~![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(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(17195,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17194, 17193])).
% 2.13/2.37 tff(17196,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17195, 112, 17189, 17170, 17149, 17160])).
% 2.13/2.37 tff(17197,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17198,plain,
% 2.13/2.37 (~b(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17197, 17099, 306, 1923, 177, 17091, 17134, 17100, 17135, 688])).
% 2.13/2.37 tff(17199,plain,
% 2.13/2.37 (r(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16239, 17198])).
% 2.13/2.37 tff(17200,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16077, 112, 177, 17199, 17134])).
% 2.13/2.37 tff(17201,plain,((~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17202,plain,
% 2.13/2.37 (~b(s(s(s(z))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17201, 177, 688, 306, 2287, 324, 179, 523])).
% 2.13/2.37 tff(17203,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[925, 17202, 5493])).
% 2.13/2.37 tff(17204,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17205,plain,
% 2.13/2.37 (~r(s(s(s(z))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17204, 15882, 15831, 7240, 303, 16883, 319, 15875])).
% 2.13/2.37 tff(17206,plain,
% 2.13/2.37 (b(s(s(s(z))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[72, 17205])).
% 2.13/2.37 tff(17207,plain,
% 2.13/2.37 (b(s(s(elem!1)), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9144, 7672, 306])).
% 2.13/2.37 tff(17208,plain,
% 2.13/2.37 (~r(s(s(z)), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16887, 689, 179, 4569, 1090])).
% 2.13/2.37 tff(17209,plain,
% 2.13/2.37 (b(s(s(z)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16577, 17208, 7672, 306, 17207, 688, 2505, 689, 1090, 5754, 324])).
% 2.13/2.37 tff(17210,plain,
% 2.13/2.37 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2412, 16441, 17209, 15957])).
% 2.13/2.37 tff(17211,plain,
% 2.13/2.37 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[249, 17210])).
% 2.13/2.37 tff(17212,plain,
% 2.13/2.37 (~r(z, s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1104, 112, 17211, 689])).
% 2.13/2.37 tff(17213,plain,
% 2.13/2.37 (b(z, s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1088, 17212])).
% 2.13/2.37 tff(17214,plain,
% 2.13/2.37 (b(s(s(elem!1)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9708, 689, 688, 362, 4569])).
% 2.13/2.37 tff(17215,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17129, 17213, 688, 2287, 16921, 306, 2505, 1118, 17214])).
% 2.13/2.37 tff(17216,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3183, 17215, 15969])).
% 2.13/2.37 tff(17217,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8884, 17216, 15900])).
% 2.13/2.37 tff(17218,plain,
% 2.13/2.37 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1579, 17217, 1090, 5754])).
% 2.13/2.37 tff(17219,plain,
% 2.13/2.37 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3252, 17218])).
% 2.13/2.37 tff(17220,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16559, 17219, 688, 689])).
% 2.13/2.37 tff(17221,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16239, 17220])).
% 2.13/2.37 tff(17222,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11263, 17219, 17211])).
% 2.13/2.37 tff(17223,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[6185, 17222])).
% 2.13/2.37 tff(17224,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[12998, 17223, 17221, 1118, 17213])).
% 2.13/2.37 tff(17225,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(z))), z)) | (s(elem!1) = elem!1) | (s(s(s(z))) = elem!1) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17226,plain,
% 2.13/2.37 (~r(z, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17225, 17083, 15882, 15856, 7240, 15831, 526, 17206, 303, 15837, 16883, 15875])).
% 2.13/2.37 tff(17227,plain,
% 2.13/2.37 (b(z, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[100, 17226])).
% 2.13/2.37 tff(17228,plain,
% 2.13/2.37 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[15831])).
% 2.13/2.37 tff(17229,plain,
% 2.13/2.37 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.37 inference(symmetry,[status(thm)],[17228])).
% 2.13/2.37 tff(17230,plain,
% 2.13/2.37 (b(elem!1, s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[15956, 15856, 15839])).
% 2.13/2.37 tff(17231,plain,
% 2.13/2.37 (b(elem!1, s(s(elem!1)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17230, 17229])).
% 2.13/2.37 tff(17232,plain,
% 2.13/2.37 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9201, 6255, 1118, 7672])).
% 2.13/2.37 tff(17233,plain,
% 2.13/2.37 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[249, 17232])).
% 2.13/2.37 tff(17234,plain,
% 2.13/2.37 (~r(s(s(z)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9359, 2274, 688, 4569, 17233, 1118])).
% 2.13/2.37 tff(17235,plain,
% 2.13/2.37 (b(s(s(z)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1135, 17234, 16527])).
% 2.13/2.37 tff(17236,plain,
% 2.13/2.37 (b(s(elem!1), elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17235, 17106])).
% 2.13/2.37 tff(17237,plain,
% 2.13/2.37 (~b(elem!1, s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16960, 17236, 688, 2287, 682, 306, 2274, 2505, 355, 7672, 4569, 6255])).
% 2.13/2.37 tff(17238,plain,
% 2.13/2.37 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[15915])).
% 2.13/2.37 tff(17239,plain,
% 2.13/2.37 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[17238])).
% 2.13/2.37 tff(17240,plain,
% 2.13/2.37 (~b(z, s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17129, 16928, 688, 2287, 682, 306, 2505, 1118, 2274])).
% 2.13/2.37 tff(17241,plain,
% 2.13/2.37 (r(z, s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1088, 17240])).
% 2.13/2.37 tff(17242,plain,
% 2.13/2.37 (r(z, s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[17241, 17239])).
% 2.13/2.37 tff(17243,plain,
% 2.13/2.37 (~r(elem!1, s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[16036, 17242, 688])).
% 2.13/2.37 tff(17244,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[515, 17243, 17237, 2506])).
% 2.13/2.37 tff(17245,plain,((~r(s(s(s(s(z)))), elem!1)) | (elem!1 = s(elem!1)) | (~r(z, elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(17246,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[17245, 327, 15882, 7240, 17231, 15831, 526, 353, 17206, 15875, 17227, 17083])).
% 2.13/2.37 tff(17247,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3183, 17246, 15841])).
% 2.13/2.38 tff(17248,plain,
% 2.13/2.38 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9201, 17227, 17083, 17206])).
% 2.13/2.38 tff(17249,plain,
% 2.13/2.38 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[249, 17248])).
% 2.13/2.38 tff(17250,plain,
% 2.13/2.38 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[15831])).
% 2.13/2.38 tff(17251,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17250])).
% 2.13/2.38 tff(17252,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[17251])).
% 2.13/2.38 tff(17253,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17247, 17252])).
% 2.13/2.38 tff(17254,plain,
% 2.13/2.38 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[15884])).
% 2.13/2.38 tff(17255,plain,
% 2.13/2.38 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.13/2.38 inference(symmetry,[status(thm)],[17254])).
% 2.13/2.38 tff(17256,plain,
% 2.13/2.38 (b(s(elem!1), z)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17083, 17255])).
% 2.13/2.38 tff(17257,plain,
% 2.13/2.38 (b(z, s(s(z))) <=> b(z, s(elem!1))),
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% 2.13/2.38 tff(17258,plain,
% 2.13/2.38 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[306])).
% 2.13/2.38 tff(17259,plain,
% 2.13/2.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[17258])).
% 2.13/2.38 tff(17260,plain,
% 2.13/2.38 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17259])).
% 2.13/2.38 tff(17261,plain,
% 2.13/2.38 (~(s(s(z)) = s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[55, 17260])).
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% 2.13/2.38 (~r(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5606, 4061, 688, 9147, 17261])).
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% 2.13/2.38 (b(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1135, 17262, 16527])).
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% 2.13/2.38 (~(elem!1 = s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1306, 15926])).
% 2.13/2.38 tff(17265,plain,
% 2.13/2.38 (~(s(elem!1) = elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[302, 17264])).
% 2.13/2.38 tff(17266,plain,
% 2.13/2.38 (~(elem!1 = s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[326, 17265])).
% 2.13/2.38 tff(17267,plain,
% 2.13/2.38 (r(z, s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[3750, 17239])).
% 2.13/2.38 tff(17268,plain,
% 2.13/2.38 (~r(elem!1, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[604, 17267, 363])).
% 2.13/2.38 tff(17269,plain,
% 2.13/2.38 (b(elem!1, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[515, 17268, 17266])).
% 2.13/2.38 tff(17270,plain,
% 2.13/2.38 (b(elem!1, s(s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17269, 16835])).
% 2.13/2.38 tff(17271,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5280, 224, 17270, 1109, 5274])).
% 2.13/2.38 tff(17272,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 17271])).
% 2.13/2.38 tff(17273,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17274,plain,
% 2.13/2.38 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17275,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17274])).
% 2.13/2.38 tff(17276,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[17275, 17273])).
% 2.13/2.38 tff(17277,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(17278,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17277, 17276])).
% 2.13/2.38 tff(17279,plain,
% 2.13/2.38 (~r(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17278, 112, 688, 3750, 17272])).
% 2.13/2.38 tff(17280,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3147, 68, 2330, 17279])).
% 2.13/2.38 tff(17281,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17282,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(17283,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17282, 17281])).
% 2.13/2.38 tff(17284,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17283, 224, 685, 7672, 5274, 17280])).
% 2.13/2.38 tff(17285,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3252, 17284])).
% 2.13/2.38 tff(17286,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3259, 112, 196, 17285, 17272])).
% 2.13/2.38 tff(17287,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17288,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17287, 17263, 5274, 306, 688, 7672, 685, 196, 16905])).
% 2.13/2.38 tff(17289,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1088, 17288])).
% 2.13/2.38 tff(17290,plain,
% 2.13/2.38 (b(z, s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17289, 17257])).
% 2.13/2.38 tff(17291,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8884, 5274, 15900])).
% 2.13/2.38 tff(17292,plain,
% 2.13/2.38 (b(s(s(z)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[14369, 354, 15899, 16516, 9138])).
% 2.13/2.38 tff(17293,plain,
% 2.13/2.38 (~(s(elem!1) = s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[318, 17264])).
% 2.13/2.38 tff(17294,plain,
% 2.13/2.38 (~r(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4126, 1181, 688, 17293])).
% 2.13/2.38 tff(17295,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[939, 17294, 17265])).
% 2.13/2.38 tff(17296,plain,
% 2.13/2.38 (b(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7872, 17295, 15899])).
% 2.13/2.38 tff(17297,plain,
% 2.13/2.38 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9201, 16531, 7672, 6255])).
% 2.13/2.38 tff(17298,plain,
% 2.13/2.38 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[249, 17297])).
% 2.13/2.38 tff(17299,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17287, 17298, 685, 7672, 5274, 688, 17296, 306, 363])).
% 2.13/2.38 tff(17300,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1088, 17299])).
% 2.13/2.38 tff(17301,plain,
% 2.13/2.38 (b(z, s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17300, 17257])).
% 2.13/2.38 tff(17302,plain,
% 2.13/2.38 (~(s(s(elem!1)) = s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[525, 17293])).
% 2.13/2.38 tff(17303,plain,
% 2.13/2.38 (~r(elem!1, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4322, 17301, 1240, 17302, 363, 1181])).
% 2.13/2.38 tff(17304,plain,
% 2.13/2.38 (b(elem!1, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[515, 17303, 17266])).
% 2.13/2.38 tff(17305,plain,
% 2.13/2.38 (b(elem!1, s(s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17304, 16835])).
% 2.13/2.38 tff(17306,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5280, 224, 17305, 17296, 5274])).
% 2.13/2.38 tff(17307,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3230, 68, 1229, 17306])).
% 2.13/2.38 tff(17308,plain,
% 2.13/2.38 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17004, 17307, 363, 685, 6255, 7672, 16914])).
% 2.13/2.38 tff(17309,plain,
% 2.13/2.38 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8303, 17308, 15900])).
% 2.13/2.38 tff(17310,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[530, 17309, 17302])).
% 2.13/2.38 tff(17311,plain,
% 2.13/2.38 (~b(s(elem!1), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4320, 17310, 1240, 17301])).
% 2.13/2.38 tff(17312,plain,
% 2.13/2.38 (r(s(elem!1), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[498, 17311])).
% 2.13/2.38 tff(17313,plain,
% 2.13/2.38 (r(s(s(z)), z)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17312, 16568])).
% 2.13/2.38 tff(17314,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[279, 17313])).
% 2.13/2.38 tff(17315,plain,(r(s(s(z)), z) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17316,plain,
% 2.13/2.38 (r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17315, 4061, 306, 16905, 17207, 6255, 7672, 5274, 685, 688])).
% 2.13/2.38 tff(17317,plain,
% 2.13/2.38 (~r(s(z), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9974, 17316, 179])).
% 2.13/2.38 tff(17318,plain,
% 2.13/2.38 (b(s(z), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1071, 17317])).
% 2.13/2.38 tff(17319,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5196, 17318, 17292, 17291])).
% 2.13/2.38 tff(17320,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6185, 17319])).
% 2.13/2.38 tff(17321,plain,
% 2.13/2.38 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17004, 17320, 7672, 16914, 16905, 6255, 685])).
% 2.13/2.38 tff(17322,plain,
% 2.13/2.38 (~r(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8303, 17321, 15900])).
% 2.13/2.38 tff(17323,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[530, 17322, 2505])).
% 2.13/2.38 tff(17324,plain,
% 2.13/2.38 (~b(z, s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4320, 17323, 17207, 500])).
% 2.13/2.38 tff(17325,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17324, 17290])).
% 2.13/2.38 tff(17326,plain,(b(s(s(elem!1)), elem!1) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | b(z, s(z)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17327,plain,
% 2.13/2.38 (b(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17326, 15831, 17256, 526, 17206, 17227, 17230, 17247, 15882, 17249, 16883, 15874, 353])).
% 2.13/2.38 tff(17328,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12082, 17327, 17231, 17253])).
% 2.13/2.38 tff(17329,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[7735, 80])).
% 2.13/2.38 tff(17330,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[17329])).
% 2.13/2.38 tff(17331,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[1571, 17330])).
% 2.13/2.38 tff(17332,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3899, 17331])).
% 2.13/2.38 tff(17333,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17334,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17333, 17328, 15840])).
% 2.13/2.38 tff(17335,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3252, 17334])).
% 2.13/2.38 tff(17336,plain,
% 2.13/2.38 (r(s(z), z) <=> r(elem!1, z)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[15839])).
% 2.13/2.38 tff(17337,plain,
% 2.13/2.38 (r(elem!1, z)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[16883, 17336])).
% 2.13/2.38 tff(17338,plain,
% 2.13/2.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11263, 17335, 17249])).
% 2.13/2.38 tff(17339,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6185, 17338])).
% 2.13/2.38 tff(17340,plain,
% 2.13/2.38 (~r(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3758, 3750, 688])).
% 2.13/2.38 tff(17341,plain,
% 2.13/2.38 (~b(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17287, 3750, 5274, 306, 688, 7672, 685, 196, 363])).
% 2.13/2.38 tff(17342,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1135, 17341, 17340, 16527])).
% 2.13/2.38 tff(17343,plain,((~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17344,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17343, 17247, 15831, 15882, 17206, 17230, 17249, 17337])).
% 2.13/2.38 tff(17345,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1088, 17344])).
% 2.13/2.38 tff(17346,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[12998, 17345, 17083, 17339])).
% 2.13/2.38 tff(17347,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[16239, 17346])).
% 2.13/2.38 tff(17348,plain,
% 2.13/2.38 (~r(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[16980, 112, 363, 2276])).
% 2.13/2.38 tff(17349,plain,
% 2.13/2.38 (b(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17002, 68, 16914, 17348])).
% 2.13/2.38 tff(17350,plain,
% 2.13/2.38 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[5537])).
% 2.13/2.38 tff(17351,plain,
% 2.13/2.38 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17350])).
% 2.13/2.38 tff(17352,plain,
% 2.13/2.38 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[1229, 17351])).
% 2.13/2.38 tff(17353,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17354,plain,
% 2.13/2.38 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17355,plain,
% 2.13/2.38 (((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17354])).
% 2.13/2.38 tff(17356,plain,
% 2.13/2.38 (((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[17355, 17353])).
% 2.13/2.38 tff(17357,plain,
% 2.13/2.38 ((~![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(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(17358,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17357, 17356])).
% 2.13/2.38 tff(17359,plain,
% 2.13/2.38 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17358, 112, 196, 3318])).
% 2.13/2.38 tff(17360,plain,
% 2.13/2.38 (((~![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))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17361,plain,
% 2.13/2.38 ((~![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))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(17362,plain,
% 2.13/2.38 ((~![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)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17361, 17360])).
% 2.13/2.38 tff(17363,plain,
% 2.13/2.38 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17362, 68, 17359])).
% 2.13/2.38 tff(17364,plain,
% 2.13/2.38 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17363, 17352])).
% 2.13/2.38 tff(17365,plain,
% 2.13/2.38 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[15903])).
% 2.13/2.38 tff(17366,plain,
% 2.13/2.38 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[15914])).
% 2.13/2.38 tff(17367,plain,
% 2.13/2.38 (s(s(z)) = s(elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[32, 17366, 123])).
% 2.13/2.38 tff(17368,plain,
% 2.13/2.38 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17367, 17365])).
% 2.13/2.38 tff(17369,plain,
% 2.13/2.38 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17368])).
% 2.13/2.38 tff(17370,plain,
% 2.13/2.38 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17359, 17369])).
% 2.13/2.38 tff(17371,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[15913])).
% 2.13/2.38 tff(17372,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[15911, 17371])).
% 2.13/2.38 tff(17373,plain,
% 2.13/2.38 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17372])).
% 2.13/2.38 tff(17374,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.13/2.38 tff(17375,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17145, 17374])).
% 2.13/2.38 tff(17376,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17375, 15909])).
% 2.13/2.38 tff(17377,plain,
% 2.13/2.38 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1884, 17376])).
% 2.13/2.38 tff(17378,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17377, 15907])).
% 2.13/2.38 tff(17379,plain,
% 2.13/2.38 (((~![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)))), 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(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))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17380,plain,
% 2.13/2.38 (((~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)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), 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))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(17381,plain,
% 2.13/2.38 (((~![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(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))), 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)))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[17380])).
% 2.13/2.38 tff(17382,plain,
% 2.13/2.38 (((~![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(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))), 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))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[17381, 17379])).
% 2.13/2.38 tff(17383,plain,
% 2.13/2.38 ((~![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(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(17384,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17383, 17382])).
% 2.13/2.38 tff(17385,plain,
% 2.13/2.38 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17384, 112, 2276, 3318, 17378])).
% 2.13/2.38 tff(17386,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 2.13/2.38 tff(17387,plain,
% 2.13/2.38 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[17386])).
% 2.13/2.38 tff(17388,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8866, 17387])).
% 2.13/2.38 tff(17389,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(17390,plain,
% 2.13/2.38 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17389, 15901])).
% 2.13/2.38 tff(17391,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[16005, 68, 17390, 17385])).
% 2.13/2.38 tff(17392,plain,
% 2.13/2.38 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[17080, 112, 196, 17378])).
% 2.13/2.38 tff(17393,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8351, 17392, 15900])).
% 2.13/2.38 tff(17394,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1345, 17393, 15937])).
% 2.13/2.38 tff(17395,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[17394, 15936])).
% 2.13/2.39 tff(17396,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17397,plain,
% 2.13/2.39 (((~b(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(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(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))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17398,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17397])).
% 2.13/2.39 tff(17399,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[17398, 17396])).
% 2.13/2.39 tff(17400,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(17401,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17400, 17399])).
% 2.13/2.39 tff(17402,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17401, 224, 11881, 17395, 17374, 17391, 17349])).
% 2.13/2.39 tff(17403,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17404,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17403, 2276, 306, 3318, 196, 363, 685, 787])).
% 2.13/2.39 tff(17405,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17404, 17373])).
% 2.13/2.39 tff(17406,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1294, 17405, 15926])).
% 2.13/2.39 tff(17407,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9092, 112, 1798, 4569, 688])).
% 2.13/2.39 tff(17408,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1338, 17407])).
% 2.13/2.39 tff(17409,plain,
% 2.13/2.39 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[12143, 224, 724, 17408, 10694])).
% 2.13/2.39 tff(17410,plain,
% 2.13/2.39 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1869, 17409, 12137])).
% 2.13/2.39 tff(17411,plain,
% 2.13/2.39 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17410])).
% 2.13/2.39 tff(17412,plain,
% 2.13/2.39 (elem!1 = s(s(s(elem!1)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[155, 17411, 989])).
% 2.13/2.39 tff(17413,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17412])).
% 2.13/2.39 tff(17414,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[17413])).
% 2.13/2.39 tff(17415,plain,
% 2.13/2.39 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17414])).
% 2.13/2.39 tff(17416,plain,
% 2.13/2.39 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17410])).
% 2.13/2.39 tff(17417,plain,
% 2.13/2.39 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17416])).
% 2.13/2.39 tff(17418,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.13/2.39 tff(17419,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17418, 17417])).
% 2.13/2.39 tff(17420,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17419, 17415])).
% 2.13/2.39 tff(17421,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1798, 17420])).
% 2.13/2.39 tff(17422,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17423,plain,
% 2.13/2.39 (~r(s(elem!1), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17422, 17406, 688, 4569, 17370])).
% 2.13/2.39 tff(17424,plain,
% 2.13/2.39 (b(s(elem!1), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[939, 17423, 324])).
% 2.13/2.39 tff(17425,plain,
% 2.13/2.39 (b(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7872, 17424, 15899])).
% 2.13/2.39 tff(17426,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17427,plain,
% 2.13/2.39 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17428,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17427])).
% 2.13/2.39 tff(17429,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[17428, 17426])).
% 2.13/2.39 tff(17430,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(17431,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17430, 17429])).
% 2.13/2.39 tff(17432,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17431, 224, 17425, 5274, 17364, 17349])).
% 2.13/2.39 tff(17433,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17434,plain,
% 2.13/2.39 (~b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17433, 17347, 303, 15882, 15875, 17337, 15831, 17335, 17249, 17230, 17247])).
% 2.13/2.39 tff(17435,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[374, 17434, 15837])).
% 2.13/2.39 tff(17436,plain,
% 2.13/2.39 (r(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17435, 15833])).
% 2.13/2.39 tff(17437,plain,
% 2.13/2.39 (b(s(s(elem!1)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9144, 17206, 15831])).
% 2.13/2.39 tff(17438,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8884, 17247, 15840])).
% 2.13/2.39 tff(17439,plain,
% 2.13/2.39 (~r(s(z), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9974, 268, 179])).
% 2.13/2.39 tff(17440,plain,
% 2.13/2.39 (b(s(z), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1071, 17439])).
% 2.13/2.39 tff(17441,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[16404, 268, 2276])).
% 2.13/2.39 tff(17442,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6185, 17441])).
% 2.13/2.39 tff(17443,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5196, 17442, 6169, 1570, 17440])).
% 2.13/2.39 tff(17444,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17445,plain,
% 2.13/2.39 (~r(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17444, 17347, 17438, 16883, 15875])).
% 2.13/2.39 tff(17446,plain,
% 2.13/2.39 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17315, 17445, 15831, 17337, 17437, 17227, 17206, 17247, 17230, 15882])).
% 2.13/2.39 tff(17447,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17446, 17436])).
% 2.13/2.39 tff(17448,plain,((elem!1 = s(s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17449,plain,
% 2.13/2.39 (elem!1 = s(s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17448, 4538])).
% 2.13/2.39 tff(17450,plain,
% 2.13/2.39 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17449])).
% 2.13/2.39 tff(17451,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.13/2.39 inference(symmetry,[status(thm)],[17450])).
% 2.13/2.39 tff(17452,plain,
% 2.13/2.39 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17449])).
% 2.13/2.39 tff(17453,plain,
% 2.13/2.39 ((~b(z, elem!1)) <=> (~b(z, s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17452])).
% 2.13/2.39 tff(17454,plain,
% 2.13/2.39 (~b(z, s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[4538, 17453])).
% 2.13/2.39 tff(17455,plain,
% 2.13/2.39 (r(z, s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[580, 68, 17454, 748])).
% 2.13/2.39 tff(17456,plain,
% 2.13/2.39 (~r(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[15713, 17455, 16883])).
% 2.13/2.39 tff(17457,plain,
% 2.13/2.39 (b(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[653, 17456])).
% 2.13/2.39 tff(17458,plain,
% 2.13/2.39 (r(elem!1, s(s(elem!1))) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17449])).
% 2.13/2.39 tff(17459,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.13/2.39 inference(symmetry,[status(thm)],[17458])).
% 2.13/2.39 tff(17460,plain,
% 2.13/2.39 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17459])).
% 2.13/2.39 tff(17461,plain,
% 2.13/2.39 (~r(elem!1, s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[5127, 17460])).
% 2.13/2.39 tff(17462,plain,
% 2.13/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17449])).
% 2.13/2.39 tff(17463,plain,
% 2.13/2.39 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[17462])).
% 2.13/2.39 tff(17464,plain,
% 2.13/2.39 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17463])).
% 2.13/2.39 tff(17465,plain,
% 2.13/2.39 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[2929, 17464])).
% 2.13/2.39 tff(17466,plain,
% 2.13/2.39 ((elem!1 = z) <=> (s(s(elem!1)) = z)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17449])).
% 2.13/2.39 tff(17467,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.39 inference(symmetry,[status(thm)],[17466])).
% 2.13/2.39 tff(17468,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[17467, 6])).
% 2.13/2.39 tff(17469,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17468])).
% 2.13/2.39 tff(17470,plain,
% 2.13/2.39 (~(z = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[566, 17469])).
% 2.13/2.39 tff(17471,plain,
% 2.13/2.39 (r(z, elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[289, 17470, 4538])).
% 2.13/2.39 tff(17472,plain,
% 2.13/2.39 (b(s(z), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[454, 3333, 16115])).
% 2.13/2.39 tff(17473,plain,
% 2.13/2.39 (~r(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9119, 689, 179])).
% 2.13/2.39 tff(17474,plain,
% 2.13/2.39 (~b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[12304, 689, 688, 684, 362])).
% 2.13/2.39 tff(17475,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 17474, 17473])).
% 2.13/2.39 tff(17476,plain,((~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17477,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17476, 688, 17472, 16118, 179])).
% 2.13/2.39 tff(17478,plain,
% 2.13/2.39 (b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[100, 17477])).
% 2.13/2.39 tff(17479,plain,
% 2.13/2.39 (~(elem!1 = s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2654, 16115])).
% 2.13/2.39 tff(17480,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17476, 688, 684, 362, 179])).
% 2.13/2.39 tff(17481,plain,
% 2.13/2.39 (b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[100, 17480])).
% 2.13/2.39 tff(17482,plain,
% 2.13/2.39 (~b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2951, 5495, 362, 354, 3333, 2440])).
% 2.13/2.39 tff(17483,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 17482, 17084])).
% 2.13/2.39 tff(17484,plain,((~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(s(z)))) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17485,plain,
% 2.13/2.39 (r(elem!1, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17484, 177, 354, 362, 179, 688])).
% 2.13/2.39 tff(17486,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[932, 112, 179, 177, 3188])).
% 2.13/2.39 tff(17487,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17488,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17487, 177, 179])).
% 2.13/2.39 tff(17489,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[925, 17488])).
% 2.13/2.39 tff(17490,plain,
% 2.13/2.39 (~b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6404, 6255, 77, 560])).
% 2.13/2.39 tff(17491,plain,
% 2.13/2.39 (r(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 17490])).
% 2.13/2.39 tff(17492,plain,
% 2.13/2.39 (~r(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1028, 1020, 17491])).
% 2.13/2.39 tff(17493,plain,
% 2.13/2.39 (b(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1277, 17492, 88])).
% 2.13/2.39 tff(17494,plain,
% 2.13/2.39 (~b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5502, 224, 684, 17493, 560])).
% 2.13/2.39 tff(17495,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[374, 17494, 362])).
% 2.13/2.39 tff(17496,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2429, 112, 688, 17495])).
% 2.13/2.39 tff(17497,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[72, 17496])).
% 2.13/2.39 tff(17498,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17499,plain,
% 2.13/2.39 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17500,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17499])).
% 2.13/2.39 tff(17501,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[17500, 17498])).
% 2.13/2.39 tff(17502,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(17503,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17502, 17501])).
% 2.13/2.39 tff(17504,plain,
% 2.13/2.39 (~b(z, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17503, 224, 77, 2212, 6255, 560])).
% 2.13/2.39 tff(17505,plain,
% 2.13/2.39 (r(z, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1088, 17504])).
% 2.13/2.39 tff(17506,plain,
% 2.13/2.39 (~b(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9199, 224, 2212, 6255, 7672])).
% 2.13/2.39 tff(17507,plain,
% 2.13/2.39 (r(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[234, 68, 42, 17506])).
% 2.13/2.39 tff(17508,plain,
% 2.13/2.39 (~r(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3470, 112, 179, 17507])).
% 2.13/2.39 tff(17509,plain,
% 2.13/2.39 (b(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[213, 68, 210, 17508])).
% 2.13/2.39 tff(17510,plain,
% 2.13/2.39 (~b(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4521, 224, 684, 2896, 17509])).
% 2.13/2.39 tff(17511,plain,
% 2.13/2.39 (r(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1135, 17510, 2796])).
% 2.13/2.39 tff(17512,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3756, 112, 688, 17511, 17505])).
% 2.13/2.39 tff(17513,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17514,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17513, 17493, 2796, 684, 688, 179, 6255, 17497, 77, 560])).
% 2.13/2.39 tff(17515,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[249, 17514])).
% 2.13/2.39 tff(17516,plain,
% 2.13/2.39 (~r(s(z), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6296, 17515, 17491])).
% 2.13/2.39 tff(17517,plain,
% 2.13/2.39 (b(s(z), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1071, 17516])).
% 2.13/2.39 tff(17518,plain,
% 2.13/2.39 (~r(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9273, 112, 17515, 1020])).
% 2.13/2.39 tff(17519,plain,
% 2.13/2.39 (b(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1135, 17518, 2796])).
% 2.13/2.39 tff(17520,plain,
% 2.13/2.39 (~r(elem!1, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9283, 112, 17515, 1020])).
% 2.13/2.39 tff(17521,plain,
% 2.13/2.39 (b(elem!1, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2874, 17520, 2786])).
% 2.13/2.39 tff(17522,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5087, 224, 684, 17521, 17519, 17517])).
% 2.13/2.39 tff(17523,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17524,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17523, 17489, 17485, 179, 688, 3789, 684, 77, 2786, 17481, 362, 88])).
% 2.13/2.39 tff(17525,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (elem!1 = s(s(z))) | (s(s(s(z))) = elem!1) | (elem!1 = s(z)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(17526,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[17525, 77, 688, 17472, 179, 2832, 16118, 17479, 2930])).
% 2.13/2.39 tff(17527,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[72, 17526])).
% 2.13/2.39 tff(17528,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9201, 1118, 17478, 17527])).
% 2.13/2.39 tff(17529,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[249, 17528])).
% 2.13/2.39 tff(17530,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5403, 1047, 2831])).
% 2.13/2.39 tff(17531,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5413, 17530, 17529])).
% 2.13/2.39 tff(17532,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5426, 17531])).
% 2.13/2.39 tff(17533,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[17532, 6056])).
% 2.13/2.39 tff(17534,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17535,plain,
% 2.13/2.39 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(17536,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[17535])).
% 2.13/2.39 tff(17537,plain,
% 2.13/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[17536, 17534])).
% 2.13/2.39 tff(17538,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(17539,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[17538, 17537])).
% 2.13/2.40 tff(17540,plain,
% 2.13/2.40 (~b(s(s(s(z))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[17539, 224, 77, 2252, 17527, 17533])).
% 2.13/2.40 tff(17541,plain,
% 2.13/2.40 (r(s(s(s(z))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[925, 17540])).
% 2.13/2.40 tff(17542,plain,
% 2.13/2.40 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[15990, 16541, 1047, 688])).
% 2.13/2.40 tff(17543,plain,
% 2.13/2.40 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3183, 17542, 3121])).
% 2.13/2.40 tff(17544,plain,
% 2.13/2.40 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[17543, 3102])).
% 2.13/2.40 tff(17545,plain,
% 2.13/2.40 (r(s(s(z)), s(s(elem!1)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2801, 1047, 2834])).
% 2.13/2.40 tff(17546,plain,
% 2.13/2.40 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[8623, 17545, 1118, 17478, 17527])).
% 2.13/2.40 tff(17547,plain,
% 2.13/2.40 (b(s(s(elem!1)), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[147, 17546, 16117])).
% 2.13/2.40 tff(17548,plain,
% 2.13/2.40 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3237, 224, 17547, 17533])).
% 2.13/2.40 tff(17549,plain,
% 2.13/2.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[17548, 17544])).
% 2.13/2.40 tff(17550,plain,
% 2.13/2.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3252, 17549])).
% 2.13/2.40 tff(17551,plain,
% 2.13/2.40 (~b(s(s(elem!1)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[10929, 17547, 17478, 17527])).
% 2.13/2.40 tff(17552,plain,
% 2.13/2.40 (r(s(s(elem!1)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[593, 17551])).
% 2.13/2.40 tff(17553,plain,
% 2.13/2.40 (~r(s(s(elem!1)), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[895, 17552, 179])).
% 2.13/2.40 tff(17554,plain,
% 2.13/2.40 (b(s(s(elem!1)), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[901, 17553])).
% 2.13/2.40 tff(17555,plain,
% 2.13/2.40 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3310, 224, 2252, 17554])).
% 2.13/2.40 tff(17556,plain,
% 2.13/2.40 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[17555, 17544])).
% 2.13/2.40 tff(17557,plain,
% 2.13/2.40 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3168, 17556])).
% 2.13/2.40 tff(17558,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3326, 17557, 17550, 17541])).
% 2.13/2.40 tff(17559,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(17560,plain,
% 2.13/2.40 (~r(s(s(z)), elem!1)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[17559, 1118, 1296, 77, 179, 688, 2252])).
% 2.13/2.40 tff(17561,plain,
% 2.13/2.40 (b(s(s(z)), elem!1)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[1135, 17560, 2833])).
% 2.13/2.40 tff(17562,plain,
% 2.13/2.40 (~b(s(s(z)), s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[5045, 17561, 77, 17472, 1118])).
% 2.23/2.40 tff(17563,plain,
% 2.23/2.40 (r(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2726, 17562])).
% 2.23/2.40 tff(17564,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3196, 17563, 17529])).
% 2.23/2.40 tff(17565,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[925, 17564])).
% 2.23/2.40 tff(17566,plain,
% 2.23/2.40 (~r(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6257, 17563, 17529])).
% 2.23/2.40 tff(17567,plain,
% 2.23/2.40 (b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[175, 17566])).
% 2.23/2.40 tff(17568,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6404, 17567, 17565, 77, 17478])).
% 2.23/2.40 tff(17569,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17570,plain,
% 2.23/2.40 (~b(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17569, 77, 1296, 179, 688, 2252])).
% 2.23/2.40 tff(17571,plain,
% 2.23/2.40 (r(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[281, 17570])).
% 2.23/2.40 tff(17572,plain,
% 2.23/2.40 (~r(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3470, 112, 179, 17571])).
% 2.23/2.40 tff(17573,plain,
% 2.23/2.40 (b(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2726, 17572])).
% 2.23/2.40 tff(17574,plain,
% 2.23/2.40 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[1296])).
% 2.23/2.40 tff(17575,plain,
% 2.23/2.40 (~r(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9974, 17571, 179])).
% 2.23/2.40 tff(17576,plain,
% 2.23/2.40 (b(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1071, 17575])).
% 2.23/2.40 tff(17577,plain,
% 2.23/2.40 (~b(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1078, 224, 77, 17576, 17573])).
% 2.23/2.40 tff(17578,plain,
% 2.23/2.40 (r(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1088, 17577])).
% 2.23/2.40 tff(17579,plain,
% 2.23/2.40 (~r(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3758, 17578, 688])).
% 2.23/2.40 tff(17580,plain,
% 2.23/2.40 (b(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1135, 17579, 2833])).
% 2.23/2.40 tff(17581,plain,
% 2.23/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17580, 17574])).
% 2.23/2.40 tff(17582,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9920, 17581, 17573, 2252])).
% 2.23/2.40 tff(17583,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[901, 17582])).
% 2.23/2.40 tff(17584,plain,
% 2.23/2.40 (~r(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[895, 17583, 179])).
% 2.23/2.40 tff(17585,plain,
% 2.23/2.40 (b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[593, 17584])).
% 2.23/2.40 tff(17586,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10929, 17585, 17478, 17527])).
% 2.23/2.40 tff(17587,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[147, 17586, 16117])).
% 2.23/2.40 tff(17588,plain,
% 2.23/2.40 (~r(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[4039, 17587, 17583])).
% 2.23/2.40 tff(17589,plain,
% 2.23/2.40 (b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[175, 17588])).
% 2.23/2.40 tff(17590,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6404, 17589, 77, 17478])).
% 2.23/2.40 tff(17591,plain,
% 2.23/2.40 (r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[925, 17590])).
% 2.23/2.40 tff(17592,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5342, 112, 17583, 17587, 17591])).
% 2.23/2.40 tff(17593,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17594,plain,
% 2.23/2.40 (~b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17593, 16883, 17457, 17449, 17471])).
% 2.23/2.40 tff(17595,plain,
% 2.23/2.40 (s(s(s(s(elem!1)))) = elem!1),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1306, 17449])).
% 2.23/2.40 tff(17596,plain,
% 2.23/2.40 (~(s(z) = elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7751, 17595])).
% 2.23/2.40 tff(17597,plain,
% 2.23/2.40 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[131, 17596])).
% 2.23/2.40 tff(17598,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5459, 17594])).
% 2.23/2.40 tff(17599,plain,
% 2.23/2.40 (~r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7338, 17598, 17597, 17457, 17455])).
% 2.23/2.40 tff(17600,plain,
% 2.23/2.40 (b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[72, 17599])).
% 2.23/2.40 tff(17601,plain,
% 2.23/2.40 (b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9581, 17600, 17594, 17470, 17465, 17461])).
% 2.23/2.40 tff(17602,plain,
% 2.23/2.40 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17449])).
% 2.23/2.40 tff(17603,plain,
% 2.23/2.40 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[17602])).
% 2.23/2.40 tff(17604,plain,
% 2.23/2.40 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.23/2.40 inference(transitivity,[status(thm)],[17603, 284])).
% 2.23/2.40 tff(17605,plain,
% 2.23/2.40 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17604])).
% 2.23/2.40 tff(17606,plain,
% 2.23/2.40 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[310, 17597])).
% 2.23/2.40 tff(17607,plain,
% 2.23/2.40 (~(s(s(s(z))) = elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17606, 17605])).
% 2.23/2.40 tff(17608,plain,
% 2.23/2.40 (~r(s(z), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3332, 17471, 16883])).
% 2.23/2.40 tff(17609,plain,
% 2.23/2.40 (b(s(z), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[454, 17608, 17596])).
% 2.23/2.40 tff(17610,plain,
% 2.23/2.40 (~r(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17476, 17471, 17609, 17607, 16883])).
% 2.23/2.40 tff(17611,plain,
% 2.23/2.40 (b(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[100, 17610])).
% 2.23/2.40 tff(17612,plain,
% 2.23/2.40 (b(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14396, 17600, 17465, 17594, 17611, 17470, 17601])).
% 2.23/2.40 tff(17613,plain,
% 2.23/2.40 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17449])).
% 2.23/2.40 tff(17614,plain,
% 2.23/2.40 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[17613, 3620])).
% 2.23/2.40 tff(17615,plain,
% 2.23/2.40 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17614])).
% 2.23/2.40 tff(17616,plain,
% 2.23/2.40 (~(elem!1 = s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2783, 17595, 17449])).
% 2.23/2.40 tff(17617,plain,
% 2.23/2.40 (~(s(s(z)) = s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17616, 17615])).
% 2.23/2.40 tff(17618,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10929, 17601, 17611, 17600])).
% 2.23/2.40 tff(17619,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[147, 17618, 17606])).
% 2.23/2.40 tff(17620,plain,
% 2.23/2.40 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17449])).
% 2.23/2.40 tff(17621,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[17620])).
% 2.23/2.40 tff(17622,plain,
% 2.23/2.40 (r(elem!1, s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17619, 17621])).
% 2.23/2.40 tff(17623,plain,
% 2.23/2.40 (~r(s(z), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[15713, 293, 179])).
% 2.23/2.40 tff(17624,plain,
% 2.23/2.40 (b(s(z), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[653, 17623])).
% 2.23/2.40 tff(17625,plain,
% 2.23/2.40 (r(elem!1, s(s(elem!1))) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[1296])).
% 2.23/2.40 tff(17626,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(symmetry,[status(thm)],[17625])).
% 2.23/2.40 tff(17627,plain,
% 2.23/2.40 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17626])).
% 2.23/2.40 tff(17628,plain,
% 2.23/2.40 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[5127, 17627])).
% 2.23/2.40 tff(17629,plain,
% 2.23/2.40 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.23/2.40 inference(transitivity,[status(thm)],[8492, 6])).
% 2.23/2.40 tff(17630,plain,
% 2.23/2.40 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17629])).
% 2.23/2.40 tff(17631,plain,
% 2.23/2.40 (~(z = elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[566, 17630])).
% 2.23/2.40 tff(17632,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17523, 77, 179, 688, 2833, 17472, 1020, 2832, 7674, 16118, 17479])).
% 2.23/2.40 tff(17633,plain,
% 2.23/2.40 (r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[925, 17632])).
% 2.23/2.40 tff(17634,plain,
% 2.23/2.40 (~r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17487, 17633, 179])).
% 2.23/2.40 tff(17635,plain,
% 2.23/2.40 (b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[72, 17634])).
% 2.23/2.40 tff(17636,plain,
% 2.23/2.40 (~b(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9201, 17635, 2212, 7674])).
% 2.23/2.40 tff(17637,plain,
% 2.23/2.40 (r(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[281, 17636])).
% 2.23/2.40 tff(17638,plain,
% 2.23/2.40 (~r(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9974, 17637, 179])).
% 2.23/2.40 tff(17639,plain,
% 2.23/2.40 (b(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1071, 17638])).
% 2.23/2.40 tff(17640,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17641,plain,
% 2.23/2.40 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17642,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17641])).
% 2.23/2.40 tff(17643,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[17642, 17640])).
% 2.23/2.40 tff(17644,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(17645,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17644, 17643])).
% 2.23/2.40 tff(17646,plain,
% 2.23/2.40 (~b(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17645, 224, 77, 2212, 7674, 17639])).
% 2.23/2.40 tff(17647,plain,
% 2.23/2.40 (r(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1088, 17646])).
% 2.23/2.40 tff(17648,plain,
% 2.23/2.40 (~r(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3758, 17647, 688])).
% 2.23/2.40 tff(17649,plain,
% 2.23/2.40 (b(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1135, 17648, 2833])).
% 2.23/2.40 tff(17650,plain,
% 2.23/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17649, 17574])).
% 2.23/2.40 tff(17651,plain,
% 2.23/2.40 (~r(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5356, 17649, 1296, 16118, 2212, 16117, 17633])).
% 2.23/2.40 tff(17652,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[901, 17651])).
% 2.23/2.40 tff(17653,plain,
% 2.23/2.40 (~b(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5850, 224, 2252, 17652, 17650])).
% 2.23/2.40 tff(17654,plain,
% 2.23/2.40 (r(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2726, 17653])).
% 2.23/2.40 tff(17655,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3470, 112, 179, 17637, 17654])).
% 2.23/2.40 tff(17656,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17657,plain,
% 2.23/2.40 (~b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17656, 1020, 17624, 1296, 2212, 688, 179])).
% 2.23/2.40 tff(17658,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5459, 17657])).
% 2.23/2.40 tff(17659,plain,
% 2.23/2.40 (~r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7338, 17658, 16116, 17624, 293])).
% 2.23/2.40 tff(17660,plain,
% 2.23/2.40 (b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[72, 17659])).
% 2.23/2.40 tff(17661,plain,
% 2.23/2.40 (b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9581, 17660, 17657, 17631, 2930, 17628])).
% 2.23/2.40 tff(17662,plain,
% 2.23/2.40 (b(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14396, 17660, 2930, 17657, 7674, 17631, 17661])).
% 2.23/2.40 tff(17663,plain,
% 2.23/2.40 (~b(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9201, 17660, 2212, 7674])).
% 2.23/2.40 tff(17664,plain,
% 2.23/2.40 (r(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[281, 17663])).
% 2.23/2.40 tff(17665,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17666,plain,
% 2.23/2.40 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17667,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[17666])).
% 2.23/2.40 tff(17668,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[17667, 17665])).
% 2.23/2.40 tff(17669,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(17670,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17669, 17668])).
% 2.23/2.40 tff(17671,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17670, 112, 4569, 293, 268, 267])).
% 2.23/2.40 tff(17672,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17673,plain,
% 2.23/2.40 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17672, 17658, 293, 17664])).
% 2.23/2.40 tff(17674,plain,
% 2.23/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[265, 17673, 16126])).
% 2.23/2.40 tff(17675,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9920, 17674, 17662, 17624])).
% 2.23/2.40 tff(17676,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[901, 17675])).
% 2.23/2.40 tff(17677,plain,
% 2.23/2.40 (r(elem!1, s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17676, 5175])).
% 2.23/2.40 tff(17678,plain,
% 2.23/2.40 (~r(elem!1, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5490, 17658, 688])).
% 2.23/2.40 tff(17679,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17678, 17677])).
% 2.23/2.40 tff(17680,plain,((~r(elem!1, s(s(s(z))))) | (~(elem!1 = s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17681,plain,
% 2.23/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17680, 17622, 17455, 17449, 17471, 16883])).
% 2.23/2.40 tff(17682,plain,
% 2.23/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[249, 17681])).
% 2.23/2.40 tff(17683,plain,
% 2.23/2.40 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8621, 112, 17682, 17619])).
% 2.23/2.40 tff(17684,plain,
% 2.23/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[265, 17683, 17617])).
% 2.23/2.40 tff(17685,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9920, 17684, 17612, 17457])).
% 2.23/2.40 tff(17686,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[901, 17685])).
% 2.23/2.40 tff(17687,plain,
% 2.23/2.40 (r(elem!1, s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17686, 17451])).
% 2.23/2.40 tff(17688,plain,
% 2.23/2.40 (~r(elem!1, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5490, 17598, 17471])).
% 2.23/2.40 tff(17689,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17688, 17687])).
% 2.23/2.40 tff(17690,plain,(b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17691,plain,
% 2.23/2.40 (b(z, s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17690, 15830])).
% 2.23/2.40 tff(17692,plain,
% 2.23/2.40 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[15829])).
% 2.23/2.40 tff(17693,plain,
% 2.23/2.40 (b(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6253, 12, 2, 15861])).
% 2.23/2.40 tff(17694,plain,
% 2.23/2.40 (~r(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6329, 4569, 2, 177, 6255])).
% 2.23/2.40 tff(17695,plain,
% 2.23/2.40 (b(s(s(elem!1)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[593, 17694])).
% 2.23/2.40 tff(17696,plain,
% 2.23/2.40 (b(elem!1, z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3641, 17695, 15829])).
% 2.23/2.40 tff(17697,plain,
% 2.23/2.40 (~b(s(z), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[4051, 17695, 1, 17691])).
% 2.23/2.40 tff(17698,plain,
% 2.23/2.40 (r(s(z), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[653, 17697])).
% 2.23/2.40 tff(17699,plain,
% 2.23/2.40 (~r(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6167, 2851, 4569])).
% 2.23/2.40 tff(17700,plain,
% 2.23/2.40 (b(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[281, 17699])).
% 2.23/2.40 tff(17701,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5939, 5244, 17700, 1180, 1240])).
% 2.23/2.40 tff(17702,plain,((~r(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17703,plain,
% 2.23/2.40 (~r(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17702, 17695, 17691, 16319, 17698, 4569])).
% 2.23/2.40 tff(17704,plain,
% 2.23/2.40 (b(s(s(z)), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2726, 17703])).
% 2.23/2.40 tff(17705,plain,
% 2.23/2.40 (~b(s(z), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6730, 17696, 17690, 1])).
% 2.23/2.40 tff(17706,plain,
% 2.23/2.40 (r(s(z), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[454, 17705, 91])).
% 2.23/2.40 tff(17707,plain,
% 2.23/2.40 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[15829])).
% 2.23/2.40 tff(17708,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[17707])).
% 2.23/2.40 tff(17709,plain,
% 2.23/2.40 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[835, 178, 656])).
% 2.23/2.40 tff(17710,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[147, 17709, 2])).
% 2.23/2.40 tff(17711,plain,
% 2.23/2.40 (b(elem!1, s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17710, 17708])).
% 2.23/2.40 tff(17712,plain,
% 2.23/2.40 (~b(elem!1, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9411, 178, 15861, 4569, 16267, 416])).
% 2.23/2.40 tff(17713,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17712, 17711])).
% 2.23/2.40 tff(17714,plain,((~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17715,plain,
% 2.23/2.40 (~r(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17714, 4569, 2, 17706, 17698])).
% 2.23/2.40 tff(17716,plain,
% 2.23/2.40 (b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[175, 17715])).
% 2.23/2.40 tff(17717,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3462, 224, 2212, 1090, 560, 2844])).
% 2.23/2.40 tff(17718,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17719,plain,
% 2.23/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17718, 1090, 5773, 2844])).
% 2.23/2.40 tff(17720,plain,
% 2.23/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[249, 17719])).
% 2.23/2.40 tff(17721,plain,
% 2.23/2.40 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8621, 112, 17720, 827])).
% 2.23/2.40 tff(17722,plain,
% 2.23/2.40 (~r(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2801, 17721, 2834])).
% 2.23/2.40 tff(17723,plain,
% 2.23/2.40 (b(s(s(z)), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1135, 17722, 2833])).
% 2.23/2.40 tff(17724,plain,
% 2.23/2.40 (~r(s(s(elem!1)), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[14384, 112, 17720, 827])).
% 2.23/2.40 tff(17725,plain,
% 2.23/2.40 (~r(elem!1, s(s(z)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[17724, 3187])).
% 2.23/2.40 tff(17726,plain,
% 2.23/2.40 (b(elem!1, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2874, 17725, 2832])).
% 2.23/2.40 tff(17727,plain,
% 2.23/2.40 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5300, 17726, 17690, 405, 17723])).
% 2.23/2.40 tff(17728,plain,
% 2.23/2.40 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3183, 17727, 3121])).
% 2.23/2.40 tff(17729,plain,
% 2.23/2.40 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[2274, 5168])).
% 2.23/2.40 tff(17730,assumption,(~r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 2.23/2.40 tff(17731,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17730, 17729])).
% 2.23/2.40 tff(17732,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(17733,plain,
% 2.23/2.40 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[17732, 17728, 1296])).
% 2.23/2.40 tff(17734,plain,
% 2.23/2.40 (~r(s(s(s(s(z)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7280, 17733, 656])).
% 2.23/2.40 tff(17735,plain,
% 2.23/2.40 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3168, 17734])).
% 2.23/2.40 tff(17736,plain,
% 2.23/2.40 (~b(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6204, 17735, 177, 5773, 1090, 2844])).
% 2.23/2.40 tff(17737,plain,
% 2.23/2.40 (r(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1071, 17736])).
% 2.23/2.40 tff(17738,plain,
% 2.23/2.40 (~b(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2869, 17726, 17690, 17723])).
% 2.23/2.40 tff(17739,plain,
% 2.23/2.40 (r(z, s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1088, 17738])).
% 2.23/2.40 tff(17740,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17741,plain,
% 2.23/2.40 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(17742,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17741])).
% 2.23/2.41 tff(17743,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17742, 17740])).
% 2.23/2.41 tff(17744,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(17745,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17744, 17743])).
% 2.23/2.41 tff(17746,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17745, 112, 4569, 656, 17739, 17737])).
% 2.23/2.41 tff(17747,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17748,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17747, 4569, 17698, 177, 17716, 17704, 15829, 17696])).
% 2.23/2.41 tff(17749,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[147, 17748, 2])).
% 2.23/2.41 tff(17750,plain,
% 2.23/2.41 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6713, 224, 17695, 1, 5773])).
% 2.23/2.41 tff(17751,plain,
% 2.23/2.41 (~b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17750, 17749])).
% 2.23/2.41 tff(17752,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17751])).
% 2.23/2.41 tff(17753,plain,
% 2.23/2.41 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.41 inference(transitivity,[status(thm)],[16268, 15829])).
% 2.23/2.41 tff(17754,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17753])).
% 2.23/2.41 tff(17755,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17754])).
% 2.23/2.41 tff(17756,plain,
% 2.23/2.41 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17755])).
% 2.23/2.41 tff(17757,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6315, 224, 1180, 152, 6255, 968])).
% 2.23/2.41 tff(17758,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17759,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17758, 17749, 17691, 6255])).
% 2.23/2.41 tff(17760,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17759, 17756])).
% 2.23/2.41 tff(17761,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5426, 17760])).
% 2.23/2.41 tff(17762,plain,
% 2.23/2.41 (~r(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5420, 17761, 16271, 5773, 17716, 16268, 17752])).
% 2.23/2.41 tff(17763,plain,
% 2.23/2.41 (b(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1135, 17762, 16270])).
% 2.23/2.41 tff(17764,plain,
% 2.23/2.41 (~b(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1126, 17763, 17690, 17696])).
% 2.23/2.41 tff(17765,plain,
% 2.23/2.41 (r(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[281, 17764])).
% 2.23/2.41 tff(17766,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17718, 17716, 5773, 17704])).
% 2.23/2.41 tff(17767,plain,
% 2.23/2.41 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[249, 17766])).
% 2.23/2.41 tff(17768,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[241, 112, 17767, 177, 17765])).
% 2.23/2.41 tff(17769,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17770,plain,
% 2.23/2.41 (~r(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17769, 73, 17693, 1, 2])).
% 2.23/2.41 tff(17771,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5459, 17770])).
% 2.23/2.41 tff(17772,plain,
% 2.23/2.41 (~r(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17769, 177, 6255, 1, 2])).
% 2.23/2.41 tff(17773,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5459, 17772])).
% 2.23/2.41 tff(17774,plain,
% 2.23/2.41 ((elem!1 = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[16317, 3621])).
% 2.23/2.41 tff(17775,plain,
% 2.23/2.41 ((~(elem!1 = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17774])).
% 2.23/2.41 tff(17776,plain,
% 2.23/2.41 (~(s(s(elem!1)) = s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[16269, 17775])).
% 2.23/2.41 tff(17777,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6392, 178, 2, 17776, 6255, 177, 1])).
% 2.23/2.41 tff(17778,plain,
% 2.23/2.41 (r(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[265, 17777, 16319])).
% 2.23/2.41 tff(17779,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3641, 1240, 15829])).
% 2.23/2.41 tff(17780,plain,
% 2.23/2.41 (~b(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6730, 17779, 17690, 1])).
% 2.23/2.41 tff(17781,plain,
% 2.23/2.41 (r(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[454, 17780, 91])).
% 2.23/2.41 tff(17782,plain,
% 2.23/2.41 (~r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2374, 17781, 178])).
% 2.23/2.41 tff(17783,plain,
% 2.23/2.41 (b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[374, 17782, 16267])).
% 2.23/2.41 tff(17784,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17783, 16289])).
% 2.23/2.41 tff(17785,plain,
% 2.23/2.41 (~b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4051, 1240, 1, 17691])).
% 2.23/2.41 tff(17786,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17785])).
% 2.23/2.41 tff(17787,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[835, 17786, 178])).
% 2.23/2.41 tff(17788,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[147, 17787, 2])).
% 2.23/2.41 tff(17789,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17758, 17788, 17691, 6255])).
% 2.23/2.41 tff(17790,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17789, 17784])).
% 2.23/2.41 tff(17791,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17792,plain,
% 2.23/2.41 (~b(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17791, 178, 2, 6255, 1])).
% 2.23/2.41 tff(17793,plain,
% 2.23/2.41 (r(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[593, 17792])).
% 2.23/2.41 tff(17794,plain,
% 2.23/2.41 (~r(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[276, 17793, 17778])).
% 2.23/2.41 tff(17795,plain,
% 2.23/2.41 (b(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[281, 17794])).
% 2.23/2.41 tff(17796,plain,
% 2.23/2.41 (~b(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2846, 17795, 1, 17773])).
% 2.23/2.41 tff(17797,plain,
% 2.23/2.41 (r(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2726, 17796])).
% 2.23/2.41 tff(17798,plain,
% 2.23/2.41 (~r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2853, 17797, 17778])).
% 2.23/2.41 tff(17799,plain,
% 2.23/2.41 (b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17798])).
% 2.23/2.41 tff(17800,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2993, 17797, 17778])).
% 2.23/2.41 tff(17801,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17800])).
% 2.23/2.41 tff(17802,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10876, 17801, 17799, 17691, 17773])).
% 2.23/2.41 tff(17803,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17804,plain,
% 2.23/2.41 (~r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17803, 17693, 2, 1, 73])).
% 2.23/2.41 tff(17805,plain,
% 2.23/2.41 (b(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[175, 17804])).
% 2.23/2.41 tff(17806,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6404, 17805, 17771, 17693])).
% 2.23/2.41 tff(17807,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[925, 17806])).
% 2.23/2.41 tff(17808,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17758, 6261, 17691, 6255])).
% 2.23/2.41 tff(17809,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[135, 68, 132, 17808, 294])).
% 2.23/2.41 tff(17810,plain,((~r(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17811,plain,
% 2.23/2.41 (~r(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17810, 17693, 2, 73])).
% 2.23/2.41 tff(17812,plain,
% 2.23/2.41 (b(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[593, 17811])).
% 2.23/2.41 tff(17813,plain,
% 2.23/2.41 (~b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4051, 17812, 1, 17691])).
% 2.23/2.41 tff(17814,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17813])).
% 2.23/2.41 tff(17815,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9107, 17814, 17807])).
% 2.23/2.41 tff(17816,plain,
% 2.23/2.41 (~b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1249, 17812, 1, 17771])).
% 2.23/2.41 tff(17817,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17816])).
% 2.23/2.41 tff(17818,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(17819,plain,
% 2.23/2.41 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(17820,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17819])).
% 2.23/2.41 tff(17821,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17820, 17818])).
% 2.23/2.41 tff(17822,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(17823,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17822, 17821])).
% 2.23/2.41 tff(17824,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17823, 112, 17817, 73, 17807])).
% 2.23/2.41 tff(17825,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[147, 17824, 2])).
% 2.23/2.41 tff(17826,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17758, 17825, 17691, 17693])).
% 2.23/2.41 tff(17827,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[135, 68, 132, 17826, 17815])).
% 2.23/2.41 tff(17828,plain,(b(s(s(s(z))), z) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17829,plain,
% 2.23/2.41 (b(s(s(s(z))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17828, 2, 1])).
% 2.23/2.41 tff(17830,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9717, 689, 16251, 16255, 17829, 15861])).
% 2.23/2.41 tff(17831,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11579, 9139, 17829, 689])).
% 2.23/2.41 tff(17832,plain,
% 2.23/2.41 (b(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17831, 17708])).
% 2.23/2.41 tff(17833,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10094, 224, 17830, 1, 17829])).
% 2.23/2.41 tff(17834,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[925, 17833])).
% 2.23/2.41 tff(17835,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12443, 17834, 689, 17830, 1])).
% 2.23/2.41 tff(17836,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[249, 17835])).
% 2.23/2.41 tff(17837,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10094, 224, 77, 1, 17829])).
% 2.23/2.41 tff(17838,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[925, 17837])).
% 2.23/2.41 tff(17839,plain,
% 2.23/2.41 (~b(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5356, 887, 15829, 16267, 17838, 2, 2212])).
% 2.23/2.41 tff(17840,plain,
% 2.23/2.41 (r(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1135, 17839, 16270])).
% 2.23/2.41 tff(17841,plain,
% 2.23/2.41 (r(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2801, 17840, 16271])).
% 2.23/2.41 tff(17842,plain,
% 2.23/2.41 (~r(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[276, 17841, 102])).
% 2.23/2.41 tff(17843,plain,
% 2.23/2.41 (b(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[281, 17842])).
% 2.23/2.41 tff(17844,plain,
% 2.23/2.41 (~r(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2993, 17841, 887])).
% 2.23/2.41 tff(17845,plain,
% 2.23/2.41 (b(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2726, 17844])).
% 2.23/2.41 tff(17846,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2846, 17845, 17843, 1, 77])).
% 2.23/2.41 tff(17847,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17848,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17847, 9146, 17830, 1, 2, 17836])).
% 2.23/2.41 tff(17849,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17848])).
% 2.23/2.41 tff(17850,plain,
% 2.23/2.41 (b(elem!1, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5385, 17849, 15829])).
% 2.23/2.41 tff(17851,plain,
% 2.23/2.41 (~b(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2904, 17850, 17690, 17830])).
% 2.23/2.41 tff(17852,plain,
% 2.23/2.41 (r(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[454, 17851, 91])).
% 2.23/2.41 tff(17853,plain,
% 2.23/2.41 (~b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2893, 17852, 17690, 15829, 689, 9146, 17832, 17830])).
% 2.23/2.41 tff(17854,plain,
% 2.23/2.41 (r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[374, 17853, 16267])).
% 2.23/2.41 tff(17855,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17854, 17692])).
% 2.23/2.41 tff(17856,plain,
% 2.23/2.41 (~b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10876, 17849, 17691, 17830])).
% 2.23/2.41 tff(17857,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17856])).
% 2.23/2.41 tff(17858,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9107, 17857, 17834])).
% 2.23/2.41 tff(17859,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17858, 17855])).
% 2.23/2.41 tff(17860,plain,(b(s(s(elem!1)), z) | (~r(z, s(s(s(z))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17861,plain,
% 2.23/2.41 (b(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17860, 689, 1, 2])).
% 2.23/2.41 tff(17862,plain,
% 2.23/2.41 (~b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4051, 17861, 1, 17691])).
% 2.23/2.41 tff(17863,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17862])).
% 2.23/2.41 tff(17864,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3641, 17861, 15829])).
% 2.23/2.41 tff(17865,plain,
% 2.23/2.41 (~r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[13863, 17864, 17690, 1, 16267, 91, 17829])).
% 2.23/2.41 tff(17866,plain,
% 2.23/2.41 (b(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[175, 17865])).
% 2.23/2.41 tff(17867,plain,
% 2.23/2.41 ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12455, 224, 1, 17836, 17829])).
% 2.23/2.41 tff(17868,plain,
% 2.23/2.41 (~b(s(z), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17867, 17866])).
% 2.23/2.41 tff(17869,plain,
% 2.23/2.41 (r(s(z), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1071, 17868])).
% 2.23/2.41 tff(17870,plain,
% 2.23/2.41 (~b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1249, 17861, 1, 17830])).
% 2.23/2.41 tff(17871,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17870])).
% 2.23/2.41 tff(17872,plain,
% 2.23/2.41 (~b(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5356, 17871, 15829, 16267, 17834, 2, 17836])).
% 2.23/2.41 tff(17873,plain,
% 2.23/2.41 (r(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1135, 17872, 16270])).
% 2.23/2.41 tff(17874,plain,
% 2.23/2.41 (r(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2801, 17873, 16271])).
% 2.23/2.41 tff(17875,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5333, 17874, 17869, 17863])).
% 2.23/2.41 tff(17876,plain,((~r(z, s(s(s(z))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17877,plain,
% 2.23/2.41 (~r(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17876, 2, 1])).
% 2.23/2.41 tff(17878,plain,
% 2.23/2.41 (b(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[100, 17877])).
% 2.23/2.41 tff(17879,plain,
% 2.23/2.41 (~b(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9179, 17878, 1, 17829])).
% 2.23/2.41 tff(17880,plain,
% 2.23/2.41 (r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[175, 17879])).
% 2.23/2.41 tff(17881,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9882, 17879, 16251, 15861, 16255, 17829])).
% 2.23/2.41 tff(17882,plain,
% 2.23/2.41 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[15829])).
% 2.23/2.41 tff(17883,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 2.23/2.41 inference(symmetry,[status(thm)],[17882])).
% 2.23/2.41 tff(17884,plain,
% 2.23/2.41 (r(s(z), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[656, 17883])).
% 2.23/2.41 tff(17885,plain,
% 2.23/2.41 (~r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2374, 17884, 178])).
% 2.23/2.41 tff(17886,plain,
% 2.23/2.41 (b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[374, 17885, 16267])).
% 2.23/2.41 tff(17887,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17886, 16289])).
% 2.23/2.41 tff(17888,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17758, 11375, 17691, 6255])).
% 2.23/2.41 tff(17889,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17888, 17887])).
% 2.23/2.41 tff(17890,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17891,plain,
% 2.23/2.41 (~r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17890, 17880, 17878, 2])).
% 2.23/2.41 tff(17892,plain,
% 2.23/2.41 (b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[653, 17891])).
% 2.23/2.41 tff(17893,plain,
% 2.23/2.41 (~b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10876, 17892, 17691, 17881])).
% 2.23/2.41 tff(17894,plain,
% 2.23/2.41 (r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[901, 17893])).
% 2.23/2.41 tff(17895,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4039, 17894, 17880])).
% 2.23/2.41 tff(17896,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[147, 17895, 2])).
% 2.23/2.41 tff(17897,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(17898,plain,
% 2.23/2.41 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(17899,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17898])).
% 2.23/2.41 tff(17900,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17899, 17897])).
% 2.23/2.41 tff(17901,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(17902,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17901, 17900])).
% 2.23/2.41 tff(17903,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17902, 224, 17881, 17892, 17691, 17896, 17878])).
% 2.23/2.41 tff(17904,plain,((s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17905,plain,
% 2.23/2.41 (s(s(elem!1)) = s(s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17904, 1])).
% 2.23/2.41 tff(17906,plain,
% 2.23/2.41 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[310, 17905])).
% 2.23/2.41 tff(17907,plain,
% 2.23/2.41 (s(z) = elem!1),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[131, 17906])).
% 2.23/2.41 tff(17908,plain,
% 2.23/2.41 (elem!1 = s(z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[90, 17907])).
% 2.23/2.41 tff(17909,plain,
% 2.23/2.41 (~(s(s(s(s(z)))) = elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8776, 17908])).
% 2.23/2.41 tff(17910,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9460, 17907, 17690])).
% 2.23/2.41 tff(17911,plain,
% 2.23/2.41 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17912,plain,
% 2.23/2.41 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17911])).
% 2.23/2.41 tff(17913,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17912])).
% 2.23/2.41 tff(17914,plain,
% 2.23/2.41 (b(s(z), z) <=> b(elem!1, z)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.41 tff(17915,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[1, 17914])).
% 2.23/2.41 tff(17916,plain,
% 2.23/2.41 (~b(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1126, 16531, 17690, 17915])).
% 2.23/2.41 tff(17917,plain,
% 2.23/2.41 (~b(s(elem!1), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[7872, 17916, 17907])).
% 2.23/2.41 tff(17918,plain,
% 2.23/2.41 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[7751, 17907])).
% 2.23/2.41 tff(17919,plain,
% 2.23/2.41 (~(elem!1 = s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1306, 17918])).
% 2.23/2.41 tff(17920,plain,
% 2.23/2.41 (~(s(elem!1) = s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[318, 17919])).
% 2.23/2.41 tff(17921,plain,
% 2.23/2.41 (~(s(s(elem!1)) = s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[525, 17920])).
% 2.23/2.41 tff(17922,plain,
% 2.23/2.41 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.41 tff(17923,plain,
% 2.23/2.41 ((s(s(z)) = s(z)) <=> (elem!1 = s(s(z)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17922, 2587])).
% 2.23/2.41 tff(17924,plain,
% 2.23/2.41 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.23/2.41 inference(transitivity,[status(thm)],[17923, 2588])).
% 2.23/2.41 tff(17925,plain,
% 2.23/2.41 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17924])).
% 2.23/2.41 tff(17926,plain,
% 2.23/2.41 (~(s(s(z)) = elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[210, 17925])).
% 2.23/2.41 tff(17927,plain,
% 2.23/2.41 (r(s(s(z)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1135, 17916, 17926])).
% 2.23/2.41 tff(17928,plain,
% 2.23/2.41 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17929,plain,
% 2.23/2.41 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.23/2.41 inference(transitivity,[status(thm)],[17928, 284])).
% 2.23/2.41 tff(17930,plain,
% 2.23/2.41 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17929])).
% 2.23/2.41 tff(17931,plain,
% 2.23/2.41 (~(s(s(s(z))) = elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17919, 17930])).
% 2.23/2.41 tff(17932,plain,
% 2.23/2.41 (~(s(elem!1) = elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[302, 17919])).
% 2.23/2.41 tff(17933,plain,
% 2.23/2.41 (r(s(elem!1), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[939, 17917, 17932])).
% 2.23/2.41 tff(17934,plain,
% 2.23/2.41 (r(s(s(z)), z)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[467, 16568])).
% 2.23/2.41 tff(17935,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[279, 17934])).
% 2.23/2.41 tff(17936,plain,((~r(s(elem!1), z)) | r(s(s(z)), z) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(17937,plain,
% 2.23/2.41 (~r(s(elem!1), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[17936, 279, 17905])).
% 2.23/2.41 tff(17938,plain,
% 2.23/2.41 (b(s(elem!1), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[498, 17937])).
% 2.23/2.41 tff(17939,plain,
% 2.23/2.41 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17940,plain,
% 2.23/2.41 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17939])).
% 2.23/2.41 tff(17941,plain,
% 2.23/2.41 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.41 tff(17942,plain,
% 2.23/2.41 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17941, 17940])).
% 2.23/2.41 tff(17943,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.41 tff(17944,plain,
% 2.23/2.41 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17943])).
% 2.23/2.41 tff(17945,plain,
% 2.23/2.41 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[352, 17919])).
% 2.23/2.41 tff(17946,plain,
% 2.23/2.41 (b(s(s(elem!1)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9144, 7672, 17905])).
% 2.23/2.41 tff(17947,plain,
% 2.23/2.41 (~b(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3407, 17946, 17690, 17915])).
% 2.23/2.41 tff(17948,plain,
% 2.23/2.41 (r(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 17947, 17945])).
% 2.23/2.41 tff(17949,plain,
% 2.23/2.41 (r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[16926, 17948, 17905])).
% 2.23/2.41 tff(17950,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17949, 17944])).
% 2.23/2.41 tff(17951,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.41 tff(17952,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17951])).
% 2.23/2.41 tff(17953,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17913, 17952])).
% 2.23/2.41 tff(17954,plain,
% 2.23/2.41 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17955,plain,
% 2.23/2.41 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17954])).
% 2.23/2.41 tff(17956,plain,
% 2.23/2.41 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17957,plain,
% 2.23/2.41 (s(elem!1) = s(s(z))),
% 2.23/2.41 inference(transitivity,[status(thm)],[164, 17956, 31])).
% 2.23/2.41 tff(17958,plain,
% 2.23/2.41 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.41 tff(17959,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17958])).
% 2.23/2.41 tff(17960,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[17959, 17955])).
% 2.23/2.41 tff(17961,plain,
% 2.23/2.41 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17912])).
% 2.23/2.41 tff(17962,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17961])).
% 2.23/2.41 tff(17963,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17962])).
% 2.23/2.41 tff(17964,plain,
% 2.23/2.41 (r(elem!1, s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[178, 17942])).
% 2.23/2.41 tff(17965,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(symmetry,[status(thm)],[17913])).
% 2.23/2.41 tff(17966,plain,
% 2.23/2.41 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17965])).
% 2.23/2.41 tff(17967,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17912, 17957])).
% 2.23/2.41 tff(17968,plain,
% 2.23/2.41 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[7790, 17907])).
% 2.23/2.41 tff(17969,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17970,plain,
% 2.23/2.41 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17969])).
% 2.23/2.41 tff(17971,plain,
% 2.23/2.41 (r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[178, 17970])).
% 2.23/2.41 tff(17972,plain,
% 2.23/2.41 (~b(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3407, 1240, 17690, 17915])).
% 2.23/2.41 tff(17973,plain,
% 2.23/2.41 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.41 tff(17974,plain,
% 2.23/2.41 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.23/2.41 inference(symmetry,[status(thm)],[17973])).
% 2.23/2.41 tff(17975,plain,
% 2.23/2.41 (r(z, s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[689, 17974])).
% 2.23/2.41 tff(17976,plain,
% 2.23/2.41 (r(s(s(elem!1)), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 17972, 17945])).
% 2.23/2.41 tff(17977,plain,
% 2.23/2.41 (r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[16926, 17976, 17905])).
% 2.23/2.41 tff(17978,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[17977, 17944])).
% 2.23/2.41 tff(17979,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12443, 689, 17978, 17910, 1])).
% 2.23/2.41 tff(17980,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[249, 17979])).
% 2.23/2.41 tff(17981,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[16811, 689, 17690, 17905, 17915, 17976])).
% 2.23/2.42 tff(17982,plain,
% 2.23/2.42 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3177, 17975, 656, 689, 1, 17910])).
% 2.23/2.42 tff(17983,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[306])).
% 2.23/2.42 tff(17984,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.42 inference(symmetry,[status(thm)],[17983])).
% 2.23/2.42 tff(17985,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[3318, 17984])).
% 2.23/2.42 tff(17986,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[17730, 17985])).
% 2.23/2.42 tff(17987,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(s(z)))), s(s(elem!1))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(17988,plain,
% 2.23/2.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[17987, 17982, 17905])).
% 2.23/2.42 tff(17989,plain,
% 2.23/2.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3252, 17988])).
% 2.23/2.42 tff(17990,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(symmetry,[status(thm)],[17967])).
% 2.23/2.42 tff(17991,plain,
% 2.23/2.42 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17990])).
% 2.23/2.42 tff(17992,plain,
% 2.23/2.42 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.42 tff(17993,plain,
% 2.23/2.42 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.23/2.42 inference(symmetry,[status(thm)],[17992])).
% 2.23/2.42 tff(17994,plain,
% 2.23/2.42 (r(s(s(elem!1)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[360, 354, 17945])).
% 2.23/2.42 tff(17995,plain,
% 2.23/2.42 (r(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16926, 17994, 17905])).
% 2.23/2.42 tff(17996,plain,
% 2.23/2.42 (((~![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(z)), 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(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(17997,plain,
% 2.23/2.42 (((~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(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(17998,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17997])).
% 2.23/2.42 tff(17999,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[17998, 17996])).
% 2.23/2.42 tff(18000,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(18001,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18000, 17999])).
% 2.23/2.42 tff(18002,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18001, 112, 690, 1047])).
% 2.23/2.42 tff(18003,plain,
% 2.23/2.42 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8303, 18002, 17908])).
% 2.23/2.42 tff(18004,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[530, 18003, 17921])).
% 2.23/2.42 tff(18005,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16648, 18004, 17905])).
% 2.23/2.42 tff(18006,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[13309, 18005, 2212, 1571])).
% 2.23/2.42 tff(18007,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6185, 18006])).
% 2.23/2.42 tff(18008,plain,
% 2.23/2.42 (~r(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16404, 18007, 268])).
% 2.23/2.42 tff(18009,plain,
% 2.23/2.42 (b(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16239, 18008])).
% 2.23/2.42 tff(18010,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16176, 18009, 1, 17910])).
% 2.23/2.42 tff(18011,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8884, 18010, 17908])).
% 2.23/2.42 tff(18012,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3183, 18011, 17909])).
% 2.23/2.42 tff(18013,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[15976, 112, 1047, 18012, 18007])).
% 2.23/2.42 tff(18014,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18015,plain,
% 2.23/2.42 (~r(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18014, 268, 1, 2212, 1571, 17995])).
% 2.23/2.42 tff(18016,plain,
% 2.23/2.42 (b(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1135, 18015, 17926])).
% 2.23/2.42 tff(18017,plain,
% 2.23/2.42 (b(s(elem!1), elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18016, 17993])).
% 2.23/2.42 tff(18018,plain,
% 2.23/2.42 (b(elem!1, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[541, 406, 3, 354])).
% 2.23/2.42 tff(18019,plain,
% 2.23/2.42 (~b(z, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6542, 18018, 17690, 1488])).
% 2.23/2.42 tff(18020,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[625, 18019, 959])).
% 2.23/2.42 tff(18021,plain,(b(s(s(elem!1)), s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18022,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18021, 18017, 293, 17919, 354])).
% 2.23/2.42 tff(18023,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16648, 18022, 17905])).
% 2.23/2.42 tff(18024,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.23/2.42 tff(18025,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16850, 224, 2212, 16821, 18024, 2211])).
% 2.23/2.42 tff(18026,plain,((~b(s(s(s(z))), 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(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18027,plain,
% 2.23/2.42 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18026, 18023, 16821, 2212])).
% 2.23/2.42 tff(18028,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18027, 17991])).
% 2.23/2.42 tff(18029,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1345, 18028, 17968])).
% 2.23/2.42 tff(18030,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17912])).
% 2.23/2.42 tff(18031,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(symmetry,[status(thm)],[18030])).
% 2.23/2.42 tff(18032,plain,
% 2.23/2.42 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[18031])).
% 2.23/2.42 tff(18033,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[13309, 18023, 2212, 1571])).
% 2.23/2.42 tff(18034,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6185, 18033])).
% 2.23/2.42 tff(18035,plain,
% 2.23/2.42 (~r(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16404, 18034, 268])).
% 2.23/2.42 tff(18036,plain,
% 2.23/2.42 (b(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16239, 18035])).
% 2.23/2.42 tff(18037,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16176, 18036, 1, 17910])).
% 2.23/2.42 tff(18038,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8884, 18037, 17908])).
% 2.23/2.42 tff(18039,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3183, 18038, 17909])).
% 2.23/2.42 tff(18040,plain,
% 2.23/2.42 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8833, 17908])).
% 2.23/2.42 tff(18041,plain,
% 2.23/2.42 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[17389, 18040])).
% 2.23/2.42 tff(18042,plain,
% 2.23/2.42 (((~![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))), 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)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18043,plain,
% 2.23/2.42 (((~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)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18044,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[18043])).
% 2.23/2.42 tff(18045,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[18044, 18042])).
% 2.23/2.42 tff(18046,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(18047,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18046, 18045])).
% 2.23/2.42 tff(18048,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18047, 112, 17995, 18039])).
% 2.23/2.42 tff(18049,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 2.23/2.42 tff(18050,plain,
% 2.23/2.42 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.23/2.42 inference(symmetry,[status(thm)],[18049])).
% 2.23/2.42 tff(18051,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3246, 18050])).
% 2.23/2.42 tff(18052,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18053,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16989, 68, 18052, 18048])).
% 2.23/2.42 tff(18054,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))), s(s(s(s(z)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18055,plain,
% 2.23/2.42 (((~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(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(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(s(z))))), s(s(s(s(z)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18056,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))))), s(s(s(s(z))))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[18055])).
% 2.23/2.42 tff(18057,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))), s(s(s(s(z)))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[18056, 18054])).
% 2.23/2.42 tff(18058,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(18059,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18058, 18057])).
% 2.23/2.42 tff(18060,plain,
% 2.23/2.42 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18059, 224, 1571, 7564, 16821])).
% 2.23/2.42 tff(18061,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.42 tff(18062,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.42 tff(18063,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16005, 68, 18062, 18061, 18060])).
% 2.23/2.42 tff(18064,plain,(r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (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)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18065,plain,
% 2.23/2.42 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18064, 18053, 1571, 18041, 16821])).
% 2.23/2.42 tff(18066,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.42 tff(18067,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), 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(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(z))))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18068,plain,
% 2.23/2.42 (((~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))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18069,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[18068])).
% 2.23/2.42 tff(18070,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[18069, 18067])).
% 2.23/2.42 tff(18071,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(18072,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18071, 18070])).
% 2.23/2.42 tff(18073,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18072, 112, 2274, 17013, 18066])).
% 2.23/2.42 tff(18074,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18075,plain,
% 2.23/2.42 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18074, 18065, 18039])).
% 2.23/2.42 tff(18076,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[17036, 18075, 17905])).
% 2.23/2.42 tff(18077,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1294, 18076, 17918])).
% 2.23/2.42 tff(18078,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18077, 17913])).
% 2.23/2.42 tff(18079,plain,
% 2.23/2.42 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16807, 224, 17915, 17690, 18078])).
% 2.23/2.42 tff(18080,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18079, 18032])).
% 2.23/2.42 tff(18081,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1338, 18080])).
% 2.23/2.42 tff(18082,plain,
% 2.23/2.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8096, 18081, 17908, 268])).
% 2.23/2.42 tff(18083,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8351, 18082, 18029, 17908])).
% 2.23/2.42 tff(18084,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18085,plain,
% 2.23/2.42 (~r(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18084, 17989, 17981, 1, 17980, 17975, 17972])).
% 2.23/2.42 tff(18086,plain,
% 2.23/2.42 (b(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[281, 18085])).
% 2.23/2.42 tff(18087,plain,
% 2.23/2.42 (~b(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1126, 18086, 17690, 17915])).
% 2.23/2.42 tff(18088,plain,
% 2.23/2.42 (~b(s(elem!1), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7872, 18087, 17907])).
% 2.23/2.42 tff(18089,plain,
% 2.23/2.42 (~r(s(elem!1), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[17936, 18085, 17905])).
% 2.23/2.42 tff(18090,plain,
% 2.23/2.42 (b(s(elem!1), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[498, 18089])).
% 2.23/2.42 tff(18091,plain,
% 2.23/2.42 (r(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1135, 18087, 17926])).
% 2.23/2.42 tff(18092,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18001, 112, 17977, 18091])).
% 2.23/2.42 tff(18093,plain,
% 2.23/2.42 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8303, 18092, 17908])).
% 2.23/2.42 tff(18094,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[530, 18093, 17921])).
% 2.23/2.42 tff(18095,plain,
% 2.23/2.42 (~b(z, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4320, 18094, 1240, 18090])).
% 2.23/2.42 tff(18096,plain,
% 2.23/2.42 (r(z, s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[625, 18095])).
% 2.23/2.42 tff(18097,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1340, 18096, 18088, 17915, 17690, 17918])).
% 2.23/2.42 tff(18098,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1345, 18097, 17968])).
% 2.23/2.42 tff(18099,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18098, 17967])).
% 2.23/2.42 tff(18100,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[16648, 18094, 17905])).
% 2.23/2.42 tff(18101,plain,
% 2.23/2.42 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18026, 18100, 17981, 17980])).
% 2.23/2.42 tff(18102,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18101, 18099])).
% 2.23/2.42 tff(18103,plain,((~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(18104,plain,
% 2.23/2.42 (~r(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[18103, 17971, 1, 17946])).
% 2.23/2.42 tff(18105,plain,
% 2.23/2.42 (b(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[100, 18104])).
% 2.23/2.42 tff(18106,plain,
% 2.23/2.42 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.42 tff(18107,plain,
% 2.23/2.42 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.23/2.42 inference(symmetry,[status(thm)],[18106])).
% 2.23/2.42 tff(18108,plain,
% 2.23/2.42 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.42 tff(18109,plain,
% 2.23/2.42 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.23/2.42 inference(transitivity,[status(thm)],[18108, 18107])).
% 2.23/2.42 tff(18110,plain,
% 2.23/2.42 (b(elem!1, s(elem!1))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[6298, 18109])).
% 2.23/2.42 tff(18111,plain,
% 2.23/2.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8132, 18110, 1, 17908, 7672, 17948, 18105, 178])).
% 2.23/2.42 tff(18112,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8351, 18111, 17908])).
% 2.23/2.42 tff(18113,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1345, 18112, 17968])).
% 2.23/2.42 tff(18114,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[18113, 17967])).
% 2.23/2.42 tff(18115,plain,
% 2.23/2.42 (r(elem!1, s(s(s(z))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[178, 17941])).
% 2.23/2.42 tff(18116,plain,
% 2.23/2.42 (~r(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9273, 112, 196, 18115])).
% 2.23/2.42 tff(18117,plain,
% 2.23/2.42 (b(s(s(z)), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1135, 18116, 17926])).
% 2.23/2.42 tff(18118,plain,
% 2.23/2.42 (b(elem!1, s(s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[6298, 18108])).
% 2.23/2.42 tff(18119,plain,
% 2.23/2.42 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(18120,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[18119])).
% 2.23/2.42 tff(18121,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18120, 17044])).
% 2.23/2.43 tff(18122,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(18123,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18122, 18121])).
% 2.23/2.43 tff(18124,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18123, 224, 18118, 18117, 18114])).
% 2.23/2.43 tff(18125,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18124, 17966])).
% 2.23/2.43 tff(18126,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1294, 18125, 17918])).
% 2.23/2.43 tff(18127,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14725, 18126, 17907, 17964])).
% 2.23/2.43 tff(18128,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1884, 18127])).
% 2.23/2.43 tff(18129,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18128, 17963])).
% 2.23/2.43 tff(18130,plain,
% 2.23/2.43 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5300, 18117, 17690, 17915, 18118])).
% 2.23/2.43 tff(18131,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3183, 18130, 17909])).
% 2.23/2.43 tff(18132,plain,
% 2.23/2.43 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18047, 112, 17949, 18131])).
% 2.23/2.43 tff(18133,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16989, 68, 18052, 18132])).
% 2.23/2.43 tff(18134,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8890, 18131, 17908])).
% 2.23/2.43 tff(18135,plain,
% 2.23/2.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3326, 18134, 17950])).
% 2.23/2.43 tff(18136,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3252, 18135])).
% 2.23/2.43 tff(18137,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[17036, 18126, 17905])).
% 2.23/2.43 tff(18138,plain,
% 2.23/2.43 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18074, 18137, 18131])).
% 2.23/2.43 tff(18139,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18064, 18138, 18136, 18133, 18041])).
% 2.23/2.43 tff(18140,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18139, 18129])).
% 2.23/2.43 tff(18141,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(18142,plain,
% 2.23/2.43 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18141, 178, 7672, 1])).
% 2.23/2.43 tff(18143,plain,
% 2.23/2.43 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[249, 18142])).
% 2.23/2.43 tff(18144,plain,
% 2.23/2.43 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18143, 17960])).
% 2.23/2.43 tff(18145,plain,
% 2.23/2.43 (~b(s(s(z)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16299, 18105, 1, 17910, 7672])).
% 2.23/2.43 tff(18146,plain,
% 2.23/2.43 (r(s(s(z)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[281, 18145])).
% 2.23/2.43 tff(18147,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8890, 2274, 78])).
% 2.23/2.43 tff(18148,plain,
% 2.23/2.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3326, 18147, 3188])).
% 2.23/2.43 tff(18149,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3252, 18148])).
% 2.23/2.43 tff(18150,plain,
% 2.23/2.43 (~b(s(s(s(s(z)))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16972, 224, 6255, 7672, 18149])).
% 2.23/2.43 tff(18151,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16239, 18150])).
% 2.23/2.43 tff(18152,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18153,plain,
% 2.23/2.43 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18154,plain,
% 2.23/2.43 (((~![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)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[18153])).
% 2.23/2.43 tff(18155,plain,
% 2.23/2.43 (((~![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)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18154, 18152])).
% 2.23/2.43 tff(18156,plain,
% 2.23/2.43 ((~![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)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(18157,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18156, 18155])).
% 2.23/2.43 tff(18158,plain,
% 2.23/2.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18157, 112, 18151, 268])).
% 2.23/2.43 tff(18159,plain,
% 2.23/2.43 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18047, 112, 690, 2274])).
% 2.23/2.43 tff(18160,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16989, 68, 18052, 18159])).
% 2.23/2.43 tff(18161,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18162,plain,
% 2.23/2.43 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18163,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(s(z))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[18162])).
% 2.23/2.43 tff(18164,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(s(z)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18163, 18161])).
% 2.23/2.43 tff(18165,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(18166,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18165, 18164])).
% 2.23/2.43 tff(18167,plain,
% 2.23/2.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18166, 224, 2212, 18149, 18160])).
% 2.23/2.43 tff(18168,plain,
% 2.23/2.43 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[17362, 68, 18167])).
% 2.23/2.43 tff(18169,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18168, 18158, 17352])).
% 2.23/2.43 tff(18170,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(18171,plain,
% 2.23/2.43 (~r(s(s(s(s(z)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18170, 18146, 18143, 18105, 7672, 17949, 17950, 17908])).
% 2.23/2.43 tff(18172,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3183, 18171, 17909])).
% 2.23/2.43 tff(18173,plain,
% 2.23/2.43 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.43 tff(18174,plain,
% 2.23/2.43 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[2212, 17960])).
% 2.23/2.43 tff(18175,plain,
% 2.23/2.43 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.43 tff(18176,plain,
% 2.23/2.43 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.23/2.43 inference(symmetry,[status(thm)],[18175])).
% 2.23/2.43 tff(18177,plain,
% 2.23/2.43 (~r(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18103, 656, 1, 17946])).
% 2.23/2.43 tff(18178,plain,
% 2.23/2.43 (b(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[100, 18177])).
% 2.23/2.43 tff(18179,plain,
% 2.23/2.43 (b(z, s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18178, 18176])).
% 2.23/2.43 tff(18180,plain,
% 2.23/2.43 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.43 tff(18181,plain,
% 2.23/2.43 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[18180])).
% 2.23/2.43 tff(18182,plain,
% 2.23/2.43 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.43 tff(18183,plain,
% 2.23/2.43 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[18182])).
% 2.23/2.43 tff(18184,plain,
% 2.23/2.43 (r(elem!1, s(s(z))) <=> r(s(z), s(elem!1))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18183, 18181])).
% 2.23/2.43 tff(18185,plain,
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% 2.23/2.43 inference(monotonicity,[status(thm)],[17923])).
% 2.23/2.43 tff(18186,plain,
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% 2.23/2.43 inference(modus_ponens,[status(thm)],[210, 18185])).
% 2.23/2.43 tff(18187,plain,
% 2.23/2.43 (~b(elem!1, s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5300, 5274, 17690, 17915, 1109])).
% 2.23/2.43 tff(18188,plain,
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[2874, 18187, 18186])).
% 2.23/2.43 tff(18189,plain,
% 2.23/2.43 (r(s(z), s(elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18188, 18184])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[664, 18189, 656])).
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% 2.23/2.43 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[530, 18190, 17921])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[4124, 18191, 18179, 18174])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[625, 18192])).
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% 2.23/2.43 inference(modus_ponens,[status(thm)],[18193, 18173])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[8078, 18194, 1, 17908, 7672, 17948])).
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% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8351, 18195, 17908])).
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% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1345, 18196, 17968])).
% 2.23/2.43 tff(18198,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18197, 17967])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[16299, 18178, 1, 17910, 7672])).
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% 2.23/2.43 inference(unit_resolution,[status(thm)],[281, 18199])).
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% 2.23/2.43 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8884, 5274, 17908])).
% 2.23/2.43 tff(18202,plain,
% 2.23/2.43 (~b(s(s(s(s(z)))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16176, 18201, 1, 17910])).
% 2.23/2.43 tff(18203,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16239, 18202])).
% 2.23/2.43 tff(18204,plain,
% 2.23/2.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16404, 18203, 18200])).
% 2.23/2.43 tff(18205,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6185, 18204])).
% 2.23/2.43 tff(18206,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18207,plain,
% 2.23/2.43 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(z)))))))) <=> ((~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18208,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[18207])).
% 2.23/2.43 tff(18209,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18208, 18206])).
% 2.23/2.43 tff(18210,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(z))))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(18211,plain,
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% 2.23/2.43 inference(modus_ponens,[status(thm)],[18210, 18209])).
% 2.23/2.43 tff(18212,plain,
% 2.23/2.43 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18211, 224, 1109, 5274, 18205, 18198])).
% 2.23/2.43 tff(18213,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8869, 68, 18040, 18212])).
% 2.23/2.43 tff(18214,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17961])).
% 2.23/2.43 tff(18215,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(symmetry,[status(thm)],[18214])).
% 2.23/2.43 tff(18216,plain,
% 2.23/2.43 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[17962])).
% 2.23/2.43 tff(18217,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16648, 18191, 17905])).
% 2.23/2.43 tff(18218,plain,
% 2.23/2.43 (((~b(s(s(s(z))), 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(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(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(18219,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[18218])).
% 2.23/2.43 tff(18220,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[18219, 16845])).
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% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
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% 2.23/2.43 inference(modus_ponens,[status(thm)],[18221, 18220])).
% 2.23/2.43 tff(18223,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18222, 224, 2212, 18198, 18217])).
% 2.23/2.43 tff(18224,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18223, 18216])).
% 2.23/2.43 tff(18225,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1884, 18224])).
% 2.23/2.43 tff(18226,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18225, 18215])).
% 2.23/2.43 tff(18227,plain,
% 2.23/2.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[13309, 18217, 2212, 18205])).
% 2.23/2.43 tff(18228,plain,
% 2.23/2.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[3252, 18227])).
% 2.23/2.43 tff(18229,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[17156, 112, 18228, 18226, 18213])).
% 2.23/2.43 tff(18230,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(18231,plain,
% 2.23/2.43 (~b(s(s(z)), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18230, 18172, 18143, 1, 7672, 17971])).
% 2.23/2.43 tff(18232,plain,
% 2.23/2.43 (~b(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7872, 18231, 17907])).
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% 2.23/2.43 (r(s(elem!1), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[939, 18232, 17932])).
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% 2.23/2.43 (r(s(s(z)), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1135, 18231, 17926])).
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% 2.23/2.43 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18001, 112, 17949, 18234])).
% 2.23/2.43 tff(18236,plain,
% 2.23/2.43 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8303, 18235, 17908])).
% 2.23/2.43 tff(18237,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[530, 18236, 17921])).
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% 2.23/2.43 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[14736, 18237, 17907, 17964, 18233, 18144])).
% 2.23/2.43 tff(18239,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1294, 18238, 17918])).
% 2.23/2.43 tff(18240,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18239, 17953])).
% 2.23/2.43 tff(18241,plain,
% 2.23/2.43 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8884, 18172, 17908])).
% 2.23/2.43 tff(18242,plain,
% 2.23/2.43 (elem!1 = s(z)),
% 2.23/2.43 inference(symmetry,[status(thm)],[17907])).
% 2.23/2.43 tff(18243,plain,
% 2.23/2.43 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[18242, 17912])).
% 2.23/2.43 tff(18244,plain,
% 2.23/2.43 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1407, 17918])).
% 2.23/2.43 tff(18245,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[16648, 18237, 17905])).
% 2.23/2.43 tff(18246,plain,
% 2.23/2.43 (b(z, s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18105, 18176])).
% 2.23/2.43 tff(18247,plain,
% 2.23/2.43 (~b(z, s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[4124, 18237, 18246, 18144])).
% 2.23/2.43 tff(18248,plain,
% 2.23/2.43 (r(z, s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[625, 18247])).
% 2.23/2.43 tff(18249,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1340, 18248, 18232, 17915, 17690, 17918])).
% 2.23/2.43 tff(18250,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1345, 18249, 17968])).
% 2.23/2.43 tff(18251,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18250, 17967])).
% 2.23/2.43 tff(18252,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[18222, 224, 18143, 18251, 18245])).
% 2.23/2.43 tff(18253,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18252, 18216])).
% 2.23/2.43 tff(18254,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1884, 18253])).
% 2.23/2.43 tff(18255,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[18254, 18215])).
% 2.23/2.43 tff(18256,plain,
% 2.23/2.43 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8786, 18255, 178])).
% 2.23/2.44 tff(18257,plain,
% 2.23/2.44 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8812, 18256, 17908])).
% 2.23/2.44 tff(18258,plain,
% 2.23/2.44 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1439, 18257, 18244])).
% 2.23/2.44 tff(18259,plain,
% 2.23/2.44 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18258, 18243])).
% 2.23/2.44 tff(18260,plain,
% 2.23/2.44 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18239, 17913])).
% 2.23/2.44 tff(18261,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16807, 224, 17915, 17690, 18260])).
% 2.23/2.44 tff(18262,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 18261])).
% 2.23/2.44 tff(18263,plain,
% 2.23/2.44 (~b(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16176, 18241, 1, 17910])).
% 2.23/2.44 tff(18264,plain,
% 2.23/2.44 (r(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16239, 18263])).
% 2.23/2.44 tff(18265,plain,
% 2.23/2.44 (((~![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(z)))), z)) | (~r(s(s(s(s(s(z))))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(18266,plain,
% 2.23/2.44 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(18267,plain,
% 2.23/2.44 (((~![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))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[18266])).
% 2.23/2.44 tff(18268,plain,
% 2.23/2.44 (((~![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))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[18267, 18265])).
% 2.23/2.44 tff(18269,plain,
% 2.23/2.44 ((~![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))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(18270,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18269, 18268])).
% 2.23/2.44 tff(18271,plain,
% 2.23/2.44 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18270, 112, 18264, 18262])).
% 2.23/2.44 tff(18272,plain,
% 2.23/2.44 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8869, 68, 18040, 18271])).
% 2.23/2.44 tff(18273,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14659, 18272, 18259, 18241, 18240])).
% 2.23/2.44 tff(18274,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(18275,plain,
% 2.23/2.44 (~r(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18274, 7672, 1])).
% 2.23/2.44 tff(18276,plain,
% 2.23/2.44 (b(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[175, 18275])).
% 2.23/2.44 tff(18277,plain,
% 2.23/2.44 (~b(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9179, 18276, 1, 7672])).
% 2.23/2.44 tff(18278,plain,
% 2.23/2.44 (r(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[100, 18277])).
% 2.23/2.44 tff(18279,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12443, 18278, 17950, 17910, 1])).
% 2.23/2.44 tff(18280,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[15956, 18276, 17907])).
% 2.23/2.44 tff(18281,plain,
% 2.23/2.44 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16811, 18278, 17690, 17905, 17915, 17948])).
% 2.23/2.44 tff(18282,plain,
% 2.23/2.44 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16865, 18281, 17905, 17919, 7672, 17915, 17947, 18280])).
% 2.23/2.44 tff(18283,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[249, 18282, 18279])).
% 2.23/2.44 tff(18284,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(18285,plain,
% 2.23/2.44 (~b(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18284, 1])).
% 2.23/2.44 tff(18286,plain,
% 2.23/2.44 (r(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[72, 18285])).
% 2.23/2.44 tff(18287,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18288,plain,
% 2.23/2.44 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.23/2.44 inference(symmetry,[status(thm)],[18287])).
% 2.23/2.44 tff(18289,plain,
% 2.23/2.44 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.44 tff(18290,plain,
% 2.23/2.44 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.23/2.44 inference(symmetry,[status(thm)],[18289])).
% 2.23/2.44 tff(18291,plain,
% 2.23/2.44 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.23/2.44 inference(transitivity,[status(thm)],[18290, 18288])).
% 2.23/2.44 tff(18292,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(z))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[787, 18291])).
% 2.23/2.44 tff(18293,plain,
% 2.23/2.44 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18294,plain,
% 2.23/2.44 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.23/2.44 inference(symmetry,[status(thm)],[18293])).
% 2.23/2.44 tff(18295,plain,
% 2.23/2.44 (r(s(s(elem!1)), z)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[177, 18294])).
% 2.23/2.44 tff(18296,plain,
% 2.23/2.44 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18297,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.23/2.44 inference(symmetry,[status(thm)],[18296])).
% 2.23/2.44 tff(18298,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[15956, 1090, 17907])).
% 2.23/2.44 tff(18299,plain,
% 2.23/2.44 (b(elem!1, s(s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18298, 18297])).
% 2.23/2.44 tff(18300,plain,
% 2.23/2.44 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18301,plain,
% 2.23/2.44 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.23/2.44 inference(symmetry,[status(thm)],[18300])).
% 2.23/2.44 tff(18302,plain,
% 2.23/2.44 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[18301])).
% 2.23/2.44 tff(18303,plain,
% 2.23/2.44 (~(s(s(z)) = s(s(elem!1)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[55, 18302])).
% 2.23/2.44 tff(18304,plain,
% 2.23/2.44 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18305,plain,
% 2.23/2.44 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.23/2.44 inference(symmetry,[status(thm)],[18304])).
% 2.23/2.44 tff(18306,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.23/2.44 inference(transitivity,[status(thm)],[18287, 18289, 18305])).
% 2.23/2.44 tff(18307,plain,
% 2.23/2.44 (b(s(s(elem!1)), elem!1)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[1241, 18306])).
% 2.23/2.44 tff(18308,plain,
% 2.23/2.44 (~b(s(s(z)), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1130, 18307, 17690, 18303, 18299, 17915, 18295])).
% 2.23/2.44 tff(18309,plain,
% 2.23/2.44 (~b(s(elem!1), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[7872, 18308, 17907])).
% 2.23/2.44 tff(18310,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.44 inference(transitivity,[status(thm)],[18287, 18289])).
% 2.23/2.44 tff(18311,plain,
% 2.23/2.44 (b(s(s(s(z))), elem!1)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[1241, 18310])).
% 2.23/2.44 tff(18312,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[15963, 224, 685, 787, 17374])).
% 2.23/2.44 tff(18313,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18312, 15909])).
% 2.23/2.44 tff(18314,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1884, 18313])).
% 2.23/2.44 tff(18315,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18314, 15907])).
% 2.23/2.44 tff(18316,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16807, 224, 405, 17690, 17374])).
% 2.23/2.44 tff(18317,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 18316])).
% 2.23/2.44 tff(18318,plain,
% 2.23/2.44 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16019, 18317, 177])).
% 2.23/2.44 tff(18319,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18318, 18315])).
% 2.23/2.44 tff(18320,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(18321,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18320, 18311, 177, 18298, 17905, 17915])).
% 2.23/2.44 tff(18322,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18321, 17966])).
% 2.23/2.44 tff(18323,plain,
% 2.23/2.44 (b(s(s(s(z))), s(z))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[1241, 18287])).
% 2.23/2.44 tff(18324,plain,
% 2.23/2.44 (~b(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16176, 1570, 1, 17910])).
% 2.23/2.44 tff(18325,plain,
% 2.23/2.44 (r(s(s(s(s(z)))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16239, 18324])).
% 2.23/2.44 tff(18326,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16077, 112, 177, 18325, 6196])).
% 2.23/2.44 tff(18327,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(18328,plain,
% 2.23/2.44 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18327, 18323, 1, 1090, 177])).
% 2.23/2.44 tff(18329,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[8884, 18328, 17908])).
% 2.23/2.44 tff(18330,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[3183, 18329, 17909])).
% 2.23/2.44 tff(18331,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[17036, 15927, 306])).
% 2.23/2.44 tff(18332,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[939, 1287, 17265])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[10270, 15927, 18333])).
% 2.23/2.44 tff(18335,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[1869, 18334, 16635])).
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% 2.23/2.44 inference(modus_ponens,[status(thm)],[18335, 16634])).
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% 2.23/2.44 inference(rewrite,[status(thm)],[])).
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% 2.23/2.44 inference(rewrite,[status(thm)],[])).
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% 2.23/2.44 inference(monotonicity,[status(thm)],[18338])).
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% 2.23/2.44 inference(modus_ponens,[status(thm)],[18341, 18340])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[18342, 224, 5188, 15940, 18336])).
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% 2.23/2.44 tff(18346,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[18345, 18330, 18322, 17905, 18309])).
% 2.23/2.44 tff(18347,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[6185, 18346])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[1135, 18308, 17926])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[15976, 112, 18348, 18330, 18347])).
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% 2.23/2.44 tff(18351,plain,
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[18350, 18292, 18286, 1])).
% 2.23/2.44 tff(18352,plain,
% 2.23/2.44 (r(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[175, 18351])).
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% 2.23/2.44 inference(modus_ponens,[status(thm)],[18352, 17942])).
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% 2.23/2.44 (r(s(s(elem!1)), z)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18286, 18294])).
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% 2.23/2.44 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.44 tff(18356,plain,
% 2.23/2.44 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.23/2.44 inference(symmetry,[status(thm)],[18355])).
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% 2.23/2.44 inference(modus_ponens,[status(thm)],[196, 18356])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[276, 18357, 18354])).
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[281, 18358])).
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% 2.23/2.44 (~r(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[243, 196, 18286, 17910, 1])).
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% 2.23/2.44 (b(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[175, 18360])).
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% 2.23/2.44 (~b(s(s(elem!1)), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18350, 18361, 18286, 1])).
% 2.23/2.44 tff(18363,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(z))),
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% 2.23/2.44 inference(unit_resolution,[status(thm)],[2993, 18357, 18363])).
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% 2.23/2.44 tff(18368,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18367, 1])).
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% 2.23/2.44 (b(s(s(z)), s(s(s(z))))),
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% 2.23/2.44 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
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% 2.23/2.44 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(z))))))),
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% 2.23/2.44 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
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% 2.23/2.44 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
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% 2.23/2.44 inference(monotonicity,[status(thm)],[18373])).
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% 2.23/2.44 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
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% 2.23/2.44 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
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% 2.23/2.44 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
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% 2.23/2.44 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
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% 2.23/2.44 tff(18388,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
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% 2.23/2.44 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
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% 2.23/2.44 tff(18393,plain,
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% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(18398,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18397, 18396])).
% 2.23/2.44 tff(18399,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18398, 224, 405, 17690, 18393])).
% 2.23/2.44 tff(18400,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18399, 18387])).
% 2.23/2.44 tff(18401,plain,
% 2.23/2.44 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14725, 16782, 15899, 545])).
% 2.23/2.44 tff(18402,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1294, 18401, 15926])).
% 2.23/2.44 tff(18403,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18402, 18400])).
% 2.23/2.44 tff(18404,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(18405,plain,
% 2.23/2.44 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18404, 545, 306, 405, 177])).
% 2.23/2.44 tff(18406,plain,
% 2.23/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[16648, 18380, 306])).
% 2.23/2.44 tff(18407,plain,
% 2.23/2.44 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[18026, 18406, 18405, 2212])).
% 2.23/2.44 tff(18408,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18407, 16834])).
% 2.23/2.44 tff(18409,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1345, 18408, 15937])).
% 2.23/2.44 tff(18410,plain,
% 2.23/2.44 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8351, 18409, 15900])).
% 2.23/2.44 tff(18411,plain,
% 2.23/2.44 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[15915])).
% 2.23/2.44 tff(18412,plain,
% 2.23/2.44 (b(z, s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9460, 15899, 17690])).
% 2.23/2.44 tff(18413,plain,
% 2.23/2.44 (~b(elem!1, s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[14870, 10122, 18412, 17264, 16652, 408])).
% 2.23/2.44 tff(18414,plain,
% 2.23/2.44 (r(elem!1, s(elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[515, 18413, 17266])).
% 2.23/2.44 tff(18415,plain,
% 2.23/2.44 (r(elem!1, s(s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[18414, 18411])).
% 2.23/2.44 tff(18416,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18417,plain,
% 2.23/2.45 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18418,plain,
% 2.23/2.45 (((~![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(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18417])).
% 2.23/2.45 tff(18419,plain,
% 2.23/2.45 (((~![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(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[18418, 18416])).
% 2.23/2.45 tff(18420,plain,
% 2.23/2.45 ((~![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(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18421,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18420, 18419])).
% 2.23/2.45 tff(18422,plain,
% 2.23/2.45 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18421, 112, 18415, 18410, 18385])).
% 2.23/2.45 tff(18423,plain,
% 2.23/2.45 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18422, 18374])).
% 2.23/2.45 tff(18424,plain,
% 2.23/2.45 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1439, 18423, 16815])).
% 2.23/2.45 tff(18425,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18424, 16816])).
% 2.23/2.45 tff(18426,plain,
% 2.23/2.45 (b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18425, 18370])).
% 2.23/2.45 tff(18427,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[15905])).
% 2.23/2.45 tff(18428,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18427])).
% 2.23/2.45 tff(18429,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[15905])).
% 2.23/2.45 tff(18430,plain,
% 2.23/2.45 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18429])).
% 2.23/2.45 tff(18431,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18432,plain,
% 2.23/2.45 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18433,plain,
% 2.23/2.45 (((~![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(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18432])).
% 2.23/2.45 tff(18434,plain,
% 2.23/2.45 (((~![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(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.23/2.45 inference(transitivity,[status(thm)],[18433, 18431])).
% 2.23/2.45 tff(18435,plain,
% 2.23/2.45 ((~![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(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18436,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18435, 18434])).
% 2.23/2.45 tff(18437,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18436, 112, 177, 18385])).
% 2.23/2.45 tff(18438,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18437, 18430])).
% 2.23/2.45 tff(18439,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5426, 18438])).
% 2.23/2.45 tff(18440,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18439, 18428])).
% 2.23/2.45 tff(18441,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18442,plain,
% 2.23/2.45 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(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)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18443,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18442])).
% 2.23/2.45 tff(18444,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[18443, 18441])).
% 2.23/2.45 tff(18445,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18446,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18445, 18444])).
% 2.23/2.45 tff(18447,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18446, 224, 787, 18383, 18440, 18426])).
% 2.23/2.45 tff(18448,plain,(r(s(s(elem!1)), s(elem!1)) | (~b(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(18449,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18448, 787, 17905, 18286, 17915, 18369, 18353, 408])).
% 2.23/2.45 tff(18450,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8303, 18449, 17908])).
% 2.23/2.45 tff(18451,plain,
% 2.23/2.45 (~(elem!1 = s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[326, 17932])).
% 2.23/2.45 tff(18452,plain,
% 2.23/2.45 (~r(elem!1, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[553, 18449, 18353])).
% 2.23/2.45 tff(18453,plain,
% 2.23/2.45 (b(elem!1, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[515, 18452, 18451])).
% 2.23/2.45 tff(18454,plain,
% 2.23/2.45 (~b(z, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[509, 18453, 17915, 500])).
% 2.23/2.45 tff(18455,plain,
% 2.23/2.45 (r(z, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[625, 18454])).
% 2.23/2.45 tff(18456,plain,
% 2.23/2.45 (r(z, s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18455, 18173])).
% 2.23/2.45 tff(18457,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8318, 112, 18286, 18456, 18450])).
% 2.23/2.45 tff(18458,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(18459,plain,
% 2.23/2.45 (~b(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18458, 17938, 17933, 1])).
% 2.23/2.45 tff(18460,plain,
% 2.23/2.45 (r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[374, 18459, 17931])).
% 2.23/2.45 tff(18461,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18001, 112, 18460, 17927])).
% 2.23/2.45 tff(18462,plain,
% 2.23/2.45 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8303, 18461, 17908])).
% 2.23/2.45 tff(18463,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[530, 18462, 17921])).
% 2.23/2.45 tff(18464,plain,
% 2.23/2.45 ((s(z) = z) <=> (elem!1 = z)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.45 tff(18465,plain,
% 2.23/2.45 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18464])).
% 2.23/2.45 tff(18466,plain,
% 2.23/2.45 (~(elem!1 = z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[190, 18465])).
% 2.23/2.45 tff(18467,plain,
% 2.23/2.45 (~b(elem!1, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[14870, 18462, 17910, 17919, 18466, 17933])).
% 2.23/2.45 tff(18468,plain,
% 2.23/2.45 (r(elem!1, s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[515, 18467, 18451])).
% 2.23/2.45 tff(18469,plain,
% 2.23/2.45 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[7239, 17919])).
% 2.23/2.45 tff(18470,plain,
% 2.23/2.45 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[17928])).
% 2.23/2.45 tff(18471,plain,
% 2.23/2.45 (~(elem!1 = s(s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[17919, 18470])).
% 2.23/2.45 tff(18472,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 2.23/2.45 tff(18473,plain,
% 2.23/2.45 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18472])).
% 2.23/2.45 tff(18474,plain,
% 2.23/2.45 (s(z) = s(s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[86, 18473])).
% 2.23/2.45 tff(18475,plain,
% 2.23/2.45 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18474])).
% 2.23/2.45 tff(18476,plain,
% 2.23/2.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18475])).
% 2.23/2.45 tff(18477,plain,
% 2.23/2.45 (s(s(s(s(s(s(z)))))) = z),
% 2.23/2.45 inference(transitivity,[status(thm)],[1706, 18476, 27])).
% 2.23/2.45 tff(18478,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1851, 18477])).
% 2.23/2.45 tff(18479,plain,((~(s(z) = elem!1)) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(18480,plain,
% 2.23/2.45 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18479, 17907])).
% 2.23/2.45 tff(18481,plain,
% 2.23/2.45 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18369, 17960])).
% 2.23/2.45 tff(18482,plain,
% 2.23/2.45 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.45 inference(symmetry,[status(thm)],[17905])).
% 2.23/2.45 tff(18483,plain,
% 2.23/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18482])).
% 2.23/2.45 tff(18484,plain,
% 2.23/2.45 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18483])).
% 2.23/2.45 tff(18485,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))), introduced(assumption)).
% 2.23/2.45 tff(18486,plain,
% 2.23/2.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(z))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18485])).
% 2.23/2.45 tff(18487,plain,
% 2.23/2.45 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 2.23/2.45 inference(transitivity,[status(thm)],[1706, 18486, 31])).
% 2.23/2.45 tff(18488,plain,
% 2.23/2.45 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18487])).
% 2.23/2.45 tff(18489,plain,
% 2.23/2.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18488])).
% 2.23/2.45 tff(18490,plain,
% 2.23/2.45 (s(z) = s(s(s(s(elem!1))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[50, 18489, 292, 7737])).
% 2.23/2.45 tff(18491,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1364, 18490])).
% 2.23/2.45 tff(18492,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(18493,plain,
% 2.23/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18492, 17908])).
% 2.23/2.45 tff(18494,plain,
% 2.23/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18493, 18484])).
% 2.23/2.45 tff(18495,plain,
% 2.23/2.45 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.45 tff(18496,plain,
% 2.23/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18495])).
% 2.23/2.45 tff(18497,plain,
% 2.23/2.45 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18496])).
% 2.23/2.45 tff(18498,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(z))), introduced(assumption)).
% 2.23/2.45 tff(18499,plain,
% 2.23/2.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18498])).
% 2.23/2.45 tff(18500,plain,
% 2.23/2.45 (s(s(s(s(s(s(z)))))) = s(z)),
% 2.23/2.45 inference(transitivity,[status(thm)],[1706, 18499, 49])).
% 2.23/2.45 tff(18501,plain,
% 2.23/2.45 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18500])).
% 2.23/2.45 tff(18502,plain,
% 2.23/2.45 (s(s(s(s(s(z))))) = z),
% 2.23/2.45 inference(transitivity,[status(thm)],[1709, 18501, 27])).
% 2.23/2.45 tff(18503,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8795, 18502])).
% 2.23/2.45 tff(18504,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(18505,plain,
% 2.23/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18504, 18497])).
% 2.23/2.45 tff(18506,plain,
% 2.23/2.45 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.45 tff(18507,plain,
% 2.23/2.45 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.23/2.45 inference(symmetry,[status(thm)],[18506])).
% 2.23/2.45 tff(18508,plain,
% 2.23/2.45 (r(s(s(elem!1)), elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18460, 18507])).
% 2.23/2.45 tff(18509,plain,
% 2.23/2.45 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11016, 18463, 18508, 17933, 18505, 18494, 18481])).
% 2.23/2.45 tff(18510,plain,
% 2.23/2.45 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1777, 18509, 18480])).
% 2.23/2.45 tff(18511,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18512,plain,
% 2.23/2.45 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18513,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18512])).
% 2.23/2.45 tff(18514,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.23/2.45 inference(transitivity,[status(thm)],[18513, 18511])).
% 2.23/2.45 tff(18515,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18516,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18515, 18514])).
% 2.23/2.45 tff(18517,plain,
% 2.23/2.45 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18516, 224, 17915, 17690, 18510])).
% 2.23/2.45 tff(18518,plain,
% 2.23/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18519,plain,
% 2.23/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18520,plain,
% 2.23/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18519, 18518])).
% 2.23/2.45 tff(18521,plain,
% 2.23/2.45 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18520, 68, 1614, 18517])).
% 2.23/2.45 tff(18522,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), 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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18523,plain,
% 2.23/2.45 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18524,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18523])).
% 2.23/2.45 tff(18525,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[18524, 18522])).
% 2.23/2.45 tff(18526,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18527,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18526, 18525])).
% 2.23/2.45 tff(18528,plain,
% 2.23/2.45 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18527, 112, 18460, 18286, 18521])).
% 2.23/2.45 tff(18529,plain,
% 2.23/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(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)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(18530,plain,
% 2.23/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(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)))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(18531,plain,
% 2.23/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(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))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[18530, 18529])).
% 2.23/2.45 tff(18532,plain,
% 2.23/2.45 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[18531, 68, 18493, 18528])).
% 2.23/2.45 tff(18533,plain,
% 2.23/2.45 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.23/2.45 inference(commutativity,[status(thm)],[])).
% 2.23/2.45 tff(18534,plain,
% 2.23/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[18533])).
% 2.23/2.45 tff(18535,plain,
% 2.23/2.45 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[18534])).
% 2.23/2.45 tff(18536,plain,
% 2.23/2.45 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18493, 18535])).
% 2.23/2.46 tff(18537,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18538,plain,
% 2.23/2.46 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18539,plain,
% 2.23/2.46 (((~![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))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18538])).
% 2.23/2.46 tff(18540,plain,
% 2.23/2.46 (((~![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))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[18539, 18537])).
% 2.23/2.46 tff(18541,plain,
% 2.23/2.46 ((~![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))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18542,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18541, 18540])).
% 2.23/2.46 tff(18543,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18542, 112, 18286, 18521])).
% 2.23/2.46 tff(18544,plain,
% 2.23/2.46 (((~![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)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18545,plain,
% 2.23/2.46 ((~![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)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18546,plain,
% 2.23/2.46 ((~![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))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18545, 18544])).
% 2.23/2.46 tff(18547,plain,
% 2.23/2.46 ((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))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18546, 68, 18543])).
% 2.23/2.46 tff(18548,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18547, 18536])).
% 2.23/2.46 tff(18549,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[16648, 18463, 17905])).
% 2.23/2.46 tff(18550,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18551,plain,
% 2.23/2.46 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(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(z)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18552,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18551])).
% 2.23/2.46 tff(18553,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[18552, 18550])).
% 2.23/2.46 tff(18554,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18555,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18554, 18553])).
% 2.23/2.46 tff(18556,plain,
% 2.23/2.46 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18555, 224, 18369, 18549, 18532])).
% 2.23/2.46 tff(18557,plain,
% 2.23/2.46 (((~![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))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18558,plain,
% 2.23/2.46 ((~![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))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18559,plain,
% 2.23/2.46 ((~![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)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18558, 18557])).
% 2.23/2.46 tff(18560,plain,
% 2.23/2.46 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18559, 68, 18504, 18556])).
% 2.23/2.46 tff(18561,plain,
% 2.23/2.46 (r(elem!1, s(s(z)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18468, 18182])).
% 2.23/2.46 tff(18562,plain,
% 2.23/2.46 (((~![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(z)))) | (~r(elem!1, s(s(s(s(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(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18563,plain,
% 2.23/2.46 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18564,plain,
% 2.23/2.46 (((~![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(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18563])).
% 2.23/2.46 tff(18565,plain,
% 2.23/2.46 (((~![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(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~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(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[18564, 18562])).
% 2.23/2.46 tff(18566,plain,
% 2.23/2.46 ((~![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(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18567,plain,
% 2.23/2.46 ((~![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(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18566, 18565])).
% 2.23/2.46 tff(18568,plain,
% 2.23/2.46 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18567, 112, 18561, 18560])).
% 2.23/2.46 tff(18569,plain,
% 2.23/2.46 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[7142, 18480])).
% 2.23/2.46 tff(18570,plain,
% 2.23/2.46 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2014, 68, 18569, 18568])).
% 2.23/2.46 tff(18571,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18572,plain,
% 2.23/2.46 (((~b(s(s(s(z))), 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))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(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))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18573,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))), s(s(s(s(s(s(s(z)))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18572])).
% 2.23/2.46 tff(18574,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[18573, 18571])).
% 2.23/2.46 tff(18575,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18576,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))), s(s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18575, 18574])).
% 2.23/2.46 tff(18577,plain,
% 2.23/2.46 (~b(elem!1, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18576, 224, 18570, 18548, 18532])).
% 2.23/2.46 tff(18578,plain,
% 2.23/2.46 (r(elem!1, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[388, 18577, 18471])).
% 2.23/2.46 tff(18579,plain,
% 2.23/2.46 (r(elem!1, s(s(elem!1)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18578, 17940])).
% 2.23/2.46 tff(18580,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[14114, 18579, 17968, 18469, 18468, 17933, 17920, 18463, 17918, 17917])).
% 2.23/2.46 tff(18581,plain,
% 2.23/2.46 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18580, 17913])).
% 2.23/2.46 tff(18582,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18583,plain,
% 2.23/2.46 (((~b(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18584,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18583])).
% 2.23/2.46 tff(18585,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.46 inference(transitivity,[status(thm)],[18584, 18582])).
% 2.23/2.46 tff(18586,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18587,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18586, 18585])).
% 2.23/2.46 tff(18588,plain,
% 2.23/2.46 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18587, 224, 18510, 18570, 18581])).
% 2.23/2.46 tff(18589,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.23/2.46 tff(18590,plain,
% 2.23/2.46 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[18589])).
% 2.23/2.46 tff(18591,plain,
% 2.23/2.46 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18590])).
% 2.23/2.46 tff(18592,plain,
% 2.23/2.46 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[18591])).
% 2.23/2.46 tff(18593,plain,
% 2.23/2.46 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[2327, 18592, 1705])).
% 2.23/2.46 tff(18594,plain,
% 2.23/2.46 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[18593])).
% 2.23/2.46 tff(18595,plain,
% 2.23/2.46 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[1679, 18594, 292, 15905])).
% 2.23/2.46 tff(18596,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1165, 18595])).
% 2.23/2.46 tff(18597,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(18598,plain,
% 2.23/2.46 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18597, 17905])).
% 2.23/2.46 tff(18599,plain,
% 2.23/2.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(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)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(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)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(18600,plain,
% 2.23/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(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)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(18601,plain,
% 2.23/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(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))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[18600, 18599])).
% 2.23/2.46 tff(18602,plain,
% 2.23/2.46 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[18601, 68, 18598, 18588])).
% 2.23/2.46 tff(18603,plain,
% 2.23/2.46 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[16807, 224, 17915, 17690, 18581])).
% 2.23/2.46 tff(18604,plain,
% 2.23/2.46 (r(s(s(s(s(s(z))))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 18603])).
% 2.23/2.47 tff(18605,plain,
% 2.23/2.47 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(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(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18606,plain,
% 2.23/2.47 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18607,plain,
% 2.23/2.47 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[18606])).
% 2.23/2.47 tff(18608,plain,
% 2.23/2.47 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[18607, 18605])).
% 2.23/2.47 tff(18609,plain,
% 2.23/2.47 ((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(18610,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18609, 18608])).
% 2.23/2.47 tff(18611,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18610, 112, 18604, 18521, 18560, 18602])).
% 2.23/2.47 tff(18612,plain,(r(s(s(z)), z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18613,plain,
% 2.23/2.47 (r(s(s(z)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18612, 1])).
% 2.23/2.47 tff(18614,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3531, 18613, 18286])).
% 2.23/2.47 tff(18615,plain,
% 2.23/2.47 (~r(s(s(elem!1)), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8303, 18614, 17908])).
% 2.23/2.47 tff(18616,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[530, 18615, 17921])).
% 2.23/2.47 tff(18617,plain,
% 2.23/2.47 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16648, 18616, 17905])).
% 2.23/2.47 tff(18618,plain,
% 2.23/2.47 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[17957])).
% 2.23/2.47 tff(18619,plain,
% 2.23/2.47 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.23/2.47 inference(symmetry,[status(thm)],[18618])).
% 2.23/2.47 tff(18620,plain,
% 2.23/2.47 (r(s(elem!1), z)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18613, 18619])).
% 2.23/2.47 tff(18621,plain,
% 2.23/2.47 (b(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[374, 2932, 17931])).
% 2.23/2.47 tff(18622,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18621, 18291])).
% 2.23/2.47 tff(18623,plain,
% 2.23/2.47 (~b(s(z), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18350, 18622, 18286, 1])).
% 2.23/2.47 tff(18624,plain,
% 2.23/2.47 (r(s(z), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[175, 18623])).
% 2.23/2.47 tff(18625,plain,
% 2.23/2.47 (r(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18624, 17942])).
% 2.23/2.47 tff(18626,plain,
% 2.23/2.47 (~r(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18448, 18625, 17905, 18286, 17915, 18369, 18615, 18621])).
% 2.23/2.47 tff(18627,plain,
% 2.23/2.47 (b(s(elem!1), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[939, 18626, 17932])).
% 2.23/2.47 tff(18628,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1337, 68, 1334, 14854])).
% 2.23/2.47 tff(18629,plain,
% 2.23/2.47 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10420, 112, 102, 18628])).
% 2.23/2.47 tff(18630,plain,
% 2.23/2.47 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1401, 68, 18629])).
% 2.23/2.47 tff(18631,plain,
% 2.23/2.47 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18630, 10355])).
% 2.23/2.47 tff(18632,plain,
% 2.23/2.47 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[14261, 112, 467, 18628])).
% 2.23/2.47 tff(18633,plain,
% 2.23/2.47 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1344, 68, 18632])).
% 2.23/2.47 tff(18634,plain,
% 2.23/2.47 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18633, 10338])).
% 2.23/2.47 tff(18635,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4777, 18634, 18631])).
% 2.23/2.47 tff(18636,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18637,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18636, 18627, 17690, 17907, 18354, 18616, 17915, 18620])).
% 2.23/2.47 tff(18638,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1294, 18637, 17918])).
% 2.23/2.47 tff(18639,plain,
% 2.23/2.47 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[17036, 18638, 17905])).
% 2.23/2.47 tff(18640,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 2.23/2.47 tff(18641,plain,
% 2.23/2.47 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[18640])).
% 2.23/2.47 tff(18642,plain,
% 2.23/2.47 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[18641, 15905])).
% 2.23/2.47 tff(18643,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1165, 18642])).
% 2.23/2.47 tff(18644,plain,((~(s(s(s(s(s(z))))) = s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18645,plain,
% 2.23/2.47 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18644, 17905])).
% 2.23/2.47 tff(18646,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[17905])).
% 2.23/2.47 tff(18647,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(transitivity,[status(thm)],[18646, 17943])).
% 2.23/2.47 tff(18648,plain,
% 2.23/2.47 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[17907])).
% 2.23/2.47 tff(18649,plain,
% 2.23/2.47 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[18648])).
% 2.23/2.47 tff(18650,plain,
% 2.23/2.47 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[18296, 18649])).
% 2.23/2.47 tff(18651,plain,
% 2.23/2.47 (~r(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18404, 16780, 17905, 17915, 18286])).
% 2.23/2.47 tff(18652,plain,
% 2.23/2.47 (b(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[558, 18651, 17919])).
% 2.23/2.47 tff(18653,plain,
% 2.23/2.47 (b(s(z), s(s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18652, 18650])).
% 2.23/2.47 tff(18654,plain,
% 2.23/2.47 (~b(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18350, 18653, 18286, 1])).
% 2.23/2.47 tff(18655,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[901, 18654])).
% 2.23/2.47 tff(18656,plain,
% 2.23/2.47 (r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18655, 18647])).
% 2.23/2.47 tff(18657,plain,
% 2.23/2.47 (r(s(s(s(z))), s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18655, 18646])).
% 2.23/2.47 tff(18658,plain,
% 2.23/2.47 (~r(s(s(s(s(z)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3326, 3318, 3188])).
% 2.23/2.47 tff(18659,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3168, 18658])).
% 2.23/2.47 tff(18660,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16176, 18659, 1, 17910])).
% 2.23/2.47 tff(18661,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16239, 18660])).
% 2.23/2.47 tff(18662,plain,
% 2.23/2.47 (((~![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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), 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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18663,plain,
% 2.23/2.47 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18664,plain,
% 2.23/2.47 (((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[18663])).
% 2.23/2.47 tff(18665,plain,
% 2.23/2.47 (((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~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))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[18664, 18662])).
% 2.23/2.47 tff(18666,plain,
% 2.23/2.47 ((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(18667,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18666, 18665])).
% 2.23/2.47 tff(18668,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18667, 112, 690, 18286, 18661, 3318])).
% 2.23/2.47 tff(18669,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18670,plain,
% 2.23/2.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18669, 18656, 1, 18657])).
% 2.23/2.47 tff(18671,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3252, 18670])).
% 2.23/2.47 tff(18672,plain,
% 2.23/2.47 (~r(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18014, 18671, 1, 18613, 18369, 18656])).
% 2.23/2.47 tff(18673,plain,
% 2.23/2.47 (b(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1135, 18672, 17926])).
% 2.23/2.47 tff(18674,plain,
% 2.23/2.47 (b(s(elem!1), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18673, 17993])).
% 2.23/2.47 tff(18675,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18636, 18674, 17690, 17907, 18354, 18616, 17915, 18620])).
% 2.23/2.47 tff(18676,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1294, 18675, 17918])).
% 2.23/2.47 tff(18677,plain,
% 2.23/2.47 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[17036, 18676, 17905])).
% 2.23/2.47 tff(18678,plain,
% 2.23/2.47 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[17019, 112, 18656, 18677])).
% 2.23/2.47 tff(18679,plain,
% 2.23/2.47 (((~![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)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18680,plain,
% 2.23/2.47 ((~![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)))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(18681,plain,
% 2.23/2.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18680, 18679])).
% 2.23/2.47 tff(18682,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18681, 68, 16780, 18678, 18645])).
% 2.23/2.47 tff(18683,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18684,plain,
% 2.23/2.47 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18683, 1])).
% 2.23/2.47 tff(18685,plain,
% 2.23/2.47 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18026, 18684, 18617, 18369])).
% 2.23/2.47 tff(18686,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18685, 17991])).
% 2.23/2.47 tff(18687,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1345, 18686, 17968])).
% 2.23/2.47 tff(18688,plain,
% 2.23/2.47 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8351, 18687, 17908])).
% 2.23/2.47 tff(18689,plain,
% 2.23/2.47 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16926, 2932, 17905])).
% 2.23/2.47 tff(18690,plain,
% 2.23/2.47 (b(s(s(elem!1)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[360, 18689, 17945])).
% 2.23/2.47 tff(18691,plain,
% 2.23/2.47 (~b(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8320, 18627, 17908, 17915, 18286, 18690])).
% 2.23/2.47 tff(18692,plain,
% 2.23/2.47 (r(elem!1, s(elem!1))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[515, 18691, 18451])).
% 2.23/2.47 tff(18693,plain,
% 2.23/2.47 (r(elem!1, s(s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18692, 18182])).
% 2.23/2.47 tff(18694,plain,
% 2.23/2.47 (r(elem!1, s(s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18624, 17941])).
% 2.23/2.47 tff(18695,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18696,plain,
% 2.23/2.47 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18697,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, 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(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[18696])).
% 2.23/2.47 tff(18698,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, 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(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[18697, 18695])).
% 2.23/2.47 tff(18699,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(18700,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18699, 18698])).
% 2.23/2.47 tff(18701,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18700, 112, 18694, 18693, 18688, 18639])).
% 2.23/2.47 tff(18702,plain,(r(s(s(s(z))), elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18703,plain,
% 2.23/2.47 (r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18702, 1])).
% 2.23/2.47 tff(18704,plain,
% 2.23/2.47 (r(s(s(s(z))), s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18703, 17944])).
% 2.23/2.47 tff(18705,plain,
% 2.23/2.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18669, 18704, 1, 18703])).
% 2.23/2.47 tff(18706,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3252, 18705])).
% 2.23/2.47 tff(18707,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[13309, 18706, 18369, 18617])).
% 2.23/2.47 tff(18708,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6185, 18707])).
% 2.23/2.47 tff(18709,plain,
% 2.23/2.47 (~r(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16404, 18708, 18613])).
% 2.23/2.47 tff(18710,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16239, 18709])).
% 2.23/2.47 tff(18711,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16176, 18710, 1, 17910])).
% 2.23/2.47 tff(18712,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8884, 18711, 17908])).
% 2.23/2.47 tff(18713,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3183, 18712, 17909])).
% 2.23/2.47 tff(18714,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18047, 112, 18703, 18713])).
% 2.23/2.47 tff(18715,plain,
% 2.23/2.47 (~r(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18014, 18706, 1, 18613, 18369, 18703])).
% 2.23/2.47 tff(18716,plain,
% 2.23/2.47 (b(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1135, 18715, 17926])).
% 2.23/2.47 tff(18717,plain,
% 2.23/2.47 (b(s(elem!1), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18716, 17993])).
% 2.23/2.47 tff(18718,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18636, 18717, 17690, 17907, 18354, 18616, 17915, 18620])).
% 2.23/2.47 tff(18719,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1294, 18718, 17918])).
% 2.23/2.47 tff(18720,plain,
% 2.23/2.47 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[17036, 18719, 17905])).
% 2.23/2.47 tff(18721,plain,
% 2.23/2.47 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18074, 18720, 18713])).
% 2.23/2.47 tff(18722,plain,
% 2.23/2.47 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18064, 18721, 18684, 18706, 18041])).
% 2.23/2.47 tff(18723,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[16989, 68, 18722, 18052, 18714])).
% 2.23/2.47 tff(18724,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18725,plain,
% 2.23/2.47 (r(s(z), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[194, 18724])).
% 2.23/2.47 tff(18726,plain,
% 2.23/2.47 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[15829])).
% 2.23/2.47 tff(18727,plain,
% 2.23/2.47 (~b(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3641, 3633, 1296])).
% 2.23/2.47 tff(18728,plain,
% 2.23/2.47 (b(z, s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[17690, 9773])).
% 2.23/2.47 tff(18729,plain,
% 2.23/2.47 (r(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[593, 18727])).
% 2.23/2.47 tff(18730,plain,
% 2.23/2.47 (~b(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10849, 18729, 18725, 18728])).
% 2.23/2.47 tff(18731,plain,
% 2.23/2.47 (r(elem!1, z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[403, 3633, 8494])).
% 2.23/2.47 tff(18732,plain,
% 2.23/2.47 (~r(s(s(s(z))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6913, 18731, 18725, 129, 362])).
% 2.23/2.47 tff(18733,plain,
% 2.23/2.47 (b(s(s(s(z))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[72, 18732])).
% 2.23/2.47 tff(18734,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[9581, 18733, 18730, 18727, 17631, 2930, 17628])).
% 2.23/2.47 tff(18735,plain,(b(elem!1, z) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(18736,plain,
% 2.23/2.47 (b(elem!1, z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[18735, 91, 16267, 15829])).
% 2.23/2.47 tff(18737,plain,
% 2.23/2.47 (b(s(s(elem!1)), z)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18736, 18726])).
% 2.23/2.47 tff(18738,plain,
% 2.23/2.47 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[7654, 224, 18737, 17691, 7672])).
% 2.23/2.47 tff(18739,plain,
% 2.23/2.47 (r(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[135, 68, 132, 18738])).
% 2.23/2.47 tff(18740,plain,
% 2.23/2.47 (b(s(z), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[9882, 9138, 16251, 15861, 16255, 7672])).
% 2.23/2.47 tff(18741,plain,
% 2.23/2.47 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18738, 17756])).
% 2.23/2.47 tff(18742,plain,
% 2.23/2.47 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5426, 18741])).
% 2.23/2.47 tff(18743,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5413, 196, 18742])).
% 2.23/2.47 tff(18744,plain,
% 2.23/2.47 (~r(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5403, 18743, 16268])).
% 2.23/2.47 tff(18745,plain,
% 2.23/2.47 (b(s(s(z)), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1135, 18744, 16270])).
% 2.23/2.47 tff(18746,plain,
% 2.23/2.47 (~b(s(s(z)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1126, 18745, 17690, 18736])).
% 2.23/2.47 tff(18747,plain,
% 2.23/2.47 (r(s(s(z)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[281, 18746])).
% 2.23/2.47 tff(18748,plain,
% 2.23/2.47 (~r(z, s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3455, 18747, 196])).
% 2.23/2.47 tff(18749,plain,
% 2.23/2.47 (b(z, s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[100, 18748])).
% 2.23/2.47 tff(18750,plain,
% 2.23/2.47 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10929, 18749, 18737, 7672])).
% 2.23/2.47 tff(18751,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[147, 18750, 2])).
% 2.23/2.47 tff(18752,plain,
% 2.23/2.47 (~r(s(s(elem!1)), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[14384, 112, 196, 18751])).
% 2.23/2.47 tff(18753,plain,
% 2.23/2.47 (~r(elem!1, s(s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[18752, 16311])).
% 2.23/2.47 tff(18754,plain,
% 2.23/2.47 (b(elem!1, s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2874, 18753, 16269])).
% 2.23/2.47 tff(18755,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5300, 18754, 17690, 18736, 18745])).
% 2.23/2.47 tff(18756,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3183, 18755, 16293])).
% 2.23/2.47 tff(18757,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[17732, 18756, 15829])).
% 2.23/2.47 tff(18758,plain,
% 2.23/2.47 (((~![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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(18759,plain,
% 2.23/2.47 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(18760,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18759])).
% 2.23/2.48 tff(18761,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[18760, 18758])).
% 2.23/2.48 tff(18762,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(18763,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18762, 18761])).
% 2.23/2.48 tff(18764,plain,
% 2.23/2.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18763, 112, 18739, 18757])).
% 2.23/2.48 tff(18765,plain,
% 2.23/2.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3252, 18764])).
% 2.23/2.48 tff(18766,plain,
% 2.23/2.48 (b(s(s(elem!1)), s(s(z)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18754, 16309])).
% 2.23/2.48 tff(18767,plain,
% 2.23/2.48 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[15829])).
% 2.23/2.48 tff(18768,plain,
% 2.23/2.48 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18745, 18767])).
% 2.23/2.48 tff(18769,plain,
% 2.23/2.48 (~r(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9974, 18747, 18725])).
% 2.23/2.48 tff(18770,plain,
% 2.23/2.48 (b(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1071, 18769])).
% 2.23/2.48 tff(18771,plain,
% 2.23/2.48 (~b(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[16394, 224, 18770, 18768, 18766])).
% 2.23/2.48 tff(18772,plain,
% 2.23/2.48 (r(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[653, 18771])).
% 2.23/2.48 tff(18773,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9107, 18772, 18739])).
% 2.23/2.48 tff(18774,plain,
% 2.23/2.48 (b(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[925, 18773])).
% 2.23/2.48 tff(18775,plain,
% 2.23/2.48 (~r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[835, 18772, 18751])).
% 2.23/2.48 tff(18776,plain,
% 2.23/2.48 (b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[175, 18775])).
% 2.23/2.48 tff(18777,plain,
% 2.23/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7280, 18772, 18757])).
% 2.23/2.48 tff(18778,plain,
% 2.23/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3168, 18777])).
% 2.23/2.48 tff(18779,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1579, 18778, 18776, 18774, 18765])).
% 2.23/2.48 tff(18780,plain,((~r(s(s(z)), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18781,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18780, 7672, 2])).
% 2.23/2.48 tff(18782,plain,
% 2.23/2.48 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[249, 18781])).
% 2.23/2.48 tff(18783,plain,
% 2.23/2.48 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(symmetry,[status(thm)],[16289])).
% 2.23/2.48 tff(18784,plain,
% 2.23/2.48 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18783])).
% 2.23/2.48 tff(18785,plain,
% 2.23/2.48 (~b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18738, 18784])).
% 2.23/2.48 tff(18786,plain,
% 2.23/2.48 (r(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[374, 18785, 16267])).
% 2.23/2.48 tff(18787,plain,
% 2.23/2.48 (~r(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9652, 9147, 2, 7672, 18786, 18740, 16319, 18737])).
% 2.23/2.48 tff(18788,plain,
% 2.23/2.48 (b(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2726, 18787])).
% 2.23/2.48 tff(18789,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17718, 18788, 18782, 18740])).
% 2.23/2.48 tff(18790,plain,
% 2.23/2.48 (r(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[925, 18789])).
% 2.23/2.48 tff(18791,plain,
% 2.23/2.48 (~r(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9107, 18790, 18739])).
% 2.23/2.48 tff(18792,plain,
% 2.23/2.48 (b(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[653, 18791])).
% 2.23/2.48 tff(18793,plain,
% 2.23/2.48 (~r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9717, 9138, 16251, 16255, 7672, 15861])).
% 2.23/2.48 tff(18794,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[100, 18793])).
% 2.23/2.48 tff(18795,plain,
% 2.23/2.48 (~b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9201, 18794, 7672, 18782])).
% 2.23/2.48 tff(18796,plain,
% 2.23/2.48 (r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[281, 18795])).
% 2.23/2.48 tff(18797,plain,
% 2.23/2.48 (~r(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9974, 18796, 18725])).
% 2.23/2.48 tff(18798,plain,
% 2.23/2.48 (b(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1071, 18797])).
% 2.23/2.48 tff(18799,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5329, 224, 2212, 1090, 5187, 2211])).
% 2.23/2.48 tff(18800,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18801,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18800, 18740, 18782, 18798])).
% 2.23/2.48 tff(18802,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3535, 68, 18801, 11591])).
% 2.23/2.48 tff(18803,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6051, 112, 3523, 267, 6847])).
% 2.23/2.48 tff(18804,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18805,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18804, 18802, 18739])).
% 2.23/2.48 tff(18806,plain,
% 2.23/2.48 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[265, 18805, 16319])).
% 2.23/2.48 tff(18807,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9920, 18806, 18788, 18792])).
% 2.23/2.48 tff(18808,plain,
% 2.23/2.48 (~r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2801, 18805, 16271])).
% 2.23/2.48 tff(18809,plain,
% 2.23/2.48 (b(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 18808, 16270])).
% 2.23/2.48 tff(18810,plain,
% 2.23/2.48 (~r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5356, 18809, 15829, 16267, 18782, 2, 18790])).
% 2.23/2.48 tff(18811,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[901, 18810, 18807])).
% 2.23/2.48 tff(18812,plain,(b(z, s(z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18813,plain,
% 2.23/2.48 (b(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18812, 7672, 2])).
% 2.23/2.48 tff(18814,plain,
% 2.23/2.48 (~r(s(z), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2374, 178, 18786])).
% 2.23/2.48 tff(18815,plain,
% 2.23/2.48 (b(s(z), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[454, 18814, 91])).
% 2.23/2.48 tff(18816,plain,
% 2.23/2.48 (~b(elem!1, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2904, 18815, 17690, 18813])).
% 2.23/2.48 tff(18817,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5385, 18816, 15829])).
% 2.23/2.48 tff(18818,plain,
% 2.23/2.48 (~r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9119, 178, 18725])).
% 2.23/2.48 tff(18819,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[100, 18818])).
% 2.23/2.48 tff(18820,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10929, 18819, 18737, 7672])).
% 2.23/2.48 tff(18821,plain,
% 2.23/2.48 (r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[147, 18820, 2])).
% 2.23/2.48 tff(18822,plain,
% 2.23/2.48 (~r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[4039, 18821, 178])).
% 2.23/2.48 tff(18823,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[901, 18822, 18817])).
% 2.23/2.48 tff(18824,plain,((~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18825,plain,
% 2.23/2.48 (~r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18824, 7672, 2])).
% 2.23/2.48 tff(18826,plain,
% 2.23/2.48 (b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[175, 18825])).
% 2.23/2.48 tff(18827,plain,
% 2.23/2.48 (~b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5939, 1118, 1180, 1240])).
% 2.23/2.48 tff(18828,plain,
% 2.23/2.48 (r(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[265, 18827, 259])).
% 2.23/2.48 tff(18829,plain,
% 2.23/2.48 (~b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9201, 1118, 7672, 2212])).
% 2.23/2.48 tff(18830,plain,
% 2.23/2.48 (r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[100, 18829])).
% 2.23/2.48 tff(18831,plain,
% 2.23/2.48 (~r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9119, 18830, 18725])).
% 2.23/2.48 tff(18832,plain,
% 2.23/2.48 (b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[175, 18831])).
% 2.23/2.48 tff(18833,plain,
% 2.23/2.48 (~b(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5447, 224, 77, 2212, 18832, 1118])).
% 2.23/2.48 tff(18834,plain,
% 2.23/2.48 (r(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2726, 18833])).
% 2.23/2.48 tff(18835,plain,
% 2.23/2.48 (~r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2993, 18834, 18828])).
% 2.23/2.48 tff(18836,plain,
% 2.23/2.48 (b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[901, 18835])).
% 2.23/2.48 tff(18837,plain,
% 2.23/2.48 (~r(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2853, 18834, 18828])).
% 2.23/2.48 tff(18838,plain,
% 2.23/2.48 (b(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[653, 18837])).
% 2.23/2.48 tff(18839,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10876, 18838, 18836, 1180, 77])).
% 2.23/2.48 tff(18840,plain,((~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18841,plain,
% 2.23/2.48 (~b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18840, 18813, 17691, 18782, 16319, 7672, 18737])).
% 2.23/2.48 tff(18842,plain,
% 2.23/2.48 (r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[281, 18841])).
% 2.23/2.48 tff(18843,plain,
% 2.23/2.48 (~r(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3470, 112, 18725, 18842])).
% 2.23/2.48 tff(18844,plain,
% 2.23/2.48 (b(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2726, 18843])).
% 2.23/2.48 tff(18845,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17718, 18844, 18782, 18826])).
% 2.23/2.48 tff(18846,plain,
% 2.23/2.48 (r(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[925, 18845])).
% 2.23/2.48 tff(18847,plain,
% 2.23/2.48 (~r(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9107, 18846, 18739])).
% 2.23/2.48 tff(18848,plain,
% 2.23/2.48 (b(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[653, 18847])).
% 2.23/2.48 tff(18849,plain,
% 2.23/2.48 (~r(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9974, 18842, 18725])).
% 2.23/2.48 tff(18850,plain,
% 2.23/2.48 (b(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1071, 18849])).
% 2.23/2.48 tff(18851,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18800, 18826, 18782, 18850])).
% 2.23/2.48 tff(18852,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3535, 68, 18851, 11591])).
% 2.23/2.48 tff(18853,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18804, 18852, 18739])).
% 2.23/2.48 tff(18854,plain,
% 2.23/2.48 (~r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2801, 18853, 16271])).
% 2.23/2.48 tff(18855,plain,
% 2.23/2.48 (b(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 18854, 16270])).
% 2.23/2.48 tff(18856,plain,
% 2.23/2.48 (~r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5356, 18846, 15829, 16267, 18782, 2, 18855])).
% 2.23/2.48 tff(18857,plain,
% 2.23/2.48 (b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[901, 18856])).
% 2.23/2.48 tff(18858,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10876, 18857, 18848, 17691, 18813])).
% 2.23/2.48 tff(18859,plain,((~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18860,plain,
% 2.23/2.48 (~b(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18859, 2])).
% 2.23/2.48 tff(18861,plain,
% 2.23/2.48 (r(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[72, 18860])).
% 2.23/2.48 tff(18862,plain,
% 2.23/2.48 (~r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[187, 18861, 18725])).
% 2.23/2.48 tff(18863,plain,
% 2.23/2.48 (b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[175, 18862])).
% 2.23/2.48 tff(18864,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17487, 18861, 18725])).
% 2.23/2.48 tff(18865,plain,
% 2.23/2.48 (b(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[925, 18864])).
% 2.23/2.48 tff(18866,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6253, 18860, 2, 15861])).
% 2.23/2.48 tff(18867,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17758, 968, 17691, 18866])).
% 2.23/2.48 tff(18868,plain,
% 2.23/2.48 (r(s(s(elem!1)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[147, 18867, 2])).
% 2.23/2.48 tff(18869,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8621, 112, 196, 18868])).
% 2.23/2.48 tff(18870,plain,
% 2.23/2.48 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[265, 18869, 16319])).
% 2.23/2.48 tff(18871,plain,
% 2.23/2.48 (~b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5939, 18870, 17691, 18737])).
% 2.23/2.48 tff(18872,plain,
% 2.23/2.48 (r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[281, 18871])).
% 2.23/2.48 tff(18873,plain,
% 2.23/2.48 (~r(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9974, 18872, 18725])).
% 2.23/2.48 tff(18874,plain,
% 2.23/2.48 (b(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1071, 18873])).
% 2.23/2.48 tff(18875,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(18876,plain,
% 2.23/2.48 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(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(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(18877,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18876])).
% 2.23/2.48 tff(18878,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[18877, 18875])).
% 2.23/2.48 tff(18879,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(18880,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18879, 18878])).
% 2.23/2.48 tff(18881,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18880, 224, 18874, 18865, 968, 18870])).
% 2.23/2.48 tff(18882,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3531, 18872, 18861])).
% 2.23/2.48 tff(18883,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3535, 68, 18882, 18881, 11591])).
% 2.23/2.48 tff(18884,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18885,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18884, 196, 2])).
% 2.23/2.48 tff(18886,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18885, 17756])).
% 2.23/2.48 tff(18887,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5426, 18886])).
% 2.23/2.48 tff(18888,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5413, 18887, 196])).
% 2.23/2.48 tff(18889,plain,
% 2.23/2.48 (~r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5403, 18888, 16268])).
% 2.23/2.48 tff(18890,plain,
% 2.23/2.48 (b(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 18889, 16270])).
% 2.23/2.48 tff(18891,plain,
% 2.23/2.48 (~b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1126, 18890, 17690, 18736])).
% 2.23/2.48 tff(18892,plain,
% 2.23/2.48 (r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[281, 18891])).
% 2.23/2.48 tff(18893,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[241, 112, 196, 18861, 18892])).
% 2.23/2.48 tff(18894,plain,((~r(s(s(z)), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18895,plain,
% 2.23/2.48 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[18894, 2])).
% 2.23/2.48 tff(18896,plain,
% 2.23/2.48 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[249, 18895])).
% 2.23/2.48 tff(18897,plain,
% 2.23/2.48 (~b(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17718, 18896, 18865, 18863])).
% 2.23/2.48 tff(18898,plain,
% 2.23/2.48 (r(s(s(z)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2726, 18897])).
% 2.23/2.48 tff(18899,plain,
% 2.23/2.48 (~b(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6404, 18865, 18866, 18863])).
% 2.23/2.48 tff(18900,plain,
% 2.23/2.48 (r(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5459, 18899])).
% 2.23/2.48 tff(18901,plain,
% 2.23/2.48 (~r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6167, 18898, 18900])).
% 2.23/2.48 tff(18902,plain,
% 2.23/2.48 (b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[281, 18901])).
% 2.23/2.48 tff(18903,plain,
% 2.23/2.48 (~b(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5939, 18902, 17691, 18737])).
% 2.23/2.48 tff(18904,plain,
% 2.23/2.48 (r(s(s(z)), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[265, 18903, 16319])).
% 2.23/2.48 tff(18905,plain,
% 2.23/2.48 (~r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2993, 18904, 18898])).
% 2.23/2.48 tff(18906,plain,
% 2.23/2.48 (~b(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1126, 18902, 17690, 18736])).
% 2.23/2.48 tff(18907,plain,
% 2.23/2.48 (r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 18906, 16270])).
% 2.23/2.48 tff(18908,plain,
% 2.23/2.48 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5403, 18907, 16268])).
% 2.23/2.48 tff(18909,plain,
% 2.23/2.48 (~r(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17702, 18898, 17691, 16319, 18737, 18900])).
% 2.23/2.48 tff(18910,plain,
% 2.23/2.48 (b(s(z), s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[653, 18909])).
% 2.23/2.48 tff(18911,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6117, 18904, 15829, 18865, 18863, 18910, 18900, 18725, 18902, 18908, 2])).
% 2.23/2.48 tff(18912,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[901, 18911, 18905])).
% 2.23/2.48 tff(18913,plain,(s(s(elem!1)) = s(s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(18914,plain,
% 2.23/2.48 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[310, 18913])).
% 2.23/2.48 tff(18915,plain,
% 2.23/2.48 (s(z) = elem!1),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[131, 18914])).
% 2.23/2.48 tff(18916,plain,
% 2.23/2.48 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18917,plain,
% 2.23/2.48 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18916])).
% 2.23/2.48 tff(18918,plain,
% 2.23/2.48 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7790, 18915])).
% 2.23/2.48 tff(18919,plain,
% 2.23/2.48 (~b(s(elem!1), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7872, 5829, 18915])).
% 2.23/2.48 tff(18920,plain,
% 2.23/2.48 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7751, 18915])).
% 2.23/2.48 tff(18921,plain,
% 2.23/2.48 (elem!1 = s(z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[90, 18915])).
% 2.23/2.48 tff(18922,plain,
% 2.23/2.48 (r(s(z), z) <=> r(elem!1, z)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18923,plain,
% 2.23/2.48 (r(elem!1, z)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18725, 18922])).
% 2.23/2.48 tff(18924,plain,
% 2.23/2.48 (~(elem!1 = s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1306, 18920])).
% 2.23/2.48 tff(18925,plain,
% 2.23/2.48 (~(s(elem!1) = elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[302, 18924])).
% 2.23/2.48 tff(18926,plain,
% 2.23/2.48 (r(s(elem!1), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[939, 18919, 18925])).
% 2.23/2.48 tff(18927,plain,
% 2.23/2.48 (~r(s(elem!1), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2694, 18926, 18923])).
% 2.23/2.48 tff(18928,plain,
% 2.23/2.48 (b(s(elem!1), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[498, 18927])).
% 2.23/2.48 tff(18929,plain,
% 2.23/2.48 (b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[16898, 18928, 18921])).
% 2.23/2.48 tff(18930,plain,
% 2.23/2.48 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18931,plain,
% 2.23/2.48 ((s(s(z)) = s(z)) <=> (elem!1 = s(s(z)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[18930, 2587])).
% 2.23/2.48 tff(18932,plain,
% 2.23/2.48 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.23/2.48 inference(transitivity,[status(thm)],[18931, 2588])).
% 2.23/2.48 tff(18933,plain,
% 2.23/2.48 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18932])).
% 2.23/2.48 tff(18934,plain,
% 2.23/2.48 (~(s(s(z)) = elem!1)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[210, 18933])).
% 2.23/2.48 tff(18935,plain,
% 2.23/2.48 (r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 5829, 18934])).
% 2.23/2.48 tff(18936,plain,
% 2.23/2.48 (elem!1 = s(z)),
% 2.23/2.48 inference(symmetry,[status(thm)],[18915])).
% 2.23/2.48 tff(18937,plain,
% 2.23/2.48 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18936])).
% 2.23/2.48 tff(18938,plain,
% 2.23/2.48 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18937])).
% 2.23/2.48 tff(18939,plain,
% 2.23/2.48 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1407, 18920])).
% 2.23/2.48 tff(18940,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18941,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18940])).
% 2.23/2.48 tff(18942,plain,
% 2.23/2.48 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.48 tff(18943,plain,
% 2.23/2.48 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18942])).
% 2.23/2.48 tff(18944,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18943])).
% 2.23/2.48 tff(18945,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(transitivity,[status(thm)],[18944, 18941])).
% 2.23/2.48 tff(18946,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[3919, 18945])).
% 2.23/2.48 tff(18947,plain,
% 2.23/2.48 (b(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9460, 18915, 17690])).
% 2.23/2.48 tff(18948,plain,
% 2.23/2.48 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18943])).
% 2.23/2.48 tff(18949,plain,
% 2.23/2.48 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18943])).
% 2.23/2.48 tff(18950,plain,
% 2.23/2.48 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18949])).
% 2.23/2.48 tff(18951,plain,
% 2.23/2.48 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, s(s(s(s(elem!1))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18950])).
% 2.23/2.48 tff(18952,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.48 inference(symmetry,[status(thm)],[18944])).
% 2.23/2.48 tff(18953,plain,
% 2.23/2.48 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18952])).
% 2.23/2.48 tff(18954,plain,
% 2.23/2.48 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.48 tff(18955,plain,
% 2.23/2.48 (s(elem!1) = s(s(z))),
% 2.23/2.48 inference(transitivity,[status(thm)],[164, 18954, 31])).
% 2.23/2.48 tff(18956,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18943, 18955])).
% 2.23/2.48 tff(18957,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.23/2.48 tff(18958,plain,
% 2.23/2.48 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18943])).
% 2.23/2.48 tff(18959,plain,
% 2.23/2.48 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18958])).
% 2.23/2.48 tff(18960,plain,
% 2.23/2.48 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18959])).
% 2.23/2.48 tff(18961,plain,
% 2.23/2.48 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.48 tff(18962,plain,
% 2.23/2.48 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18961])).
% 2.23/2.48 tff(18963,plain,
% 2.23/2.48 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18958])).
% 2.23/2.48 tff(18964,plain,
% 2.23/2.48 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18963])).
% 2.23/2.48 tff(18965,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18956])).
% 2.23/2.48 tff(18966,plain,
% 2.23/2.48 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18965])).
% 2.23/2.48 tff(18967,plain,
% 2.23/2.48 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.48 tff(18968,plain,
% 2.23/2.48 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18967])).
% 2.23/2.48 tff(18969,plain,
% 2.23/2.48 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18955])).
% 2.23/2.48 tff(18970,plain,
% 2.23/2.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18969])).
% 2.23/2.48 tff(18971,plain,
% 2.23/2.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[18970, 18968])).
% 2.23/2.48 tff(18972,plain,
% 2.23/2.48 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18971])).
% 2.23/2.48 tff(18973,plain,
% 2.23/2.48 (~b(s(elem!1), s(s(elem!1)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18957, 18972])).
% 2.23/2.48 tff(18974,plain,
% 2.23/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[249, 18957])).
% 2.23/2.48 tff(18975,plain,
% 2.23/2.48 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18948])).
% 2.23/2.48 tff(18976,plain,
% 2.23/2.48 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(s(s(s(elem!1))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18975])).
% 2.23/2.48 tff(18977,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18936])).
% 2.23/2.48 tff(18978,plain,
% 2.23/2.48 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[18977])).
% 2.23/2.48 tff(18979,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18936, 18943])).
% 2.23/2.48 tff(18980,plain,
% 2.23/2.48 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8807, 18819, 18725, 18921, 178])).
% 2.23/2.48 tff(18981,plain,
% 2.23/2.48 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8812, 18980, 18921])).
% 2.23/2.48 tff(18982,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1439, 18981, 18939])).
% 2.23/2.48 tff(18983,plain,
% 2.23/2.48 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18982, 18979])).
% 2.23/2.48 tff(18984,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18983, 18978])).
% 2.23/2.48 tff(18985,plain,
% 2.23/2.48 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18986,plain,
% 2.23/2.48 (r(elem!1, s(s(s(z))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[178, 18985])).
% 2.23/2.48 tff(18987,plain,
% 2.23/2.48 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.48 tff(18988,plain,
% 2.23/2.48 (~r(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6296, 178, 196])).
% 2.23/2.48 tff(18989,plain,
% 2.23/2.48 (b(s(z), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1071, 18988])).
% 2.23/2.48 tff(18990,plain,
% 2.23/2.48 (b(elem!1, s(s(z)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18989, 18987])).
% 2.23/2.48 tff(18991,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1294, 1807, 18920])).
% 2.23/2.48 tff(18992,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18991, 18944])).
% 2.23/2.48 tff(18993,plain,
% 2.23/2.48 (~r(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[9273, 112, 196, 1020])).
% 2.23/2.48 tff(18994,plain,
% 2.23/2.48 (b(s(s(z)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1135, 18993, 18934])).
% 2.23/2.48 tff(18995,plain,
% 2.23/2.48 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17049, 224, 2861, 18994, 18992])).
% 2.23/2.48 tff(18996,plain,
% 2.23/2.48 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[18995, 18966])).
% 2.23/2.48 tff(18997,plain,
% 2.23/2.48 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[1787, 18964])).
% 2.23/2.48 tff(18998,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[17080, 112, 196, 18997])).
% 2.23/2.48 tff(18999,plain,
% 2.23/2.48 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8351, 18998, 18921])).
% 2.23/2.48 tff(19000,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1345, 18999, 18918])).
% 2.23/2.48 tff(19001,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[19000, 18996])).
% 2.23/2.48 tff(19002,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(19003,plain,
% 2.23/2.48 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[19002, 18990, 196, 18986])).
% 2.23/2.48 tff(19004,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1884, 19003])).
% 2.23/2.48 tff(19005,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[18958])).
% 2.23/2.48 tff(19006,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[19005])).
% 2.23/2.48 tff(19007,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[4753, 19006])).
% 2.23/2.48 tff(19008,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[16780, 19007])).
% 2.23/2.48 tff(19009,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(19010,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[19009, 19004])).
% 2.23/2.49 tff(19011,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(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))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(19012,plain,
% 2.23/2.49 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(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))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(19013,plain,
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% 2.23/2.49 inference(monotonicity,[status(thm)],[19012])).
% 2.23/2.49 tff(19014,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(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))))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[19013, 19011])).
% 2.23/2.49 tff(19015,plain,
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% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(19016,plain,
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% 2.23/2.49 inference(modus_ponens,[status(thm)],[19015, 19014])).
% 2.23/2.49 tff(19017,plain,
% 2.23/2.49 ((~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[19016, 224, 17690, 18819, 19010])).
% 2.23/2.49 tff(19018,plain,
% 2.23/2.49 (~b(z, s(s(s(s(s(z))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[19017, 18984])).
% 2.23/2.49 tff(19019,plain,
% 2.23/2.49 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19018, 18976])).
% 2.23/2.49 tff(19020,plain,
% 2.23/2.49 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[4412, 19019])).
% 2.23/2.49 tff(19021,plain,
% 2.23/2.49 (r(z, s(s(s(s(s(z))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19020, 18949])).
% 2.23/2.49 tff(19022,plain,
% 2.23/2.49 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[7825, 224, 18819, 7672, 19010])).
% 2.23/2.49 tff(19023,plain,
% 2.23/2.49 (r(s(s(s(s(s(z))))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19022])).
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% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(19025,plain,
% 2.23/2.49 (((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(19026,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, 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, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[19025])).
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% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, 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, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.49 inference(transitivity,[status(thm)],[19026, 19024])).
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% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
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% 2.23/2.49 inference(modus_ponens,[status(thm)],[19028, 19027])).
% 2.23/2.49 tff(19030,plain,
% 2.23/2.49 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[19029, 112, 18923, 19023])).
% 2.23/2.49 tff(19031,plain,
% 2.23/2.49 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[17036, 19030, 18913])).
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% 2.23/2.49 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1294, 19031, 18920])).
% 2.23/2.49 tff(19033,plain,
% 2.23/2.49 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19032, 18944])).
% 2.23/2.49 tff(19034,plain,
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[9273, 112, 196, 18986])).
% 2.23/2.49 tff(19035,plain,
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[1135, 19034, 18934])).
% 2.23/2.49 tff(19036,plain,
% 2.23/2.49 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[17049, 224, 18990, 19035, 19033])).
% 2.23/2.49 tff(19037,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19036, 18966])).
% 2.23/2.49 tff(19038,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1345, 19037, 18918])).
% 2.23/2.49 tff(19039,plain,
% 2.23/2.49 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[8351, 19038, 18921])).
% 2.23/2.49 tff(19040,plain,
% 2.23/2.49 (~b(z, s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2869, 19035, 17690, 18990])).
% 2.23/2.49 tff(19041,plain,
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[1088, 19040])).
% 2.23/2.49 tff(19042,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[8037, 112, 19041, 19039, 19021])).
% 2.23/2.49 tff(19043,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(19044,plain,
% 2.23/2.49 (~r(s(z), s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[19043, 7672, 18974])).
% 2.23/2.49 tff(19045,plain,
% 2.23/2.49 (b(s(z), s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[175, 19044])).
% 2.23/2.49 tff(19046,plain,
% 2.23/2.49 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.49 tff(19047,plain,
% 2.23/2.49 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(z)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[19046])).
% 2.23/2.49 tff(19048,plain,
% 2.23/2.49 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18913])).
% 2.23/2.49 tff(19049,plain,
% 2.23/2.49 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(symmetry,[status(thm)],[19048])).
% 2.23/2.49 tff(19050,plain,
% 2.23/2.49 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18955])).
% 2.23/2.49 tff(19051,plain,
% 2.23/2.49 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.23/2.49 inference(symmetry,[status(thm)],[19050])).
% 2.23/2.49 tff(19052,plain,
% 2.23/2.49 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(transitivity,[status(thm)],[19051, 19049])).
% 2.23/2.49 tff(19053,plain,
% 2.23/2.49 (r(s(elem!1), s(s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[196, 19052])).
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% 2.23/2.49 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[6557, 18926, 19053])).
% 2.23/2.49 tff(19055,plain,
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[14947, 19054, 17690, 18924, 18919, 1515])).
% 2.23/2.49 tff(19056,plain,
% 2.23/2.49 (~b(z, s(s(s(z))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19055, 19047])).
% 2.23/2.49 tff(19057,plain,
% 2.23/2.49 (r(z, s(s(s(z))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[100, 19056])).
% 2.23/2.49 tff(19058,plain,
% 2.23/2.49 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18915])).
% 2.23/2.49 tff(19059,plain,
% 2.23/2.49 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.23/2.49 inference(symmetry,[status(thm)],[19058])).
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% 2.23/2.49 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18913])).
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% 2.23/2.49 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.23/2.49 inference(transitivity,[status(thm)],[19060, 19059])).
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% 2.23/2.49 inference(monotonicity,[status(thm)],[19061])).
% 2.23/2.49 tff(19063,plain,
% 2.23/2.49 (~r(s(s(s(z))), s(z))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19054, 19062])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[925, 19063])).
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% 2.23/2.49 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[306])).
% 2.23/2.49 tff(19066,plain,
% 2.23/2.49 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
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% 2.23/2.49 inference(modus_ponens,[status(thm)],[196, 19066])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[3300, 19067, 689, 16655, 12441])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[17987, 19068, 306])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[3252, 19069])).
% 2.23/2.49 tff(19071,plain,
% 2.23/2.49 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1579, 19070, 1090, 560])).
% 2.23/2.49 tff(19072,plain,
% 2.23/2.49 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[8884, 19071, 15900])).
% 2.23/2.49 tff(19073,plain,
% 2.23/2.49 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3183, 19072, 15969])).
% 2.23/2.49 tff(19074,plain,
% 2.23/2.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[18345, 19073, 1290, 306, 1287])).
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% 2.23/2.49 tff(19078,plain,
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% 2.23/2.49 inference(modus_ponens,[status(thm)],[19078, 18944])).
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% 2.23/2.49 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[18913])).
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% 2.23/2.49 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
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% 2.23/2.49 inference(monotonicity,[status(thm)],[19081])).
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% 2.23/2.49 (~(s(s(s(z))) = elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[18924, 19082])).
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% 2.23/2.49 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[19060])).
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% 2.23/2.49 (~r(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[19054, 19084])).
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% 2.23/2.49 (b(s(s(s(z))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[374, 19085, 19083])).
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% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19158,plain,
% 2.33/2.50 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19159,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19158])).
% 2.33/2.50 tff(19160,plain,
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% 2.33/2.50 inference(transitivity,[status(thm)],[19159, 19157])).
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% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[19161, 19160])).
% 2.33/2.50 tff(19163,plain,
% 2.33/2.50 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19162, 224, 7672, 19118, 19122, 19156])).
% 2.33/2.50 tff(19164,plain,
% 2.33/2.50 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19163])).
% 2.33/2.50 tff(19165,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19029, 112, 18923, 19144, 19164])).
% 2.33/2.50 tff(19166,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(19167,plain,
% 2.33/2.50 (~r(z, s(s(s(z))))),
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% 2.33/2.50 tff(19168,plain,
% 2.33/2.50 (b(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[100, 19167])).
% 2.33/2.50 tff(19169,plain,
% 2.33/2.50 (~b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6404, 19168, 18947, 19045])).
% 2.33/2.50 tff(19170,plain,
% 2.33/2.50 (r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[925, 19169])).
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% 2.33/2.50 (r(s(s(elem!1)), elem!1)),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19170, 19109])).
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% 2.33/2.50 (~r(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12485, 19171, 18923, 19107, 19106])).
% 2.33/2.50 tff(19173,plain,
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% 2.33/2.50 inference(unit_resolution,[status(thm)],[515, 19172, 19104])).
% 2.33/2.50 tff(19174,plain,
% 2.33/2.50 (b(elem!1, s(s(z)))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19173, 19103])).
% 2.33/2.50 tff(19175,plain,
% 2.33/2.50 (r(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19170, 19058])).
% 2.33/2.50 tff(19176,plain,
% 2.33/2.50 (b(elem!1, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[15956, 19045, 18915])).
% 2.33/2.50 tff(19177,plain,
% 2.33/2.50 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(symmetry,[status(thm)],[18979])).
% 2.33/2.50 tff(19178,plain,
% 2.33/2.50 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[18977, 19177])).
% 2.33/2.50 tff(19179,plain,
% 2.33/2.50 ((~b(elem!1, s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19178])).
% 2.33/2.50 tff(19180,plain,
% 2.33/2.50 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[18958])).
% 2.33/2.50 tff(19181,plain,
% 2.33/2.50 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19180])).
% 2.33/2.50 tff(19182,plain,
% 2.33/2.50 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[18123, 224, 2861, 1109, 18024])).
% 2.33/2.50 tff(19183,plain,
% 2.33/2.50 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19182, 18953])).
% 2.33/2.50 tff(19184,plain,
% 2.33/2.50 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1294, 19183, 18920])).
% 2.33/2.50 tff(19185,plain,
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% 2.33/2.50 inference(unit_resolution,[status(thm)],[17036, 19184, 18913])).
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% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(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(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
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% 2.33/2.50 (((~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(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
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% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19187])).
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% 2.33/2.50 inference(transitivity,[status(thm)],[19188, 19186])).
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% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[19190, 19189])).
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% 2.33/2.50 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19191, 112, 690, 19185])).
% 2.33/2.50 tff(19193,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19192, 19181])).
% 2.33/2.50 tff(19194,plain,
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% 2.33/2.50 inference(unit_resolution,[status(thm)],[5426, 19193])).
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% 2.33/2.50 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19194, 18960])).
% 2.33/2.50 tff(19196,plain,
% 2.33/2.50 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[17019, 112, 690, 19185])).
% 2.33/2.50 tff(19197,plain,
% 2.33/2.50 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[18681, 68, 19196, 19110])).
% 2.33/2.50 tff(19198,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19199,plain,
% 2.33/2.50 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, 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(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))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19200,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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)))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19199])).
% 2.33/2.50 tff(19201,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[19200, 19198])).
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% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[19202, 19201])).
% 2.33/2.50 tff(19204,plain,
% 2.33/2.50 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19203, 224, 685, 19197, 19195])).
% 2.33/2.50 tff(19205,plain,
% 2.33/2.50 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19204, 19179])).
% 2.33/2.50 tff(19206,plain,
% 2.33/2.50 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1439, 19205, 18939])).
% 2.33/2.50 tff(19207,plain,
% 2.33/2.50 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8812, 19206, 18921])).
% 2.33/2.50 tff(19208,plain,
% 2.33/2.50 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19207, 18938])).
% 2.33/2.50 tff(19209,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.33/2.50 tff(19210,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19211,plain,
% 2.33/2.50 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19212,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19211])).
% 2.33/2.50 tff(19213,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[19212, 19210])).
% 2.33/2.50 tff(19214,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(19215,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19214, 19213])).
% 2.33/2.50 tff(19216,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19215, 224, 6255, 1118, 19209, 16821, 18024])).
% 2.33/2.50 tff(19217,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(19218,plain,
% 2.33/2.50 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19217, 19197, 6255, 1118, 18024])).
% 2.33/2.50 tff(19219,plain,
% 2.33/2.50 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19218])).
% 2.33/2.50 tff(19220,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), 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, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19221,plain,
% 2.33/2.50 (((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(19222,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), 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, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[19221])).
% 2.33/2.50 tff(19223,plain,
% 2.33/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), 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, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[19222, 19220])).
% 2.33/2.50 tff(19224,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(19225,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19224, 19223])).
% 2.33/2.50 tff(19226,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19225, 112, 18923, 19219, 19208])).
% 2.33/2.50 tff(19227,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(19228,plain,
% 2.33/2.50 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19227, 19176, 19168, 1118, 19175, 19174, 19102])).
% 2.33/2.50 tff(19229,plain,
% 2.33/2.50 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19228, 18966])).
% 2.33/2.50 tff(19230,plain,
% 2.33/2.50 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1345, 19229, 18918])).
% 2.33/2.50 tff(19231,plain,
% 2.33/2.50 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8351, 19230, 18921])).
% 2.33/2.50 tff(19232,plain,
% 2.33/2.50 (~b(z, s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[9227, 224, 17690, 19176, 19102, 19168])).
% 2.33/2.50 tff(19233,plain,
% 2.33/2.50 (r(z, s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1088, 19232])).
% 2.33/2.50 tff(19234,plain,
% 2.33/2.50 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8023, 112, 19233, 19231])).
% 2.33/2.50 tff(19235,plain,
% 2.33/2.50 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19234])).
% 2.33/2.50 tff(19236,plain,
% 2.33/2.50 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[8104, 224, 19168, 7672, 19235])).
% 2.33/2.50 tff(19237,plain,
% 2.33/2.50 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19009, 19236])).
% 2.33/2.50 tff(19238,plain,
% 2.33/2.50 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1884, 19237])).
% 2.33/2.50 tff(19239,plain,
% 2.33/2.50 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[19238, 18964])).
% 2.33/2.50 tff(19240,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[17080, 112, 18974, 19231, 19239])).
% 2.33/2.50 tff(19241,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(19242,plain,
% 2.33/2.50 (~b(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[19241, 1118, 18957])).
% 2.33/2.50 tff(19243,plain,
% 2.33/2.50 (r(s(s(s(z))), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[72, 19242])).
% 2.33/2.50 tff(19244,plain,
% 2.33/2.50 (~r(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[187, 19243, 18725])).
% 2.33/2.50 tff(19245,plain,
% 2.33/2.50 (b(s(z), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[175, 19244])).
% 2.33/2.50 tff(19246,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[17487, 19243, 18725])).
% 2.33/2.50 tff(19247,plain,
% 2.33/2.50 (b(s(s(s(z))), s(z))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[925, 19246])).
% 2.33/2.50 tff(19248,plain,
% 2.33/2.50 (~b(z, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6404, 19247, 18947, 19245])).
% 2.33/2.51 tff(19249,plain,
% 2.33/2.51 (r(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[100, 19248])).
% 2.33/2.51 tff(19250,plain,
% 2.33/2.51 (r(z, s(s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19249, 18962])).
% 2.33/2.51 tff(19251,plain,
% 2.33/2.51 (b(s(s(z)), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19101, 18973, 18974, 1118, 19245])).
% 2.33/2.51 tff(19252,plain,
% 2.33/2.51 (~r(z, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1104, 112, 18974, 19249])).
% 2.33/2.51 tff(19253,plain,
% 2.33/2.51 (b(z, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1088, 19252])).
% 2.33/2.51 tff(19254,plain,
% 2.33/2.51 (~b(elem!1, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2869, 19253, 17690, 19251])).
% 2.33/2.51 tff(19255,plain,
% 2.33/2.51 (r(elem!1, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2874, 19254, 19126])).
% 2.33/2.51 tff(19256,plain,
% 2.33/2.51 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19120, 19249, 1118, 18974])).
% 2.33/2.51 tff(19257,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 2.33/2.51 tff(19258,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[19257, 18997])).
% 2.33/2.51 tff(19259,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(19260,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19259, 19256])).
% 2.33/2.51 tff(19261,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1884, 19260])).
% 2.33/2.51 tff(19262,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19009, 19261])).
% 2.33/2.51 tff(19263,plain,
% 2.33/2.51 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[18915])).
% 2.33/2.51 tff(19264,plain,
% 2.33/2.51 (b(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19247, 19263])).
% 2.33/2.51 tff(19265,plain,
% 2.33/2.51 (b(elem!1, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15956, 19245, 18915])).
% 2.33/2.51 tff(19266,plain,
% 2.33/2.51 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19140, 224, 19265, 19264, 19262])).
% 2.33/2.51 tff(19267,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19266, 18953])).
% 2.33/2.51 tff(19268,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1294, 19267, 18920])).
% 2.33/2.51 tff(19269,plain,
% 2.33/2.51 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[17036, 19268, 18913])).
% 2.33/2.51 tff(19270,plain,
% 2.33/2.51 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19152, 19269, 19255])).
% 2.33/2.51 tff(19271,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8351, 19270, 18921])).
% 2.33/2.51 tff(19272,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1345, 19271, 18918])).
% 2.33/2.51 tff(19273,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19272, 18956])).
% 2.33/2.51 tff(19274,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19275,plain,
% 2.33/2.51 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19276,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19275])).
% 2.33/2.51 tff(19277,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[19276, 19274])).
% 2.33/2.51 tff(19278,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(19279,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19278, 19277])).
% 2.33/2.51 tff(19280,plain,
% 2.33/2.51 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19279, 224, 17690, 19251, 19253, 19273])).
% 2.33/2.51 tff(19281,plain,
% 2.33/2.51 (~b(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19280, 18976])).
% 2.33/2.51 tff(19282,plain,
% 2.33/2.51 (r(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[4412, 19281])).
% 2.33/2.51 tff(19283,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10247, 19282, 18915, 19250])).
% 2.33/2.51 tff(19284,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[5426, 19283])).
% 2.33/2.51 tff(19285,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19284, 18960])).
% 2.33/2.51 tff(19286,plain,
% 2.33/2.51 (~(s(s(s(s(z)))) = elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8776, 18921])).
% 2.33/2.51 tff(19287,plain,
% 2.33/2.51 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[18913])).
% 2.33/2.51 tff(19288,plain,
% 2.33/2.51 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.33/2.51 inference(symmetry,[status(thm)],[19287])).
% 2.33/2.51 tff(19289,plain,
% 2.33/2.51 (r(s(s(z)), s(s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[18974, 19288])).
% 2.33/2.51 tff(19290,plain,
% 2.33/2.51 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[3300, 19250, 19289, 19249, 1118])).
% 2.33/2.51 tff(19291,plain,
% 2.33/2.51 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[17987, 19290, 18913])).
% 2.33/2.51 tff(19292,plain,
% 2.33/2.51 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[3252, 19291])).
% 2.33/2.51 tff(19293,plain,
% 2.33/2.51 (~b(s(s(s(s(z)))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1579, 19292, 19245, 19247])).
% 2.33/2.51 tff(19294,plain,
% 2.33/2.51 (~b(s(s(s(s(z)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8884, 19293, 18921])).
% 2.33/2.51 tff(19295,plain,
% 2.33/2.51 (r(s(s(s(s(z)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[3183, 19294, 19286])).
% 2.33/2.51 tff(19296,plain,
% 2.33/2.51 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[16943, 112, 19295, 19269])).
% 2.33/2.51 tff(19297,plain,
% 2.33/2.51 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8833, 18921])).
% 2.33/2.51 tff(19298,plain,
% 2.33/2.51 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8869, 68, 19297, 19296])).
% 2.33/2.51 tff(19299,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19300,plain,
% 2.33/2.51 (((~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(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(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(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19301,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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)))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19300])).
% 2.33/2.51 tff(19302,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[19301, 19299])).
% 2.33/2.51 tff(19303,plain,
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% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(19304,plain,
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% 2.33/2.51 inference(modus_ponens,[status(thm)],[19303, 19302])).
% 2.33/2.51 tff(19305,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[19304, 224, 19292, 19262, 19298, 19285])).
% 2.33/2.51 tff(19306,plain,((~b(s(s(z)), z)) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(19307,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[19306, 18957])).
% 2.33/2.51 tff(19308,plain,
% 2.33/2.51 (r(s(s(z)), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[281, 19307])).
% 2.33/2.51 tff(19309,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[18943])).
% 2.33/2.51 tff(19310,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(symmetry,[status(thm)],[19309])).
% 2.33/2.51 tff(19311,plain,
% 2.33/2.51 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19310])).
% 2.33/2.51 tff(19312,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[16898, 19307, 18921])).
% 2.33/2.51 tff(19313,plain,
% 2.33/2.51 (r(s(elem!1), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[498, 19312])).
% 2.33/2.51 tff(19314,plain,
% 2.33/2.51 (~r(s(elem!1), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2694, 19313, 18923])).
% 2.33/2.51 tff(19315,plain,
% 2.33/2.51 (b(s(elem!1), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[939, 19314, 18925])).
% 2.33/2.51 tff(19316,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[7872, 19315, 18915])).
% 2.33/2.51 tff(19317,plain,
% 2.33/2.51 (~r(s(z), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[9974, 19308, 18725])).
% 2.33/2.51 tff(19318,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[1071, 19317])).
% 2.33/2.51 tff(19319,plain,
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% 2.33/2.51 inference(modus_ponens,[status(thm)],[19318, 18987])).
% 2.33/2.51 tff(19320,plain,
% 2.33/2.51 (~r(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[3455, 19308, 18974])).
% 2.33/2.51 tff(19321,plain,
% 2.33/2.51 (b(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[100, 19320])).
% 2.33/2.51 tff(19322,plain,
% 2.33/2.51 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
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% 2.33/2.51 tff(19323,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[276, 19308, 19289])).
% 2.33/2.51 tff(19324,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[593, 19323])).
% 2.33/2.51 tff(19325,plain,
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% 2.33/2.51 inference(modus_ponens,[status(thm)],[19324, 19322])).
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% 2.33/2.51 (~r(s(z), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19043, 19325, 18974])).
% 2.33/2.51 tff(19327,plain,
% 2.33/2.51 (b(s(z), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[175, 19326])).
% 2.33/2.51 tff(19328,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(z))),
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% 2.33/2.51 tff(19329,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[925, 19328])).
% 2.33/2.51 tff(19330,plain,
% 2.33/2.51 (r(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19329, 19058])).
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% 2.33/2.51 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[18123, 224, 2861, 1109, 19114])).
% 2.33/2.51 tff(19332,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19331, 18953])).
% 2.33/2.51 tff(19333,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1294, 19332, 18920])).
% 2.33/2.51 tff(19334,plain,
% 2.33/2.51 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[17036, 19333, 18913])).
% 2.33/2.51 tff(19335,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[17019, 112, 690, 8784, 19334])).
% 2.33/2.51 tff(19336,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(19337,plain,
% 2.33/2.51 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
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% 2.33/2.51 tff(19338,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19259, 19337])).
% 2.33/2.51 tff(19339,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1884, 19338])).
% 2.33/2.51 tff(19340,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19009, 19339])).
% 2.33/2.51 tff(19341,plain,
% 2.33/2.51 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7825, 224, 19321, 19325, 19340])).
% 2.33/2.51 tff(19342,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19341, 19311])).
% 2.33/2.51 tff(19343,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1338, 19342])).
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% 2.33/2.51 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8096, 19343, 18921, 19308])).
% 2.33/2.51 tff(19345,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8351, 19344, 18921])).
% 2.33/2.51 tff(19346,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1345, 19345, 18918])).
% 2.33/2.51 tff(19347,plain,
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% 2.33/2.51 inference(modus_ponens,[status(thm)],[19346, 18956])).
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[18123, 224, 19319, 19316, 19347])).
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% 2.33/2.51 inference(modus_ponens,[status(thm)],[19348, 18953])).
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% 2.33/2.51 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19341])).
% 2.33/2.51 tff(19351,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[19029, 112, 18923, 19350])).
% 2.33/2.51 tff(19352,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[17036, 19351, 18913])).
% 2.33/2.51 tff(19353,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[1294, 19352, 18920])).
% 2.33/2.51 tff(19354,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[19353, 19349])).
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% 2.33/2.51 tff(19356,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[9201, 6255, 19355, 1118])).
% 2.33/2.51 tff(19357,plain,
% 2.33/2.51 (r(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[72, 19356])).
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[187, 19357, 18725])).
% 2.33/2.51 tff(19359,plain,
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[175, 19358])).
% 2.33/2.51 tff(19360,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[17487, 19357, 18725])).
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% 2.33/2.51 (b(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[925, 19360])).
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% 2.33/2.51 inference(unit_resolution,[status(thm)],[6404, 19361, 19359, 18947, 6255])).
% 2.33/2.51 tff(19363,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(19364,plain,
% 2.33/2.51 (~b(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19363, 1118])).
% 2.33/2.51 tff(19365,plain,
% 2.33/2.51 (r(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[100, 19364])).
% 2.33/2.51 tff(19366,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[3919, 18944])).
% 2.33/2.51 tff(19367,plain,
% 2.33/2.51 (r(z, s(s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[689, 18962])).
% 2.33/2.51 tff(19368,plain,
% 2.33/2.51 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[18936, 18943])).
% 2.33/2.51 tff(19369,plain,
% 2.33/2.51 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[19368])).
% 2.33/2.51 tff(19370,plain,
% 2.33/2.51 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[18937, 19369])).
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% 2.33/2.51 ((~r(elem!1, s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19370])).
% 2.33/2.51 tff(19372,plain,
% 2.33/2.51 (~r(s(z), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[9119, 689, 18725])).
% 2.33/2.51 tff(19373,plain,
% 2.33/2.51 (b(s(z), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[175, 19372])).
% 2.33/2.51 tff(19374,plain,
% 2.33/2.51 (b(elem!1, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[15956, 19373, 18915])).
% 2.33/2.51 tff(19375,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19376,plain,
% 2.33/2.51 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19377,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19376])).
% 2.33/2.51 tff(19378,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.33/2.51 inference(transitivity,[status(thm)],[19377, 19375])).
% 2.33/2.51 tff(19379,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(19380,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19379, 19378])).
% 2.33/2.51 tff(19381,plain,
% 2.33/2.51 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19380, 224, 17690, 19374, 16821, 17374])).
% 2.33/2.51 tff(19382,plain,
% 2.33/2.51 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19381])).
% 2.33/2.51 tff(19383,plain,
% 2.33/2.51 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[19225, 112, 18923, 19382])).
% 2.33/2.51 tff(19384,plain,
% 2.33/2.51 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19383, 19371])).
% 2.33/2.51 tff(19385,plain,
% 2.33/2.51 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1439, 19384, 18939])).
% 2.33/2.51 tff(19386,plain,
% 2.33/2.51 (b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19385, 18979])).
% 2.33/2.51 tff(19387,plain,
% 2.33/2.51 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[19386, 18978])).
% 2.33/2.51 tff(19388,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(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))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19389,plain,
% 2.33/2.51 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(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))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(19390,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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)))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[19389])).
% 2.33/2.51 tff(19391,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(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))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[19390, 19388])).
% 2.33/2.52 tff(19392,plain,
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% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(19393,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19392, 19391])).
% 2.33/2.52 tff(19394,plain,
% 2.33/2.52 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19393, 224, 17690, 17374, 19387])).
% 2.33/2.52 tff(19395,plain,
% 2.33/2.52 (~b(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19394, 18976])).
% 2.33/2.52 tff(19396,plain,
% 2.33/2.52 (r(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4412, 19395])).
% 2.33/2.52 tff(19397,plain,
% 2.33/2.52 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10247, 19396, 18915, 19367])).
% 2.33/2.52 tff(19398,plain,
% 2.33/2.52 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[5426, 19397])).
% 2.33/2.52 tff(19399,plain,
% 2.33/2.52 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19398, 18960])).
% 2.33/2.52 tff(19400,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19203, 224, 19374, 16821, 19387])).
% 2.33/2.52 tff(19401,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19400, 19399])).
% 2.33/2.52 tff(19402,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19403,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19402, 19366, 19365])).
% 2.33/2.52 tff(19404,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19009, 19403])).
% 2.33/2.52 tff(19405,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1884, 19404])).
% 2.33/2.52 tff(19406,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19259, 19405])).
% 2.33/2.52 tff(19407,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19408,plain,
% 2.33/2.52 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19409,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19408])).
% 2.33/2.52 tff(19410,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19409, 19407])).
% 2.33/2.52 tff(19411,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(19412,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19411, 19410])).
% 2.33/2.52 tff(19413,plain,
% 2.33/2.52 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19412, 112, 19365, 19406])).
% 2.33/2.52 tff(19414,plain,
% 2.33/2.52 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19413, 18951])).
% 2.33/2.52 tff(19415,plain,
% 2.33/2.52 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4412, 19414])).
% 2.33/2.52 tff(19416,plain,
% 2.33/2.52 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19415, 18948])).
% 2.33/2.52 tff(19417,plain,
% 2.33/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4503, 19416, 18947, 18946])).
% 2.33/2.52 tff(19418,plain,
% 2.33/2.52 (b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[1412, 18979])).
% 2.33/2.52 tff(19419,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4509, 19418])).
% 2.33/2.52 tff(19420,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19421,plain,
% 2.33/2.52 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19420, 19417])).
% 2.33/2.52 tff(19422,plain,
% 2.33/2.52 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1439, 19421, 18939])).
% 2.33/2.52 tff(19423,plain,
% 2.33/2.52 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8812, 19422, 18921])).
% 2.33/2.52 tff(19424,plain,
% 2.33/2.52 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19423, 18938])).
% 2.33/2.52 tff(19425,plain,
% 2.33/2.52 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18958])).
% 2.33/2.52 tff(19426,plain,
% 2.33/2.52 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[19425])).
% 2.33/2.52 tff(19427,plain,
% 2.33/2.52 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18955])).
% 2.33/2.52 tff(19428,plain,
% 2.33/2.52 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19427, 19426])).
% 2.33/2.52 tff(19429,plain,
% 2.33/2.52 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8842, 18915])).
% 2.33/2.52 tff(19430,plain,
% 2.33/2.52 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18955, 18943])).
% 2.33/2.52 tff(19431,plain,
% 2.33/2.52 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[19430])).
% 2.33/2.52 tff(19432,plain,
% 2.33/2.52 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19431])).
% 2.33/2.52 tff(19433,plain,
% 2.33/2.52 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[16789, 112, 19365, 19406])).
% 2.33/2.52 tff(19434,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19433])).
% 2.33/2.52 tff(19435,plain,
% 2.33/2.52 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[3480, 224, 1118, 19434, 19416])).
% 2.33/2.52 tff(19436,plain,
% 2.33/2.52 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19435, 19432])).
% 2.33/2.52 tff(19437,plain,
% 2.33/2.52 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1869, 19436, 19429])).
% 2.33/2.52 tff(19438,plain,
% 2.33/2.52 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19437, 19428])).
% 2.33/2.52 tff(19439,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(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(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19440,plain,
% 2.33/2.52 (((~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(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19441,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19440])).
% 2.33/2.52 tff(19442,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19441, 19439])).
% 2.33/2.52 tff(19443,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(19444,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19443, 19442])).
% 2.33/2.52 tff(19445,plain,
% 2.33/2.52 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19444, 112, 1047, 19438])).
% 2.33/2.52 tff(19446,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19445, 19424])).
% 2.33/2.52 tff(19447,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19448,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19447, 18935, 18929])).
% 2.33/2.52 tff(19449,plain,
% 2.33/2.52 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1317, 19448, 18920, 18919])).
% 2.33/2.52 tff(19450,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1345, 19449, 18918])).
% 2.33/2.52 tff(19451,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[1409, 18956])).
% 2.33/2.52 tff(19452,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.33/2.52 tff(19453,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19452, 19451])).
% 2.33/2.52 tff(19454,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | b(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19455,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19454, 19450])).
% 2.33/2.52 tff(19456,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1294, 19448, 18920])).
% 2.33/2.52 tff(19457,plain,
% 2.33/2.52 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10270, 19456, 18926])).
% 2.33/2.52 tff(19458,plain,
% 2.33/2.52 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1869, 19457, 19429])).
% 2.33/2.52 tff(19459,plain,
% 2.33/2.52 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19458, 19430])).
% 2.33/2.52 tff(19460,plain,
% 2.33/2.52 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19412, 112, 19365, 8784])).
% 2.33/2.52 tff(19461,plain,
% 2.33/2.52 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19460, 18951])).
% 2.33/2.52 tff(19462,plain,
% 2.33/2.52 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4412, 19461])).
% 2.33/2.52 tff(19463,plain,
% 2.33/2.52 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19462, 18948])).
% 2.33/2.52 tff(19464,plain,
% 2.33/2.52 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[16789, 112, 19365, 8784])).
% 2.33/2.52 tff(19465,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19464])).
% 2.33/2.52 tff(19466,plain,
% 2.33/2.52 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19467,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19466])).
% 2.33/2.52 tff(19468,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19467, 3475])).
% 2.33/2.52 tff(19469,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(19470,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19469, 19468])).
% 2.33/2.52 tff(19471,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19470, 224, 1118, 19465, 9861, 19463])).
% 2.33/2.52 tff(19472,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19473,plain,
% 2.33/2.52 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19472, 18929, 19459])).
% 2.33/2.52 tff(19474,plain,
% 2.33/2.52 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19259, 19473])).
% 2.33/2.52 tff(19475,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1884, 19474])).
% 2.33/2.52 tff(19476,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19009, 19475])).
% 2.33/2.52 tff(19477,plain,
% 2.33/2.52 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18955])).
% 2.33/2.52 tff(19478,plain,
% 2.33/2.52 (~b(z, s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19363, 18929])).
% 2.33/2.52 tff(19479,plain,
% 2.33/2.52 (r(z, s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[100, 19478])).
% 2.33/2.52 tff(19480,plain,
% 2.33/2.52 (r(z, s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19479, 18962])).
% 2.33/2.52 tff(19481,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[18026, 19476, 19355, 19455])).
% 2.33/2.52 tff(19482,plain,
% 2.33/2.52 (~b(s(s(elem!1)), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[16648, 19481, 18913])).
% 2.33/2.52 tff(19483,plain,
% 2.33/2.52 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[530, 19482, 19106])).
% 2.33/2.52 tff(19484,plain,
% 2.33/2.52 (~r(z, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[576, 19483, 19480])).
% 2.33/2.52 tff(19485,plain,
% 2.33/2.52 (b(z, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[625, 19484])).
% 2.33/2.52 tff(19486,plain,
% 2.33/2.52 (b(z, s(s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19485, 19477])).
% 2.33/2.52 tff(19487,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19488,plain,
% 2.33/2.52 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(19489,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19488])).
% 2.33/2.52 tff(19490,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19489, 19487])).
% 2.33/2.52 tff(19491,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(19492,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19491, 19490])).
% 2.33/2.52 tff(19493,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19492, 224, 19355, 19486, 19476, 19455])).
% 2.33/2.52 tff(19494,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19493])).
% 2.33/2.52 tff(19495,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[17036, 19456, 18913])).
% 2.33/2.52 tff(19496,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19029, 112, 18923, 19495, 19494])).
% 2.33/2.52 tff(19497,plain,(b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19498,plain,
% 2.33/2.52 (b(s(s(z)), s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19497, 18917])).
% 2.33/2.52 tff(19499,plain,
% 2.33/2.52 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.33/2.52 inference(symmetry,[status(thm)],[19046])).
% 2.33/2.52 tff(19500,plain,
% 2.33/2.52 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19499])).
% 2.33/2.52 tff(19501,plain,
% 2.33/2.52 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18915])).
% 2.33/2.52 tff(19502,plain,
% 2.33/2.52 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 2.33/2.52 inference(transitivity,[status(thm)],[19501, 320])).
% 2.33/2.52 tff(19503,plain,
% 2.33/2.52 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 2.33/2.52 inference(symmetry,[status(thm)],[19502])).
% 2.33/2.52 tff(19504,plain,
% 2.33/2.52 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19503])).
% 2.33/2.52 tff(19505,plain,
% 2.33/2.52 (~(s(elem!1) = s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19104, 19504])).
% 2.33/2.52 tff(19506,plain,
% 2.33/2.52 (~b(s(elem!1), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[16898, 278, 18921])).
% 2.33/2.52 tff(19507,plain,
% 2.33/2.52 (r(s(elem!1), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[498, 19506])).
% 2.33/2.52 tff(19508,plain,
% 2.33/2.52 (~r(s(s(elem!1)), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12361, 19507, 18725, 19105, 19505])).
% 2.33/2.52 tff(19509,plain,
% 2.33/2.52 (b(s(s(elem!1)), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[593, 19508])).
% 2.33/2.52 tff(19510,plain,
% 2.33/2.52 (~r(elem!1, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4310, 19507, 18923])).
% 2.33/2.52 tff(19511,plain,
% 2.33/2.52 (b(elem!1, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[515, 19510, 19104])).
% 2.33/2.52 tff(19512,plain,
% 2.33/2.52 (~r(s(z), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[9974, 268, 18725])).
% 2.33/2.52 tff(19513,plain,
% 2.33/2.52 (b(s(z), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1071, 19512])).
% 2.33/2.52 tff(19514,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18913])).
% 2.33/2.52 tff(19515,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.52 inference(symmetry,[status(thm)],[19514])).
% 2.33/2.52 tff(19516,plain,
% 2.33/2.52 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[19515])).
% 2.33/2.52 tff(19517,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19009, 4753])).
% 2.33/2.52 tff(19518,plain,
% 2.33/2.52 (b(s(s(s(z))), z)),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[1240, 19322])).
% 2.33/2.52 tff(19519,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[7825, 224, 6255, 19518, 19517])).
% 2.33/2.52 tff(19520,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8798, 68, 8795, 19519])).
% 2.33/2.52 tff(19521,plain,
% 2.33/2.52 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18955])).
% 2.33/2.52 tff(19522,plain,
% 2.33/2.52 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.33/2.52 inference(symmetry,[status(thm)],[19521])).
% 2.33/2.52 tff(19523,plain,
% 2.33/2.52 (b(s(elem!1), elem!1)),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19497, 19522])).
% 2.33/2.52 tff(19524,plain,
% 2.33/2.52 (~b(z, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[6542, 501, 17690, 19523])).
% 2.33/2.52 tff(19525,plain,
% 2.33/2.52 (r(z, s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[625, 19524])).
% 2.33/2.52 tff(19526,plain,
% 2.33/2.52 (b(s(elem!1), s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19355, 18971])).
% 2.33/2.52 tff(19527,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[4753, 19515])).
% 2.33/2.52 tff(19528,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[14780, 19527, 17690, 19526, 1240, 18918, 501, 19525])).
% 2.33/2.52 tff(19529,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1294, 19528, 18920])).
% 2.33/2.52 tff(19530,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[17036, 19529, 18913])).
% 2.33/2.52 tff(19531,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19029, 112, 18923, 19530, 19520])).
% 2.33/2.52 tff(19532,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19533,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19532, 6255, 501, 1240])).
% 2.33/2.52 tff(19534,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19533, 19516])).
% 2.33/2.52 tff(19535,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1884, 19533])).
% 2.33/2.52 tff(19536,plain,
% 2.33/2.52 (b(z, s(s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[6255, 19499])).
% 2.33/2.52 tff(19537,plain,
% 2.33/2.52 (~(s(s(elem!1)) = elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[352, 18924])).
% 2.33/2.52 tff(19538,plain,
% 2.33/2.52 (~r(s(s(elem!1)), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4920, 1290, 4916, 18920])).
% 2.33/2.52 tff(19539,plain,
% 2.33/2.52 (b(s(s(elem!1)), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[360, 19538, 19537])).
% 2.33/2.52 tff(19540,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1294, 1290, 18920])).
% 2.33/2.52 tff(19541,plain,
% 2.33/2.52 (~r(elem!1, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[14725, 19540, 18915, 1787])).
% 2.33/2.52 tff(19542,plain,
% 2.33/2.52 (b(elem!1, s(s(elem!1)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[558, 19541, 18924])).
% 2.33/2.52 tff(19543,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[743, 19542, 19539, 17690, 1180])).
% 2.33/2.52 tff(19544,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(19545,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19544, 19536, 19535, 19534])).
% 2.33/2.52 tff(19546,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19545, 18945])).
% 2.33/2.52 tff(19547,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19545, 18944])).
% 2.33/2.52 tff(19548,plain,
% 2.33/2.52 (b(elem!1, s(s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19513, 18987])).
% 2.33/2.52 tff(19549,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[17049, 224, 19548, 19497, 19547])).
% 2.33/2.52 tff(19550,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19454, 19549])).
% 2.33/2.52 tff(19551,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1345, 19550, 18918])).
% 2.33/2.52 tff(19552,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8351, 19551, 18921])).
% 2.33/2.52 tff(19553,plain,
% 2.33/2.52 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[18955])).
% 2.33/2.52 tff(19554,plain,
% 2.33/2.52 (r(z, s(s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19525, 19553])).
% 2.33/2.52 tff(19555,plain,
% 2.33/2.52 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8037, 112, 19554, 19552])).
% 2.33/2.52 tff(19556,plain,
% 2.33/2.52 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19555, 18951])).
% 2.33/2.52 tff(19557,plain,
% 2.33/2.52 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4412, 19556])).
% 2.33/2.52 tff(19558,plain,
% 2.33/2.52 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[19557, 18948])).
% 2.33/2.52 tff(19559,plain,
% 2.33/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4503, 19558, 18947, 19546])).
% 2.33/2.52 tff(19560,plain,
% 2.33/2.52 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[19420, 19559])).
% 2.33/2.52 tff(19561,plain,
% 2.33/2.52 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1439, 19560, 18939])).
% 2.33/2.52 tff(19562,plain,
% 2.33/2.52 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8812, 19561, 18921])).
% 2.33/2.52 tff(19563,plain,
% 2.33/2.52 (~r(s(z), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8807, 19562, 18725, 18921, 6255])).
% 2.33/2.52 tff(19564,plain,
% 2.33/2.52 (b(s(z), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[175, 19563])).
% 2.33/2.52 tff(19565,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[17718, 19564, 19355, 19498])).
% 2.33/2.52 tff(19566,plain,
% 2.33/2.52 (r(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[925, 19565])).
% 2.33/2.52 tff(19567,plain,
% 2.33/2.52 (b(elem!1, s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[15956, 19564, 18915])).
% 2.33/2.52 tff(19568,plain,
% 2.33/2.52 (~b(s(s(s(z))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2412, 19567, 19355, 19497])).
% 2.33/2.52 tff(19569,plain,
% 2.33/2.52 (r(s(s(s(z))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[374, 19568, 19083])).
% 2.33/2.52 tff(19570,plain,
% 2.33/2.52 (~r(s(s(s(s(z)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[18170, 19569, 18921, 19355, 19518, 6255, 19566, 268])).
% 2.33/2.52 tff(19571,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[3183, 19570, 19286])).
% 2.33/2.52 tff(19572,plain,
% 2.33/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8884, 19571, 18921])).
% 2.33/2.53 tff(19573,plain,
% 2.33/2.53 (~(elem!1 = s(s(s(s(z)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[16913, 19286])).
% 2.33/2.53 tff(19574,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[18800, 19564, 19355, 19513])).
% 2.33/2.53 tff(19575,plain,
% 2.33/2.53 (~b(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[16648, 19574, 18913])).
% 2.33/2.53 tff(19576,plain,
% 2.33/2.53 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[530, 19575, 19106])).
% 2.33/2.53 tff(19577,plain,
% 2.33/2.53 (r(s(s(s(z))), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[8303, 19576, 18921])).
% 2.33/2.53 tff(19578,plain,
% 2.33/2.53 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[17004, 19577, 18923, 19573, 19518, 19567, 6255])).
% 2.33/2.53 tff(19579,plain,
% 2.33/2.53 (b(s(s(s(s(z)))), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[6185, 19578])).
% 2.33/2.53 tff(19580,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[5196, 19579, 19572, 19513, 19498])).
% 2.33/2.53 tff(19581,plain,((~b(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(19582,plain,
% 2.33/2.53 (~b(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[19581, 16884, 19511, 19509])).
% 2.33/2.53 tff(19583,plain,
% 2.33/2.53 (~b(z, s(s(elem!1)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[19582, 19500])).
% 2.33/2.53 tff(19584,plain,
% 2.33/2.53 (~b(z, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[6542, 19511, 17690, 19523])).
% 2.33/2.53 tff(19585,plain,
% 2.33/2.53 (r(z, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[625, 19584])).
% 2.33/2.53 tff(19586,plain,
% 2.33/2.53 (~r(s(z), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[9974, 16884, 18725])).
% 2.33/2.53 tff(19587,plain,
% 2.33/2.53 (b(s(z), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1071, 19586])).
% 2.33/2.53 tff(19588,plain,
% 2.33/2.53 (r(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[100, 19582])).
% 2.33/2.53 tff(19589,plain,
% 2.33/2.53 (~r(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[9119, 19588, 18725])).
% 2.33/2.53 tff(19590,plain,
% 2.33/2.53 (b(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[175, 19589])).
% 2.33/2.53 tff(19591,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(s(z)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[18800, 19590, 19355, 19587])).
% 2.33/2.53 tff(19592,plain,
% 2.33/2.53 (~b(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[16648, 19591, 18913])).
% 2.33/2.53 tff(19593,plain,
% 2.33/2.53 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[530, 19592, 19106])).
% 2.33/2.53 tff(19594,plain,
% 2.33/2.53 (~r(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[576, 19593, 19585])).
% 2.33/2.53 tff(19595,plain,
% 2.33/2.53 (b(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[752, 19594])).
% 2.33/2.53 tff(19596,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[19595, 19583])).
% 2.33/2.53 tff(19597,plain,(b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(19598,plain,
% 2.33/2.53 (~b(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[19363, 19597])).
% 2.33/2.53 tff(19599,plain,
% 2.33/2.53 (r(z, s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[100, 19598])).
% 2.33/2.53 tff(19600,plain,
% 2.33/2.53 (~r(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[9119, 19599, 18725])).
% 2.33/2.53 tff(19601,plain,
% 2.33/2.53 (b(s(z), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[175, 19600])).
% 2.33/2.53 tff(19602,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[17718, 19601, 19355, 19498])).
% 2.33/2.53 tff(19603,plain,
% 2.33/2.53 (r(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[925, 19602])).
% 2.33/2.53 tff(19604,plain,
% 2.33/2.53 (~r(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[17487, 19603, 18725])).
% 2.33/2.53 tff(19605,plain,
% 2.33/2.53 (b(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[72, 19604])).
% 2.33/2.53 tff(19606,plain,
% 2.33/2.53 (b(s(s(elem!1)), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[9144, 19605, 18913])).
% 2.33/2.53 tff(19607,plain,
% 2.33/2.53 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[18913])).
% 2.33/2.53 tff(19608,plain,
% 2.33/2.53 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.33/2.53 inference(symmetry,[status(thm)],[19607])).
% 2.33/2.53 tff(19609,plain,
% 2.33/2.53 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[19608])).
% 2.33/2.53 tff(19610,plain,
% 2.33/2.53 (~(s(s(z)) = s(s(elem!1)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[55, 19609])).
% 2.33/2.53 tff(19611,plain,
% 2.33/2.53 (~b(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[18840, 19605, 18947, 19355, 19610, 19597, 19606])).
% 2.33/2.53 tff(19612,plain,
% 2.33/2.53 (r(z, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[752, 19611])).
% 2.33/2.53 tff(19613,plain,
% 2.33/2.53 (~r(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[15713, 19612, 18725])).
% 2.33/2.53 tff(19614,plain,
% 2.33/2.53 (b(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[653, 19613])).
% 2.33/2.53 tff(19615,plain,
% 2.33/2.53 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[86])).
% 2.33/2.53 tff(19616,plain,
% 2.33/2.53 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(symmetry,[status(thm)],[19615])).
% 2.33/2.53 tff(19617,plain,
% 2.33/2.53 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[19616])).
% 2.33/2.53 tff(19618,plain,
% 2.33/2.53 (~b(s(z), s(s(elem!1)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[10519, 19617])).
% 2.33/2.53 tff(19619,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2252, 19618])).
% 2.33/2.53 tff(19620,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(elem!1)))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(19621,plain,
% 2.33/2.53 (b(elem!1, s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[19620, 19614, 18915])).
% 2.33/2.53 tff(19622,plain,
% 2.33/2.53 (~b(s(elem!1), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13567, 19621, 19526, 19523, 19606])).
% 2.33/2.53 tff(19623,plain,
% 2.33/2.53 (r(s(elem!1), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[498, 19622])).
% 2.33/2.53 tff(19624,plain,
% 2.33/2.53 (~r(elem!1, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[4310, 19623, 18923])).
% 2.33/2.53 tff(19625,plain,
% 2.33/2.53 (b(elem!1, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[515, 19624, 19104])).
% 2.33/2.53 tff(19626,plain,
% 2.33/2.53 (~b(z, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[6542, 19625, 17690, 19523])).
% 2.33/2.53 tff(19627,plain,
% 2.33/2.53 (r(z, s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[625, 19626])).
% 2.33/2.53 tff(19628,plain,
% 2.33/2.53 (~b(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[3570, 19625, 19526, 19621])).
% 2.33/2.53 tff(19629,plain,
% 2.33/2.53 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[530, 19628, 19106])).
% 2.33/2.53 tff(19630,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[576, 19629, 19627, 19612])).
% 2.33/2.53 % SZS output end Proof
% 2.33/2.53 % E exiting
%------------------------------------------------------------------------------