%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA142-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:51 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.84s
% Output : Proof 3.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA142-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:21:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 1.65/1.84 % SZS status Unsatisfiable
% 1.65/1.84 % SZS output start Proof
% 1.65/1.84 tff(r_type, type, (
% 1.65/1.84 r: ( $i * $i ) > $o)).
% 1.65/1.84 tff(s_type, type, (
% 1.65/1.84 s: $i > $i)).
% 1.65/1.84 tff(z_type, type, (
% 1.65/1.84 z: $i)).
% 1.65/1.84 tff(b_type, type, (
% 1.65/1.84 b: ( $i * $i ) > $o)).
% 1.65/1.84 tff(elem_1_type, type, (
% 1.65/1.84 elem_1: $i)).
% 1.65/1.84 tff(inj_0_type, type, (
% 1.65/1.84 inj_0: $i > $i)).
% 1.65/1.84 tff(1,assumption,(~b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.84 tff(2,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.65/1.84 tff(3,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.65/1.84 tff(4,plain,
% 1.65/1.84 ((z = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 1.65/1.84 inference(commutativity,[status(thm)],[])).
% 1.65/1.84 tff(5,plain,
% 1.65/1.84 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(symmetry,[status(thm)],[4])).
% 1.65/1.84 tff(6,plain,
% 1.65/1.84 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[5])).
% 1.65/1.84 tff(7,plain,
% 1.65/1.84 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.65/1.84 inference(bind,[status(th)],[])).
% 1.65/1.84 tff(8,plain,
% 1.65/1.84 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.65/1.84 inference(quant_intro,[status(thm)],[7])).
% 1.65/1.84 tff(9,plain,
% 1.65/1.84 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(10,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.65/1.84 tff(11,plain,
% 1.65/1.84 (![X: $i] : (~(s(X) = z))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.65/1.84 tff(12,plain,(
% 1.65/1.84 ![X: $i] : (~(s(X) = z))),
% 1.65/1.84 inference(skolemize,[status(sab)],[11])).
% 1.65/1.84 tff(13,plain,
% 1.65/1.84 (![X: $i] : (~(s(X) = z))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.65/1.84 tff(14,plain,
% 1.65/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(15,plain,
% 1.65/1.84 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[14, 13])).
% 1.65/1.84 tff(16,plain,
% 1.65/1.84 (~(z = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[15, 6])).
% 1.65/1.84 tff(17,plain,
% 1.65/1.84 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.65/1.84 inference(bind,[status(th)],[])).
% 1.65/1.84 tff(18,plain,
% 1.65/1.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(quant_intro,[status(thm)],[17])).
% 1.65/1.84 tff(19,plain,
% 1.65/1.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(20,plain,
% 1.65/1.84 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.65/1.84 inference(bind,[status(th)],[])).
% 1.65/1.84 tff(21,plain,
% 1.65/1.84 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(quant_intro,[status(thm)],[20])).
% 1.65/1.84 tff(22,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.65/1.84 tff(23,plain,
% 1.65/1.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.65/1.84 tff(24,plain,
% 1.65/1.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[23, 19])).
% 1.65/1.84 tff(25,plain,(
% 1.65/1.84 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(skolemize,[status(sab)],[24])).
% 1.65/1.84 tff(26,plain,
% 1.65/1.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[25, 18])).
% 1.65/1.84 tff(27,plain,
% 1.65/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(28,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(29,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.65/1.84 tff(30,plain,
% 1.65/1.84 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[29, 26])).
% 1.65/1.84 tff(31,plain,
% 1.65/1.84 (b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[30, 16])).
% 1.65/1.84 tff(32,plain,
% 1.65/1.84 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[31, 1])).
% 1.65/1.84 tff(33,assumption,(r(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.84 tff(34,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.65/1.84 tff(35,plain,
% 1.65/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(36,plain,
% 1.65/1.84 (~(s(z) = z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[35, 13])).
% 1.65/1.84 tff(37,plain,
% 1.65/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(38,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(39,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.65/1.84 tff(40,plain,
% 1.65/1.84 (b(s(z), z) | r(s(z), z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[39, 26, 36])).
% 1.65/1.84 tff(41,plain,
% 1.65/1.84 (r(s(z), z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[40, 34])).
% 1.65/1.84 tff(42,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.65/1.84 tff(43,assumption,(z = s(s(z))), introduced(assumption)).
% 1.65/1.84 tff(44,plain,
% 1.65/1.84 (s(s(z)) = z),
% 1.65/1.84 inference(symmetry,[status(thm)],[43])).
% 1.65/1.84 tff(45,plain,
% 1.65/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(46,plain,
% 1.65/1.84 (~(s(s(z)) = z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[45, 13])).
% 1.65/1.84 tff(47,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[46, 44])).
% 1.65/1.84 tff(48,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(49,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 1.65/1.84 tff(50,plain,
% 1.65/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(51,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(52,plain,
% 1.65/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.65/1.84 tff(53,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[52, 26, 49, 42, 48])).
% 1.65/1.84 tff(54,plain,(r(z, s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(55,plain,
% 1.65/1.84 (r(z, s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[54, 42])).
% 1.65/1.84 tff(56,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.65/1.84 tff(57,assumption,(z = elem!1), introduced(assumption)).
% 1.65/1.84 tff(58,plain,
% 1.65/1.84 (s(z) = s(elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[57])).
% 1.65/1.84 tff(59,plain,
% 1.65/1.84 (s(s(z)) = s(s(elem!1))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[58])).
% 1.65/1.84 tff(60,plain,
% 1.65/1.84 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[59])).
% 1.65/1.84 tff(61,plain,
% 1.65/1.84 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[57])).
% 1.65/1.84 tff(62,plain,
% 1.65/1.84 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 1.65/1.84 inference(symmetry,[status(thm)],[61])).
% 1.65/1.84 tff(63,plain,
% 1.65/1.84 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[57])).
% 1.65/1.84 tff(64,plain,
% 1.65/1.84 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[63])).
% 1.65/1.84 tff(65,plain,
% 1.65/1.84 (~(s(s(z)) = elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[46, 64])).
% 1.65/1.84 tff(66,plain,
% 1.65/1.84 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[57, 59])).
% 1.65/1.85 tff(67,plain,
% 1.65/1.85 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[66])).
% 1.65/1.85 tff(68,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(69,plain,
% 1.65/1.85 (b(z, s(s(z)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.65/1.85 tff(70,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[42, 69])).
% 1.65/1.85 tff(71,plain,((~(z = elem!1)) | b(z, s(s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(72,plain,
% 1.65/1.85 (~b(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[71, 57, 42])).
% 1.65/1.85 tff(73,plain,
% 1.65/1.85 ((elem!1 = z) <=> (z = elem!1)),
% 1.65/1.85 inference(commutativity,[status(thm)],[])).
% 1.65/1.85 tff(74,plain,
% 1.65/1.85 ((z = elem!1) <=> (elem!1 = z)),
% 1.65/1.85 inference(symmetry,[status(thm)],[73])).
% 1.65/1.85 tff(75,plain,
% 1.65/1.85 (elem!1 = z),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[57, 74])).
% 1.65/1.85 tff(76,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.65/1.85 tff(77,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[76, 75])).
% 1.65/1.85 tff(78,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(79,plain,
% 1.65/1.85 (elem!1 = z),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[78, 57])).
% 1.65/1.85 tff(80,assumption,(elem!1 = z), introduced(assumption)).
% 1.65/1.85 tff(81,plain,
% 1.65/1.85 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[80])).
% 1.65/1.85 tff(82,plain,
% 1.65/1.85 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[81])).
% 1.65/1.85 tff(83,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(84,plain,
% 1.65/1.85 (b(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.65/1.85 tff(85,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(86,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.65/1.85 tff(87,plain,((~(elem!1 = z)) | b(elem!1, s(s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(88,plain,
% 1.65/1.85 (~b(z, s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[87, 79, 72])).
% 1.65/1.85 tff(89,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(90,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.65/1.85 tff(91,plain,
% 1.65/1.85 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[90])).
% 1.65/1.85 tff(92,plain,
% 1.65/1.85 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[91])).
% 1.65/1.85 tff(93,plain,
% 1.65/1.85 ((~b(z, s(s(elem!1)))) <=> (~b(z, elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[92])).
% 1.65/1.85 tff(94,plain,
% 1.65/1.85 (~b(z, elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[89, 93])).
% 1.65/1.85 tff(95,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.65/1.85 tff(96,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[95, 94])).
% 1.65/1.85 tff(97,plain,((~(elem!1 = s(s(elem!1)))) | (~b(z, elem!1)) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(98,plain,
% 1.65/1.85 (~b(z, elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[97, 90, 89])).
% 1.65/1.85 tff(99,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(100,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(101,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.65/1.85 tff(102,plain,
% 1.65/1.85 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[101, 26])).
% 1.65/1.85 tff(103,plain,
% 1.65/1.85 (z = elem!1),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[102, 98, 56])).
% 1.65/1.85 tff(104,plain,
% 1.65/1.85 (elem!1 = z),
% 1.65/1.85 inference(symmetry,[status(thm)],[103])).
% 1.65/1.85 tff(105,plain,
% 1.65/1.85 (s(s(elem!1)) = elem!1),
% 1.65/1.85 inference(symmetry,[status(thm)],[90])).
% 1.65/1.85 tff(106,plain,
% 1.65/1.85 (s(s(elem!1)) = z),
% 1.65/1.85 inference(transitivity,[status(thm)],[105, 104])).
% 1.65/1.85 tff(107,plain,
% 1.65/1.85 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(108,plain,
% 1.65/1.85 (~(s(s(elem!1)) = z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[107, 13])).
% 1.65/1.85 tff(109,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[108, 106])).
% 1.65/1.85 tff(110,plain,((~(elem!1 = s(s(elem!1)))) | r(z, elem!1) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(111,plain,
% 1.65/1.85 (~(elem!1 = s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[110, 88, 56])).
% 1.65/1.85 tff(112,plain,
% 1.65/1.85 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.85 inference(commutativity,[status(thm)],[])).
% 1.65/1.85 tff(113,plain,
% 1.65/1.85 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[112])).
% 1.65/1.85 tff(114,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.65/1.85 tff(115,plain,
% 1.65/1.85 (elem!1 = s(s(elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.65/1.85 tff(116,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(117,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[116, 115])).
% 1.65/1.85 tff(118,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(119,plain,
% 1.65/1.85 (~(s(s(elem!1)) = elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[118, 111])).
% 1.65/1.85 tff(120,plain,
% 1.65/1.85 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(121,plain,
% 1.65/1.85 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(122,plain,
% 1.65/1.85 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(123,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.65/1.85 tff(124,plain,
% 1.65/1.85 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.65/1.85 tff(125,plain,(
% 1.65/1.85 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.65/1.85 inference(skolemize,[status(sab)],[124])).
% 1.65/1.85 tff(126,plain,
% 1.65/1.85 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.65/1.85 tff(127,plain,
% 1.65/1.85 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[126, 120])).
% 1.65/1.85 tff(128,plain,
% 1.65/1.85 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(129,plain,
% 1.65/1.85 (inj_0(s(elem!1)) = elem!1),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.65/1.85 tff(130,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.65/1.85 tff(131,plain,
% 1.65/1.85 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[130])).
% 1.65/1.85 tff(132,plain,
% 1.65/1.85 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 1.65/1.85 inference(symmetry,[status(thm)],[131])).
% 1.65/1.85 tff(133,plain,
% 1.65/1.85 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(134,plain,
% 1.65/1.85 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[133, 127])).
% 1.65/1.85 tff(135,plain,
% 1.65/1.85 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[134])).
% 1.65/1.85 tff(136,plain,
% 1.65/1.85 (s(s(elem!1)) = s(elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[130])).
% 1.65/1.85 tff(137,plain,
% 1.65/1.85 (s(s(elem!1)) = elem!1),
% 1.65/1.85 inference(transitivity,[status(thm)],[136, 135, 132, 129])).
% 1.65/1.85 tff(138,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.65/1.85 tff(139,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[138, 137])).
% 1.65/1.85 tff(140,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(141,plain,
% 1.65/1.85 (~(s(elem!1) = s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[140, 119])).
% 1.65/1.85 tff(142,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.85 tff(143,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(144,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(145,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.65/1.85 tff(146,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[145, 26, 85, 142, 116])).
% 1.65/1.85 tff(147,plain,(b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(148,plain,
% 1.65/1.85 (r(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[147, 111, 72])).
% 1.65/1.85 tff(149,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.65/1.85 tff(150,assumption,(r(s(z), z)), introduced(assumption)).
% 1.65/1.85 tff(151,assumption,(r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.85 tff(152,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.65/1.85 tff(153,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.65/1.85 tff(154,plain,
% 1.65/1.85 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.65/1.85 inference(bind,[status(th)],[])).
% 1.65/1.85 tff(155,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(quant_intro,[status(thm)],[154])).
% 1.65/1.85 tff(156,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(157,plain,
% 1.65/1.85 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 1.65/1.85 inference(bind,[status(th)],[])).
% 1.65/1.85 tff(158,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(quant_intro,[status(thm)],[157])).
% 1.65/1.85 tff(159,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.65/1.85 tff(160,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.65/1.85 tff(161,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[160, 156])).
% 1.65/1.85 tff(162,plain,(
% 1.65/1.85 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(skolemize,[status(sab)],[161])).
% 1.65/1.85 tff(163,plain,
% 1.65/1.85 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[162, 155])).
% 1.65/1.85 tff(164,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(165,plain,
% 1.65/1.85 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(166,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[165])).
% 1.65/1.85 tff(167,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[166, 164])).
% 1.65/1.85 tff(168,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(169,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.65/1.85 tff(170,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[169, 163, 150, 153, 151, 152])).
% 1.65/1.85 tff(171,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(172,plain,
% 1.65/1.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[171, 151, 55, 150])).
% 1.65/1.85 tff(173,plain,
% 1.65/1.85 (((~![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))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(174,plain,
% 1.65/1.85 ((~![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))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(175,plain,
% 1.65/1.85 ((~![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)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.65/1.85 tff(176,plain,
% 1.65/1.85 (b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[175, 26, 15])).
% 1.65/1.85 tff(177,plain,
% 1.65/1.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[176, 172])).
% 1.65/1.85 tff(178,plain,
% 1.65/1.85 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[171, 151, 153, 150])).
% 1.65/1.85 tff(179,plain,
% 1.65/1.85 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[176, 178])).
% 1.65/1.85 tff(180,plain,
% 1.65/1.85 (~(elem!1 = z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[87, 85, 83])).
% 1.65/1.85 tff(181,plain,
% 1.65/1.85 (~(z = elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[78, 180])).
% 1.65/1.85 tff(182,plain,
% 1.65/1.85 (b(z, elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[102, 181, 56])).
% 1.65/1.85 tff(183,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.65/1.85 tff(184,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(185,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(186,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.65/1.85 tff(187,plain,
% 1.65/1.85 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[186, 26])).
% 1.65/1.85 tff(188,plain,
% 1.65/1.85 (b(elem!1, z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[187, 183, 180])).
% 1.65/1.85 tff(189,plain,
% 1.65/1.85 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 1.65/1.85 inference(bind,[status(th)],[])).
% 1.65/1.85 tff(190,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(quant_intro,[status(thm)],[189])).
% 1.65/1.85 tff(191,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(192,plain,
% 1.65/1.85 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) <=> (((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 1.65/1.85 inference(bind,[status(th)],[])).
% 1.65/1.85 tff(193,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(quant_intro,[status(thm)],[192])).
% 1.65/1.85 tff(194,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.65/1.85 tff(195,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.65/1.85 tff(196,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.65/1.85 tff(197,plain,(
% 1.65/1.85 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(skolemize,[status(sab)],[196])).
% 1.65/1.85 tff(198,plain,
% 1.65/1.85 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[197, 190])).
% 1.65/1.85 tff(199,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(200,plain,
% 1.65/1.85 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(201,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[200])).
% 1.65/1.85 tff(202,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[201, 199])).
% 1.65/1.85 tff(203,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(204,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.65/1.85 tff(205,plain,
% 1.65/1.85 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[204, 198, 95, 188, 179])).
% 1.65/1.85 tff(206,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.65/1.85 tff(207,plain,
% 1.65/1.85 (r(s(z), z) <=> r(elem!1, z)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[206])).
% 1.65/1.85 tff(208,plain,
% 1.65/1.85 (r(elem!1, z) <=> r(s(z), z)),
% 1.65/1.85 inference(symmetry,[status(thm)],[207])).
% 1.65/1.85 tff(209,plain,
% 1.65/1.85 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[208])).
% 1.65/1.85 tff(210,plain,
% 1.65/1.85 (~r(s(z), z)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[183, 209])).
% 1.65/1.85 tff(211,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[150, 210])).
% 1.65/1.85 tff(212,plain,((~(s(z) = elem!1)) | (~r(s(z), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(213,plain,
% 1.65/1.85 (~(s(z) = elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[212, 183, 150])).
% 1.65/1.85 tff(214,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(215,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(216,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.65/1.85 tff(217,plain,
% 1.65/1.85 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[216, 26])).
% 1.65/1.85 tff(218,plain,
% 1.65/1.85 (r(s(z), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[217, 213, 149])).
% 1.65/1.85 tff(219,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.65/1.85 tff(220,plain,
% 1.65/1.85 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[219])).
% 1.65/1.85 tff(221,plain,
% 1.65/1.85 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(222,plain,
% 1.65/1.85 (inj_0(s(s(z))) = s(z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[221, 127])).
% 1.65/1.85 tff(223,plain,
% 1.65/1.85 (s(z) = inj_0(s(s(z)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[222])).
% 1.65/1.85 tff(224,plain,
% 1.65/1.85 (s(z) = elem!1),
% 1.65/1.85 inference(transitivity,[status(thm)],[223, 220, 129])).
% 1.65/1.85 tff(225,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.65/1.85 tff(226,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[225, 224])).
% 1.65/1.85 tff(227,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(228,plain,
% 1.65/1.85 (~(s(s(z)) = s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[227, 213])).
% 1.65/1.85 tff(229,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.65/1.85 tff(230,plain,
% 1.65/1.85 (s(elem!1) = s(s(z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[229])).
% 1.65/1.85 tff(231,plain,
% 1.65/1.85 (s(s(z)) = s(elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[230])).
% 1.65/1.85 tff(232,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.65/1.85 tff(233,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[232, 231])).
% 1.65/1.85 tff(234,plain,((~(elem!1 = s(z))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(235,plain,
% 1.65/1.85 (~(elem!1 = s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[234, 228])).
% 1.65/1.85 tff(236,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.65/1.85 tff(237,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.65/1.85 tff(238,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.65/1.85 tff(239,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(240,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(241,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.65/1.85 tff(242,plain,
% 1.65/1.85 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[241, 26])).
% 1.65/1.85 tff(243,plain,
% 1.65/1.85 (r(elem!1, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[242, 238, 237])).
% 1.65/1.85 tff(244,assumption,(~b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.65/1.85 tff(245,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 1.65/1.85 tff(246,plain,
% 1.65/1.85 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(elem!1, s(z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[245])).
% 1.65/1.85 tff(247,plain,
% 1.65/1.85 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.65/1.85 inference(symmetry,[status(thm)],[246])).
% 1.65/1.85 tff(248,plain,
% 1.65/1.85 ((~b(elem!1, s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[247])).
% 1.65/1.85 tff(249,plain,
% 1.65/1.85 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[238, 248])).
% 1.65/1.85 tff(250,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2, 249])).
% 1.65/1.85 tff(251,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(252,plain,
% 1.65/1.85 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[251, 238, 2])).
% 1.65/1.85 tff(253,plain,
% 1.65/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(254,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(255,plain,
% 1.65/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.65/1.85 tff(256,plain,
% 1.65/1.85 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[255, 26])).
% 1.65/1.85 tff(257,plain,
% 1.65/1.85 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[256, 252, 244])).
% 1.65/1.85 tff(258,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.65/1.85 tff(259,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.65/1.85 tff(260,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(261,plain,
% 1.65/1.85 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(262,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[261])).
% 1.65/1.86 tff(263,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[262, 260])).
% 1.65/1.86 tff(264,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(265,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.65/1.86 tff(266,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[265, 163, 236, 259, 151, 258])).
% 1.65/1.86 tff(267,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(268,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[267, 257, 243, 236, 151])).
% 1.65/1.86 tff(269,plain,(b(elem!1, s(z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (elem!1 = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(270,plain,
% 1.65/1.86 (b(elem!1, s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[269, 218, 151, 205, 235, 2])).
% 1.65/1.86 tff(271,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.65/1.86 tff(272,plain,
% 1.65/1.86 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.65/1.86 inference(transitivity,[status(thm)],[245, 90])).
% 1.65/1.86 tff(273,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[272])).
% 1.65/1.86 tff(274,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(275,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[274, 127])).
% 1.65/1.86 tff(276,plain,
% 1.65/1.86 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[275])).
% 1.65/1.86 tff(277,plain,
% 1.65/1.86 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.65/1.86 inference(transitivity,[status(thm)],[276, 273, 134])).
% 1.65/1.86 tff(278,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[277])).
% 1.65/1.86 tff(279,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(280,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[279, 127])).
% 1.65/1.86 tff(281,plain,
% 1.65/1.86 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[280])).
% 1.65/1.86 tff(282,plain,
% 1.65/1.86 (s(s(s(s(s(z))))) = elem!1),
% 1.65/1.86 inference(transitivity,[status(thm)],[281, 278, 129])).
% 1.65/1.86 tff(283,plain,
% 1.65/1.86 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.86 inference(monotonicity,[status(thm)],[245])).
% 1.65/1.86 tff(284,plain,
% 1.65/1.86 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[283])).
% 1.65/1.86 tff(285,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.65/1.86 tff(286,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[285])).
% 1.65/1.86 tff(287,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(288,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[287, 127])).
% 1.65/1.86 tff(289,plain,
% 1.65/1.86 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[288])).
% 1.65/1.86 tff(290,plain,
% 1.65/1.86 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[289, 286, 275])).
% 1.65/1.86 tff(291,plain,
% 1.65/1.86 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[290])).
% 1.65/1.86 tff(292,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(293,plain,
% 1.65/1.86 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[292, 127])).
% 1.65/1.86 tff(294,plain,
% 1.65/1.86 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[293])).
% 1.65/1.86 tff(295,plain,
% 1.65/1.86 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[294, 291, 280, 285])).
% 1.65/1.86 tff(296,plain,
% 1.65/1.86 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[295])).
% 1.65/1.86 tff(297,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(298,plain,
% 1.65/1.86 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[297, 127])).
% 1.65/1.86 tff(299,plain,
% 1.65/1.86 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[298])).
% 1.65/1.86 tff(300,plain,
% 1.65/1.86 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[299, 296, 275])).
% 1.65/1.86 tff(301,plain,
% 1.65/1.86 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[300])).
% 1.65/1.86 tff(302,plain,
% 1.65/1.86 (s(z) = s(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[223, 301, 280, 285])).
% 1.65/1.86 tff(303,plain,
% 1.65/1.86 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(304,plain,
% 1.65/1.86 (inj_0(s(z)) = z),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[303, 127])).
% 1.65/1.86 tff(305,assumption,(s(z) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.65/1.86 tff(306,plain,
% 1.65/1.86 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[305])).
% 1.65/1.86 tff(307,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.65/1.86 inference(symmetry,[status(thm)],[306])).
% 1.65/1.86 tff(308,plain,
% 1.65/1.86 (s(s(s(s(s(s(z)))))) = z),
% 1.65/1.86 inference(transitivity,[status(thm)],[276, 307, 304])).
% 1.65/1.86 tff(309,plain,
% 1.65/1.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(310,plain,
% 1.65/1.86 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[309, 13])).
% 1.65/1.86 tff(311,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[310, 308])).
% 1.65/1.86 tff(312,plain,(~(s(z) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(313,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[312, 302])).
% 1.65/1.86 tff(314,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(315,plain,
% 1.65/1.86 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[314, 284])).
% 1.65/1.86 tff(316,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[315, 282])).
% 1.65/1.86 tff(317,plain,((~(elem!1 = s(s(elem!1)))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(318,plain,
% 1.65/1.86 (~(elem!1 = s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[317, 245])).
% 1.65/1.86 tff(319,plain,
% 1.65/1.86 (r(elem!1, s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[147, 318, 85])).
% 1.65/1.86 tff(320,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.65/1.86 tff(321,plain,
% 1.65/1.86 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[245])).
% 1.65/1.86 tff(322,plain,
% 1.65/1.86 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[245])).
% 1.65/1.86 tff(323,plain,
% 1.65/1.86 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[322])).
% 1.65/1.86 tff(324,plain,
% 1.65/1.86 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[323])).
% 1.65/1.86 tff(325,plain,
% 1.65/1.86 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, elem!1)),
% 1.65/1.86 inference(monotonicity,[status(thm)],[245])).
% 1.65/1.86 tff(326,plain,
% 1.65/1.86 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[325])).
% 1.65/1.86 tff(327,plain,
% 1.65/1.86 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[95, 326])).
% 1.65/1.86 tff(328,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.65/1.86 tff(329,plain,
% 1.65/1.86 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), elem!1)),
% 1.65/1.86 inference(monotonicity,[status(thm)],[245])).
% 1.65/1.86 tff(330,assumption,(b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.65/1.86 tff(331,assumption,(b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.86 tff(332,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.65/1.86 tff(333,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(334,plain,
% 1.65/1.86 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(335,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[334])).
% 1.65/1.86 tff(336,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[335, 333])).
% 1.65/1.86 tff(337,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(338,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.65/1.86 tff(339,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[338, 163, 150, 328, 153, 332])).
% 1.65/1.86 tff(340,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(341,plain,
% 1.65/1.86 (~r(s(s(z)), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[340, 328, 150, 153])).
% 1.65/1.86 tff(342,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(343,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(344,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.65/1.86 tff(345,plain,
% 1.65/1.86 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[344, 26, 46])).
% 1.65/1.86 tff(346,plain,
% 1.65/1.86 (b(s(s(z)), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[345, 341])).
% 1.65/1.86 tff(347,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.65/1.86 tff(348,assumption,(b(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.86 tff(349,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(350,plain,
% 1.65/1.86 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(351,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[350])).
% 1.65/1.86 tff(352,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[351, 349])).
% 1.65/1.86 tff(353,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(354,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.65/1.86 tff(355,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[354, 198, 348, 347, 331, 330])).
% 1.65/1.86 tff(356,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(357,plain,
% 1.65/1.86 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[356, 346, 331, 330])).
% 1.65/1.86 tff(358,plain,
% 1.65/1.86 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(commutativity,[status(thm)],[])).
% 1.65/1.86 tff(359,plain,
% 1.65/1.86 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[358])).
% 1.65/1.86 tff(360,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(z))), introduced(assumption)).
% 1.65/1.86 tff(361,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[360])).
% 1.65/1.86 tff(362,plain,
% 1.65/1.86 (s(s(s(s(s(s(z)))))) = s(z)),
% 1.65/1.86 inference(transitivity,[status(thm)],[276, 361, 222])).
% 1.65/1.86 tff(363,plain,
% 1.65/1.86 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[362])).
% 1.65/1.86 tff(364,plain,
% 1.65/1.86 (s(s(s(s(s(z))))) = z),
% 1.65/1.86 inference(transitivity,[status(thm)],[281, 363, 304])).
% 1.65/1.86 tff(365,plain,
% 1.65/1.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(366,plain,
% 1.65/1.86 (~(s(s(s(s(s(z))))) = z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[365, 13])).
% 1.65/1.86 tff(367,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[366, 364])).
% 1.65/1.86 tff(368,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(369,plain,
% 1.65/1.86 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[368, 359])).
% 1.65/1.86 tff(370,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(371,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(372,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.65/1.86 tff(373,plain,
% 1.65/1.86 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[372, 26])).
% 1.65/1.86 tff(374,plain,
% 1.65/1.86 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[373, 369])).
% 1.65/1.86 tff(375,plain,
% 1.65/1.86 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[374, 357])).
% 1.65/1.86 tff(376,plain,
% 1.65/1.86 (r(s(s(z)), elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[375, 329])).
% 1.65/1.86 tff(377,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(378,plain,
% 1.65/1.86 (((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(379,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[378])).
% 1.65/1.86 tff(380,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[379, 377])).
% 1.65/1.86 tff(381,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(382,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.65/1.86 tff(383,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[382, 163, 150, 376, 328, 153])).
% 1.65/1.86 tff(384,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(385,plain,
% 1.65/1.86 (~r(s(z), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[384, 245, 153, 150, 327, 179])).
% 1.65/1.86 tff(386,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.65/1.86 tff(387,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.65/1.86 tff(388,plain,
% 1.65/1.86 (s(s(z)) = s(z)),
% 1.65/1.86 inference(symmetry,[status(thm)],[387])).
% 1.65/1.86 tff(389,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.65/1.86 tff(390,plain,
% 1.65/1.86 (s(z) = s(s(z))),
% 1.65/1.86 inference(symmetry,[status(thm)],[389])).
% 1.65/1.86 tff(391,plain,
% 1.65/1.86 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[390])).
% 1.65/1.86 tff(392,plain,
% 1.65/1.86 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.65/1.86 inference(symmetry,[status(thm)],[391])).
% 1.65/1.86 tff(393,plain,
% 1.65/1.86 (s(z) = z),
% 1.65/1.86 inference(transitivity,[status(thm)],[223, 392, 304])).
% 1.65/1.86 tff(394,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[36, 393])).
% 1.65/1.86 tff(395,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(396,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[395, 388])).
% 1.65/1.86 tff(397,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(398,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.65/1.86 tff(399,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(400,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(401,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.65/1.86 tff(402,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[401, 26, 398, 397, 386])).
% 1.65/1.86 tff(403,plain,(r(s(z), s(s(z))) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(404,plain,
% 1.65/1.86 (b(s(z), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[403, 385])).
% 1.65/1.86 tff(405,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.65/1.86 tff(406,assumption,(r(z, s(z))), introduced(assumption)).
% 1.65/1.86 tff(407,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.65/1.86 tff(408,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(409,plain,
% 1.65/1.86 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(410,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[409])).
% 1.65/1.86 tff(411,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[410, 408])).
% 1.65/1.86 tff(412,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(413,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.65/1.86 tff(414,plain,
% 1.65/1.86 (~b(elem!1, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[413, 198, 271, 320, 407, 347])).
% 1.65/1.86 tff(415,plain,
% 1.65/1.86 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[414, 324])).
% 1.65/1.86 tff(416,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(417,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(418,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.65/1.86 tff(419,plain,
% 1.65/1.86 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[418, 26])).
% 1.65/1.86 tff(420,plain,
% 1.65/1.86 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[419, 368])).
% 1.65/1.86 tff(421,plain,
% 1.65/1.86 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[420, 415])).
% 1.65/1.86 tff(422,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.65/1.86 tff(423,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 1.65/1.86 tff(424,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.86 tff(425,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(426,plain,
% 1.65/1.87 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(427,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[426])).
% 1.65/1.87 tff(428,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[427, 425])).
% 1.65/1.87 tff(429,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(430,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.65/1.87 tff(431,plain,
% 1.65/1.87 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[430, 163, 406, 151, 422])).
% 1.65/1.87 tff(432,plain,
% 1.65/1.87 (((~![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))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(433,plain,
% 1.65/1.87 ((~![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))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(434,plain,
% 1.65/1.87 ((~![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)),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.65/1.87 tff(435,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[434, 26, 366, 431])).
% 1.65/1.87 tff(436,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(437,plain,
% 1.65/1.87 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(438,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[437])).
% 1.65/1.87 tff(439,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[438, 436])).
% 1.65/1.87 tff(440,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(441,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[440, 439])).
% 1.65/1.87 tff(442,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[441, 198, 331, 330, 435])).
% 1.65/1.87 tff(443,plain,
% 1.65/1.87 (((~![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)))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(444,plain,
% 1.65/1.87 ((~![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)))))))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(445,plain,
% 1.65/1.87 ((~![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))))))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.65/1.87 tff(446,plain,
% 1.65/1.87 ((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))))))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[445, 26])).
% 1.65/1.87 tff(447,plain,
% 1.65/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[446, 442, 424])).
% 1.65/1.87 tff(448,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(449,plain,
% 1.65/1.87 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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))))))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(450,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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)))))))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[449])).
% 1.65/1.87 tff(451,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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))))))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[450, 448])).
% 1.65/1.87 tff(452,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(453,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.65/1.87 tff(454,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[453, 163, 447, 151, 423, 422])).
% 1.65/1.87 tff(455,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(456,plain,
% 1.65/1.87 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[455, 314])).
% 1.65/1.87 tff(457,plain,
% 1.65/1.87 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[456, 421, 151, 330, 327, 406])).
% 1.65/1.87 tff(458,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.65/1.87 tff(459,plain,
% 1.65/1.87 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[458])).
% 1.65/1.87 tff(460,plain,
% 1.65/1.87 (s(s(s(s(z)))) = z),
% 1.65/1.87 inference(transitivity,[status(thm)],[289, 459, 304])).
% 1.65/1.87 tff(461,plain,
% 1.65/1.87 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(462,plain,
% 1.65/1.87 (~(s(s(s(s(z)))) = z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[461, 13])).
% 1.65/1.87 tff(463,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[462, 460])).
% 1.65/1.87 tff(464,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(465,plain,
% 1.65/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(466,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(467,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.65/1.87 tff(468,plain,
% 1.65/1.87 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[467, 26])).
% 1.65/1.87 tff(469,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[468, 464])).
% 1.65/1.87 tff(470,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[469, 457])).
% 1.65/1.87 tff(471,plain,
% 1.65/1.87 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[356, 347, 327, 330])).
% 1.65/1.87 tff(472,plain,
% 1.65/1.87 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[374, 471])).
% 1.65/1.87 tff(473,plain,
% 1.65/1.87 (r(s(s(z)), elem!1)),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[472, 329])).
% 1.65/1.87 tff(474,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(475,plain,
% 1.65/1.87 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(476,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[475])).
% 1.65/1.87 tff(477,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.65/1.87 inference(transitivity,[status(thm)],[476, 474])).
% 1.65/1.87 tff(478,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(479,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.65/1.87 tff(480,plain,
% 1.65/1.87 (~r(s(s(z)), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[479, 163, 236, 405, 473])).
% 1.65/1.87 tff(481,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.65/1.87 tff(482,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.65/1.87 tff(483,plain,
% 1.65/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(484,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(485,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.65/1.87 tff(486,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[485, 26, 395, 482, 481])).
% 1.65/1.87 tff(487,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(488,plain,
% 1.65/1.87 (b(s(s(z)), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[487, 480])).
% 1.65/1.87 tff(489,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(490,plain,
% 1.65/1.87 (((~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(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(491,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[490])).
% 1.65/1.87 tff(492,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[491, 489])).
% 1.65/1.87 tff(493,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(494,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.65/1.87 tff(495,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[494, 198, 488, 407, 470])).
% 1.65/1.87 tff(496,plain,
% 1.65/1.87 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.65/1.87 inference(commutativity,[status(thm)],[])).
% 1.65/1.87 tff(497,plain,
% 1.65/1.87 ((~(s(s(z)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(z))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[496])).
% 1.65/1.87 tff(498,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.87 tff(499,plain,
% 1.65/1.87 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[498])).
% 1.65/1.87 tff(500,plain,
% 1.65/1.87 (s(z) = s(s(s(s(z))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[223, 499, 288])).
% 1.65/1.87 tff(501,plain,
% 1.65/1.87 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[500])).
% 1.65/1.87 tff(502,plain,
% 1.65/1.87 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.65/1.87 inference(symmetry,[status(thm)],[501])).
% 1.65/1.87 tff(503,plain,
% 1.65/1.87 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[498])).
% 1.65/1.87 tff(504,plain,
% 1.65/1.87 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.65/1.87 inference(symmetry,[status(thm)],[503])).
% 1.65/1.88 tff(505,plain,
% 1.65/1.88 (s(s(s(s(s(s(z)))))) = z),
% 1.65/1.88 inference(transitivity,[status(thm)],[504, 294, 502, 304])).
% 1.65/1.88 tff(506,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[310, 505])).
% 1.65/1.88 tff(507,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(508,plain,
% 1.65/1.88 (~(s(s(s(s(s(z))))) = s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[507, 497])).
% 1.65/1.88 tff(509,plain,
% 1.65/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(510,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(511,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.65/1.88 tff(512,plain,
% 1.65/1.88 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[511, 26, 508, 495])).
% 1.65/1.88 tff(513,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(514,plain,
% 1.65/1.88 (((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(515,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[514])).
% 1.65/1.88 tff(516,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[515, 513])).
% 1.65/1.88 tff(517,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(518,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.65/1.88 tff(519,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[518, 163, 473, 153, 512])).
% 1.65/1.88 tff(520,plain,
% 1.65/1.88 (r(elem!1, s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[421, 321])).
% 1.65/1.88 tff(521,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(522,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(523,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.65/1.88 tff(524,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[523, 163, 473, 512, 520])).
% 1.65/1.88 tff(525,plain,
% 1.65/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(526,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(527,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.65/1.88 tff(528,plain,
% 1.65/1.88 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[527, 26])).
% 1.65/1.88 tff(529,plain,
% 1.65/1.88 (b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[528, 524, 315])).
% 1.65/1.88 tff(530,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(531,plain,
% 1.65/1.88 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(532,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[531])).
% 1.65/1.88 tff(533,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(transitivity,[status(thm)],[532, 530])).
% 1.65/1.88 tff(534,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(535,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.65/1.88 tff(536,plain,
% 1.65/1.88 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[535, 198, 95, 320, 470])).
% 1.65/1.88 tff(537,plain,
% 1.65/1.88 (~b(s(s(s(s(s(z))))), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[536, 529])).
% 1.65/1.88 tff(538,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[434, 26, 366, 537, 519])).
% 1.65/1.88 tff(539,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(540,plain,
% 1.65/1.88 (~b(s(s(z)), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[539, 406, 320, 153, 404, 245, 151, 179, 95, 236, 405, 271])).
% 1.65/1.88 tff(541,plain,
% 1.65/1.88 (r(s(s(z)), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[345, 540])).
% 1.65/1.88 tff(542,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(543,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(544,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.65/1.88 tff(545,plain,
% 1.65/1.88 (~r(s(s(z)), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[544, 163, 150, 406, 541])).
% 1.65/1.88 tff(546,plain,
% 1.65/1.88 (b(s(s(z)), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[487, 545])).
% 1.65/1.88 tff(547,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(548,plain,
% 1.65/1.88 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(549,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[548])).
% 1.65/1.88 tff(550,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[549, 547])).
% 1.65/1.88 tff(551,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(552,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.65/1.88 tff(553,plain,
% 1.65/1.88 (~b(elem!1, s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[552, 198, 320, 546, 404])).
% 1.65/1.88 tff(554,plain,
% 1.65/1.88 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[553, 324])).
% 1.65/1.88 tff(555,plain,
% 1.65/1.88 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[420, 554])).
% 1.65/1.88 tff(556,plain,
% 1.65/1.88 (r(elem!1, s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[555, 321])).
% 1.65/1.88 tff(557,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[456, 555, 151, 179, 327, 406])).
% 1.65/1.88 tff(558,plain,
% 1.65/1.88 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[469, 557])).
% 1.65/1.88 tff(559,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.65/1.88 tff(560,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.65/1.88 tff(561,plain,
% 1.65/1.88 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[494, 198, 560, 407, 559])).
% 1.65/1.88 tff(562,plain,
% 1.65/1.88 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[511, 26, 508, 561])).
% 1.65/1.88 tff(563,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(564,plain,
% 1.65/1.88 (((~r(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))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(565,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[564])).
% 1.65/1.88 tff(566,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[565, 563])).
% 1.65/1.88 tff(567,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(568,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.65/1.88 tff(569,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[568, 163, 153, 332, 562])).
% 1.65/1.88 tff(570,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.65/1.88 tff(571,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.65/1.88 tff(572,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(573,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(574,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.65/1.88 tff(575,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[574, 163, 332, 562, 571])).
% 1.65/1.88 tff(576,plain,
% 1.65/1.88 (b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[528, 575, 570])).
% 1.65/1.88 tff(577,plain,
% 1.65/1.88 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[535, 198, 95, 320, 559])).
% 1.65/1.88 tff(578,plain,
% 1.65/1.88 (~b(s(s(s(s(s(z))))), z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[577, 576])).
% 1.65/1.88 tff(579,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[434, 26, 366, 578, 569])).
% 1.65/1.88 tff(580,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(581,plain,
% 1.65/1.88 (~r(elem!1, s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[580, 558, 320, 315, 95, 541, 153, 546, 404])).
% 1.65/1.88 tff(582,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[581, 556])).
% 1.65/1.88 tff(583,plain,((~r(z, s(z))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(584,plain,
% 1.65/1.88 (~r(z, s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[583, 245, 320, 95, 153, 151, 150, 236, 319, 271])).
% 1.65/1.88 tff(585,plain,
% 1.65/1.88 ((z = s(z)) <=> (s(z) = z)),
% 1.65/1.88 inference(commutativity,[status(thm)],[])).
% 1.65/1.88 tff(586,plain,
% 1.65/1.88 ((s(z) = z) <=> (z = s(z))),
% 1.65/1.88 inference(symmetry,[status(thm)],[585])).
% 1.65/1.88 tff(587,plain,
% 1.65/1.88 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[586])).
% 1.65/1.88 tff(588,plain,
% 1.65/1.88 (~(z = s(z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[36, 587])).
% 1.65/1.88 tff(589,plain,
% 1.65/1.88 (((~![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)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(590,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(591,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.65/1.88 tff(592,plain,
% 1.65/1.88 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[591, 26])).
% 1.65/1.88 tff(593,plain,
% 1.65/1.88 (b(z, s(z)) | r(z, s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[592, 588])).
% 1.65/1.88 tff(594,plain,
% 1.65/1.88 (b(z, s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[593, 584])).
% 1.65/1.88 tff(595,assumption,(b(z, s(z))), introduced(assumption)).
% 1.65/1.88 tff(596,plain,
% 1.65/1.88 (r(elem!1, s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[147, 116, 85])).
% 1.65/1.88 tff(597,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.65/1.88 tff(598,plain,
% 1.65/1.88 (~(s(s(elem!1)) = elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[118, 116])).
% 1.65/1.88 tff(599,plain,
% 1.65/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(600,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(601,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.65/1.88 tff(602,plain,
% 1.65/1.88 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[601, 26])).
% 1.65/1.88 tff(603,plain,
% 1.65/1.88 (r(s(s(elem!1)), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[602, 598, 597])).
% 1.65/1.88 tff(604,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(605,plain,
% 1.65/1.88 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(606,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[605])).
% 1.65/1.88 tff(607,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[606, 604])).
% 1.65/1.88 tff(608,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(609,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.65/1.88 tff(610,plain,
% 1.65/1.88 (~r(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[609, 163, 603, 236, 596])).
% 1.65/1.88 tff(611,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.65/1.88 tff(612,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.65/1.88 tff(613,plain,
% 1.65/1.88 (s(z) = s(s(elem!1))),
% 1.65/1.88 inference(symmetry,[status(thm)],[612])).
% 1.65/1.88 tff(614,plain,
% 1.65/1.88 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[613])).
% 1.65/1.88 tff(615,plain,
% 1.65/1.88 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.65/1.88 inference(symmetry,[status(thm)],[614])).
% 1.65/1.88 tff(616,plain,
% 1.65/1.88 (s(elem!1) = z),
% 1.65/1.88 inference(transitivity,[status(thm)],[135, 615, 304])).
% 1.65/1.88 tff(617,plain,
% 1.65/1.88 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(618,plain,
% 1.65/1.88 (~(s(elem!1) = z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[617, 13])).
% 1.65/1.88 tff(619,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[618, 616])).
% 1.65/1.88 tff(620,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(621,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.65/1.88 tff(622,plain,
% 1.65/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(623,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(624,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[623, 622])).
% 1.65/1.88 tff(625,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[624, 26, 621, 620, 611])).
% 1.65/1.88 tff(626,plain,(b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(627,plain,
% 1.65/1.88 (b(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[626, 610])).
% 1.65/1.88 tff(628,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(629,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(630,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.65/1.89 tff(631,plain,
% 1.65/1.89 (~r(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[630, 163, 603, 236, 596])).
% 1.65/1.89 tff(632,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.65/1.89 tff(633,plain,
% 1.65/1.89 (s(s(elem!1)) = s(z)),
% 1.65/1.89 inference(symmetry,[status(thm)],[632])).
% 1.65/1.89 tff(634,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[620, 633])).
% 1.65/1.89 tff(635,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(636,assumption,(~r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.65/1.89 tff(637,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.65/1.89 tff(638,plain,
% 1.65/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(639,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(640,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.65/1.89 tff(641,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[640, 26, 637, 636, 635])).
% 1.65/1.89 tff(642,plain,(b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(643,plain,
% 1.65/1.89 (b(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[642, 631])).
% 1.65/1.89 tff(644,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(645,plain,
% 1.65/1.89 (((~b(s(s(elem!1)), s(z))) | (~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(s(z), s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(646,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[645])).
% 1.65/1.89 tff(647,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[646, 644])).
% 1.65/1.89 tff(648,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(649,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[648, 647])).
% 1.65/1.89 tff(650,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[649, 198, 643, 627, 595, 83])).
% 1.65/1.89 tff(651,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(652,plain,
% 1.65/1.89 (b(s(s(elem!1)), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[651, 594, 83, 236, 318, 85])).
% 1.65/1.89 tff(653,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(654,plain,
% 1.65/1.89 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(655,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[654])).
% 1.65/1.89 tff(656,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[655, 653])).
% 1.65/1.89 tff(657,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(658,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[657, 656])).
% 1.65/1.89 tff(659,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[658, 198, 95, 652, 320, 594, 83])).
% 1.65/1.89 tff(660,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | b(elem!1, s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(661,plain,
% 1.65/1.89 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[660, 270, 95, 83, 218, 85, 153, 151, 150, 188])).
% 1.65/1.89 tff(662,plain,
% 1.65/1.89 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[256, 661, 205])).
% 1.65/1.89 tff(663,plain,
% 1.65/1.89 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(commutativity,[status(thm)],[])).
% 1.65/1.89 tff(664,plain,
% 1.65/1.89 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[663])).
% 1.65/1.89 tff(665,plain,
% 1.65/1.89 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[661, 664])).
% 1.65/1.89 tff(666,plain,
% 1.65/1.89 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[105])).
% 1.65/1.89 tff(667,plain,
% 1.65/1.89 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.65/1.89 inference(symmetry,[status(thm)],[666])).
% 1.65/1.89 tff(668,plain,
% 1.65/1.89 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[258, 667])).
% 1.65/1.89 tff(669,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.65/1.89 tff(670,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[669, 668])).
% 1.65/1.89 tff(671,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(672,plain,
% 1.65/1.89 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[671, 90, 258])).
% 1.65/1.89 tff(673,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(674,plain,
% 1.65/1.89 (s(s(elem!1)) = elem!1),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[90, 112])).
% 1.65/1.89 tff(675,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[138, 674])).
% 1.65/1.89 tff(676,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(677,plain,
% 1.65/1.89 (s(s(elem!1)) = elem!1),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[676, 90])).
% 1.65/1.89 tff(678,plain,
% 1.65/1.89 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[90])).
% 1.65/1.89 tff(679,plain,
% 1.65/1.89 (r(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[236, 678])).
% 1.65/1.89 tff(680,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.65/1.89 tff(681,assumption,(r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(682,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.65/1.89 tff(683,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(684,plain,
% 1.65/1.89 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(685,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[684])).
% 1.65/1.89 tff(686,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[685, 683])).
% 1.65/1.89 tff(687,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(688,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.65/1.89 tff(689,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[688, 163, 682, 151, 681, 680])).
% 1.65/1.89 tff(690,plain,((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(691,plain,
% 1.65/1.89 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[690, 679, 151, 672])).
% 1.65/1.89 tff(692,plain,
% 1.65/1.89 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[114])).
% 1.65/1.89 tff(693,plain,
% 1.65/1.89 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[692])).
% 1.65/1.89 tff(694,assumption,(r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(695,plain,
% 1.65/1.89 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[694, 693])).
% 1.65/1.89 tff(696,assumption,(~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(697,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[696, 695])).
% 1.65/1.89 tff(698,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(699,plain,
% 1.65/1.89 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[698, 691, 677])).
% 1.65/1.89 tff(700,plain,
% 1.65/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(701,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(702,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.65/1.89 tff(703,plain,
% 1.65/1.89 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[702, 26])).
% 1.65/1.89 tff(704,plain,
% 1.65/1.89 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[703, 699, 673])).
% 1.65/1.89 tff(705,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[105])).
% 1.65/1.89 tff(706,plain,
% 1.65/1.89 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[705])).
% 1.65/1.89 tff(707,assumption,(b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(708,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.65/1.89 tff(709,assumption,(~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(710,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[709, 708])).
% 1.65/1.89 tff(711,plain,(b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(712,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[711, 704, 90])).
% 1.65/1.89 tff(713,plain,
% 1.65/1.89 (elem!1 = s(s(elem!1))),
% 1.65/1.89 inference(symmetry,[status(thm)],[114])).
% 1.65/1.89 tff(714,plain,
% 1.65/1.89 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[713])).
% 1.65/1.89 tff(715,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[320, 714])).
% 1.65/1.89 tff(716,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[621, 715])).
% 1.65/1.89 tff(717,plain,((~b(elem!1, s(z))) | b(s(s(elem!1)), s(z)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(718,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[717, 677, 320])).
% 1.65/1.89 tff(719,plain,
% 1.65/1.89 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[90])).
% 1.65/1.89 tff(720,plain,
% 1.65/1.89 (b(s(s(elem!1)), z)),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[271, 719])).
% 1.65/1.89 tff(721,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.65/1.89 tff(722,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.65/1.89 tff(723,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.65/1.89 tff(724,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, 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(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, 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(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(725,plain,
% 1.65/1.89 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(726,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, 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(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[725])).
% 1.65/1.89 tff(727,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, 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(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[726, 724])).
% 1.65/1.89 tff(728,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(729,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[728, 727])).
% 1.65/1.89 tff(730,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[729, 198, 723, 722, 83, 331, 2, 721])).
% 1.65/1.89 tff(731,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(732,plain,
% 1.65/1.89 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[731, 720, 718, 83, 2, 712])).
% 1.65/1.89 tff(733,plain,
% 1.65/1.89 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[31, 732])).
% 1.65/1.89 tff(734,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(735,plain,
% 1.65/1.89 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(736,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[735])).
% 1.65/1.90 tff(737,plain,
% 1.65/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.90 inference(transitivity,[status(thm)],[736, 734])).
% 1.65/1.90 tff(738,plain,
% 1.65/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.90 inference(quant_inst,[status(thm)],[])).
% 1.65/1.90 tff(739,plain,
% 1.65/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.65/1.90 tff(740,plain,
% 1.65/1.90 ($false),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[739, 198, 723, 722, 595, 330, 721])).
% 1.65/1.90 tff(741,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.90 tff(742,plain,
% 1.65/1.90 (~b(z, s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[741, 720, 718, 330, 712])).
% 1.65/1.90 tff(743,plain,
% 1.65/1.90 (r(z, s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[593, 742])).
% 1.65/1.90 tff(744,plain,
% 1.65/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.90 inference(rewrite,[status(thm)],[])).
% 1.65/1.90 tff(745,plain,
% 1.65/1.90 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.65/1.90 inference(rewrite,[status(thm)],[])).
% 1.65/1.90 tff(746,plain,
% 1.65/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[745])).
% 1.65/1.90 tff(747,plain,
% 1.65/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.90 inference(transitivity,[status(thm)],[746, 744])).
% 1.75/1.90 tff(748,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(749,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.75/1.90 tff(750,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[749, 163, 743, 151, 733, 672])).
% 1.75/1.90 tff(751,plain,((~(elem!1 = s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(752,plain,
% 1.75/1.90 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[751, 665, 83, 2, 179, 151, 662, 218, 188, 270])).
% 1.75/1.90 tff(753,plain,
% 1.75/1.90 (r(elem!1, s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[147, 752, 85])).
% 1.75/1.90 tff(754,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(755,plain,
% 1.75/1.90 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(756,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[755])).
% 1.75/1.90 tff(757,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.90 inference(transitivity,[status(thm)],[756, 754])).
% 1.75/1.90 tff(758,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(759,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.75/1.90 tff(760,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[759, 163, 218, 753, 151, 662])).
% 1.75/1.90 tff(761,plain,(r(elem!1, z) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(762,plain,
% 1.75/1.90 (r(elem!1, z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[761, 85, 151, 83, 2, 182, 153, 150, 149])).
% 1.75/1.90 tff(763,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(764,plain,
% 1.75/1.90 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(765,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[764])).
% 1.75/1.90 tff(766,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.75/1.90 inference(transitivity,[status(thm)],[765, 763])).
% 1.75/1.90 tff(767,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(768,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.75/1.90 tff(769,plain,
% 1.75/1.90 (~r(s(z), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[768, 163, 762, 150, 153])).
% 1.75/1.90 tff(770,plain,
% 1.75/1.90 (s(z) = elem!1),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[217, 769, 149])).
% 1.75/1.90 tff(771,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.75/1.90 tff(772,plain,
% 1.75/1.90 (elem!1 = s(elem!1)),
% 1.75/1.90 inference(symmetry,[status(thm)],[771])).
% 1.75/1.90 tff(773,plain,
% 1.75/1.90 (s(z) = s(elem!1)),
% 1.75/1.90 inference(transitivity,[status(thm)],[206, 772])).
% 1.75/1.90 tff(774,plain,
% 1.75/1.90 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[773])).
% 1.75/1.90 tff(775,plain,
% 1.75/1.90 (z = inj_0(s(z))),
% 1.75/1.90 inference(symmetry,[status(thm)],[304])).
% 1.75/1.90 tff(776,plain,
% 1.75/1.90 (z = elem!1),
% 1.75/1.90 inference(transitivity,[status(thm)],[775, 774, 129])).
% 1.75/1.90 tff(777,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[3, 776])).
% 1.75/1.90 tff(778,plain,((~(s(elem!1) = elem!1)) | (z = elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(779,plain,
% 1.75/1.90 (~(s(elem!1) = elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[778, 770, 181])).
% 1.75/1.90 tff(780,plain,
% 1.75/1.90 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[770])).
% 1.75/1.90 tff(781,plain,
% 1.75/1.90 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[2, 780])).
% 1.75/1.90 tff(782,plain,
% 1.75/1.90 (s(s(z)) = s(elem!1)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[770])).
% 1.75/1.90 tff(783,plain,
% 1.75/1.90 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[782])).
% 1.75/1.90 tff(784,plain,
% 1.75/1.90 (r(z, s(elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[153, 783])).
% 1.75/1.90 tff(785,plain,
% 1.75/1.90 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[770])).
% 1.75/1.90 tff(786,plain,
% 1.75/1.90 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.75/1.90 inference(symmetry,[status(thm)],[785])).
% 1.75/1.90 tff(787,plain,
% 1.75/1.90 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[786])).
% 1.75/1.90 tff(788,plain,
% 1.75/1.90 (~b(s(z), s(s(elem!1)))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[85, 787])).
% 1.75/1.90 tff(789,plain,
% 1.75/1.90 (r(s(z), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[642, 788])).
% 1.75/1.90 tff(790,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.75/1.90 tff(791,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.75/1.90 tff(792,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(793,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(794,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.75/1.90 tff(795,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[794, 163, 791, 790, 150, 682])).
% 1.75/1.90 tff(796,plain,((~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(797,plain,
% 1.75/1.90 (~r(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[796, 789, 784, 150])).
% 1.75/1.90 tff(798,plain,
% 1.75/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(799,plain,
% 1.75/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(800,plain,
% 1.75/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.75/1.90 tff(801,plain,
% 1.75/1.90 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[800, 26, 108])).
% 1.75/1.90 tff(802,plain,
% 1.75/1.90 (b(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[801, 797])).
% 1.75/1.90 tff(803,plain,
% 1.75/1.90 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.75/1.90 inference(commutativity,[status(thm)],[])).
% 1.75/1.90 tff(804,plain,
% 1.75/1.90 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.75/1.90 inference(symmetry,[status(thm)],[803])).
% 1.75/1.90 tff(805,plain,
% 1.75/1.90 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[782])).
% 1.75/1.90 tff(806,plain,
% 1.75/1.90 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.75/1.90 inference(transitivity,[status(thm)],[805, 803])).
% 1.75/1.90 tff(807,plain,
% 1.75/1.90 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.75/1.90 inference(transitivity,[status(thm)],[806, 804])).
% 1.75/1.90 tff(808,plain,
% 1.75/1.90 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[807])).
% 1.75/1.90 tff(809,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.75/1.90 tff(810,plain,
% 1.75/1.90 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[809])).
% 1.75/1.90 tff(811,plain,
% 1.75/1.90 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.75/1.90 inference(symmetry,[status(thm)],[810])).
% 1.75/1.90 tff(812,plain,
% 1.75/1.90 (z = elem!1),
% 1.75/1.90 inference(transitivity,[status(thm)],[775, 811, 129])).
% 1.75/1.90 tff(813,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[3, 812])).
% 1.75/1.90 tff(814,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(815,plain,
% 1.75/1.90 (~(s(elem!1) = s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[814, 181])).
% 1.75/1.90 tff(816,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.75/1.90 tff(817,plain,
% 1.75/1.90 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[816])).
% 1.75/1.90 tff(818,plain,
% 1.75/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.75/1.90 inference(symmetry,[status(thm)],[817])).
% 1.75/1.90 tff(819,plain,
% 1.75/1.90 (s(elem!1) = s(z)),
% 1.75/1.90 inference(transitivity,[status(thm)],[135, 818, 222])).
% 1.75/1.90 tff(820,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.75/1.90 tff(821,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[820, 819])).
% 1.75/1.90 tff(822,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(823,plain,
% 1.75/1.90 (~(s(s(z)) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[822, 815])).
% 1.75/1.90 tff(824,plain,
% 1.75/1.90 (~(s(elem!1) = s(s(elem!1)))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[823, 808])).
% 1.75/1.90 tff(825,plain,
% 1.75/1.90 (s(s(z)) = s(elem!1)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.90 tff(826,plain,
% 1.75/1.90 (s(elem!1) = s(s(z))),
% 1.75/1.90 inference(symmetry,[status(thm)],[825])).
% 1.75/1.90 tff(827,plain,
% 1.75/1.90 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[826])).
% 1.75/1.90 tff(828,plain,
% 1.75/1.90 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.90 inference(symmetry,[status(thm)],[827])).
% 1.75/1.90 tff(829,plain,
% 1.75/1.90 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[826])).
% 1.75/1.90 tff(830,plain,
% 1.75/1.90 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[829])).
% 1.75/1.90 tff(831,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.75/1.90 tff(832,plain,
% 1.75/1.90 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[825])).
% 1.75/1.90 tff(833,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.75/1.90 tff(834,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.75/1.90 tff(835,plain,
% 1.75/1.90 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[206, 825])).
% 1.75/1.90 tff(836,plain,
% 1.75/1.90 (~r(s(z), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[340, 332, 150, 153])).
% 1.75/1.90 tff(837,plain,
% 1.75/1.90 (b(s(z), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[403, 836])).
% 1.75/1.90 tff(838,plain,
% 1.75/1.90 (b(elem!1, s(elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[837, 835])).
% 1.75/1.90 tff(839,plain,
% 1.75/1.90 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[825])).
% 1.75/1.90 tff(840,plain,
% 1.75/1.90 (r(s(elem!1), z)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[332, 839])).
% 1.75/1.90 tff(841,plain,
% 1.75/1.90 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[825])).
% 1.75/1.90 tff(842,plain,
% 1.75/1.90 (r(z, s(elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[153, 841])).
% 1.75/1.90 tff(843,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(844,plain,
% 1.75/1.90 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(845,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[844])).
% 1.75/1.90 tff(846,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.75/1.90 inference(transitivity,[status(thm)],[845, 843])).
% 1.75/1.90 tff(847,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(848,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.75/1.90 tff(849,plain,
% 1.75/1.90 (~r(s(elem!1), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[848, 163, 833, 842, 840])).
% 1.75/1.90 tff(850,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.75/1.90 tff(851,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.75/1.90 tff(852,plain,
% 1.75/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(853,plain,
% 1.75/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(854,plain,
% 1.75/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.75/1.90 tff(855,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[854, 26, 851, 834, 850])).
% 1.75/1.90 tff(856,plain,(r(s(elem!1), elem!1) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(857,plain,
% 1.75/1.90 (b(s(elem!1), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[856, 849, 834])).
% 1.75/1.90 tff(858,plain,
% 1.75/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(859,plain,
% 1.75/1.90 (((~b(s(elem!1), elem!1)) | (~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(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(elem!1), 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)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(860,plain,
% 1.75/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[859])).
% 1.75/1.90 tff(861,plain,
% 1.75/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[860, 858])).
% 1.75/1.91 tff(862,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(863,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.75/1.91 tff(864,plain,
% 1.75/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[863, 198, 857, 838, 831])).
% 1.75/1.91 tff(865,plain,
% 1.75/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[864, 830])).
% 1.75/1.91 tff(866,plain,
% 1.75/1.91 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[420, 865])).
% 1.75/1.91 tff(867,plain,
% 1.75/1.91 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[866, 828])).
% 1.75/1.91 tff(868,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(869,plain,
% 1.75/1.91 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(870,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[869])).
% 1.75/1.91 tff(871,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(transitivity,[status(thm)],[870, 868])).
% 1.75/1.91 tff(872,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(873,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[872, 871])).
% 1.75/1.91 tff(874,plain,
% 1.75/1.91 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[873, 163, 842, 840, 33])).
% 1.75/1.91 tff(875,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[874, 867])).
% 1.75/1.91 tff(876,plain,((~r(s(s(z)), z)) | (~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.91 tff(877,plain,
% 1.75/1.91 (~r(s(s(z)), z)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[876, 33, 206, 831, 834, 833, 150, 153])).
% 1.75/1.91 tff(878,plain,
% 1.75/1.91 (b(s(s(z)), z)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[345, 877])).
% 1.75/1.91 tff(879,plain,
% 1.75/1.91 (b(s(elem!1), z)),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[878, 832])).
% 1.75/1.91 tff(880,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(881,plain,
% 1.75/1.91 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(882,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[881])).
% 1.75/1.91 tff(883,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[882, 880])).
% 1.75/1.91 tff(884,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(885,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.75/1.91 tff(886,plain,
% 1.75/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[885, 198, 95, 879, 831, 330])).
% 1.75/1.91 tff(887,plain,
% 1.75/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[886, 830])).
% 1.75/1.91 tff(888,plain,
% 1.75/1.91 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[420, 887])).
% 1.75/1.91 tff(889,plain,
% 1.75/1.91 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[888, 828])).
% 1.75/1.91 tff(890,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.75/1.91 tff(891,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(892,plain,
% 1.75/1.91 (((~b(s(s(elem!1)), z)) | (~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(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(893,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[892])).
% 1.75/1.91 tff(894,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.75/1.91 inference(transitivity,[status(thm)],[893, 891])).
% 1.75/1.91 tff(895,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(896,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[895, 894])).
% 1.75/1.91 tff(897,plain,
% 1.75/1.91 (~b(s(elem!1), s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[896, 198, 879, 723, 83])).
% 1.75/1.91 tff(898,plain,
% 1.75/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(899,plain,
% 1.75/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(900,plain,
% 1.75/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[899, 898])).
% 1.75/1.91 tff(901,plain,
% 1.75/1.91 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[900, 26])).
% 1.75/1.91 tff(902,plain,
% 1.75/1.91 (r(s(elem!1), s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[901, 897, 890])).
% 1.75/1.91 tff(903,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(904,plain,
% 1.75/1.91 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(905,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[904])).
% 1.75/1.91 tff(906,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.75/1.91 inference(transitivity,[status(thm)],[905, 903])).
% 1.75/1.91 tff(907,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(908,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.75/1.91 tff(909,plain,
% 1.75/1.91 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[908, 163, 842, 902, 33])).
% 1.75/1.91 tff(910,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[909, 889])).
% 1.75/1.91 tff(911,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = elem!1) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.91 tff(912,plain,
% 1.75/1.91 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[911, 770, 824, 802, 83, 182, 781, 179, 779, 762, 150, 153])).
% 1.75/1.91 tff(913,plain,
% 1.75/1.91 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[31, 912])).
% 1.75/1.91 tff(914,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(915,plain,
% 1.75/1.91 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(916,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[915])).
% 1.75/1.91 tff(917,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.91 inference(transitivity,[status(thm)],[916, 914])).
% 1.75/1.91 tff(918,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(919,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[918, 917])).
% 1.75/1.91 tff(920,plain,
% 1.75/1.91 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[919, 198, 802, 83, 913, 179])).
% 1.75/1.91 tff(921,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(922,plain,
% 1.75/1.91 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(923,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[922])).
% 1.75/1.91 tff(924,plain,
% 1.75/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[923, 921])).
% 1.75/1.91 tff(925,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(926,plain,
% 1.75/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.75/1.91 tff(927,plain,
% 1.75/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[926, 198, 182, 802, 781, 179])).
% 1.75/1.91 tff(928,plain,
% 1.75/1.91 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.75/1.91 inference(commutativity,[status(thm)],[])).
% 1.75/1.91 tff(929,plain,
% 1.75/1.91 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[928])).
% 1.75/1.91 tff(930,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.75/1.91 tff(931,plain,
% 1.75/1.91 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.75/1.91 tff(932,plain,
% 1.75/1.91 (((~![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)))))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(933,plain,
% 1.75/1.92 ((~![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)))))))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(934,plain,
% 1.75/1.92 ((~![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))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.75/1.92 tff(935,plain,
% 1.75/1.92 ((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))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[934, 26, 709])).
% 1.75/1.92 tff(936,plain,
% 1.75/1.92 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[935, 930])).
% 1.75/1.92 tff(937,plain,
% 1.75/1.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[690, 936, 151, 682])).
% 1.75/1.92 tff(938,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.75/1.92 tff(939,plain,
% 1.75/1.92 (((~![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))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(940,plain,
% 1.75/1.92 ((~![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))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(941,plain,
% 1.75/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.75/1.92 tff(942,plain,
% 1.75/1.92 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[941, 26, 938])).
% 1.75/1.92 tff(943,plain,
% 1.75/1.92 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[942, 937])).
% 1.75/1.92 tff(944,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[943, 931])).
% 1.75/1.92 tff(945,plain,((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(946,plain,
% 1.75/1.92 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[945, 927, 151, 789, 920])).
% 1.75/1.92 tff(947,plain,
% 1.75/1.92 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.75/1.92 inference(symmetry,[status(thm)],[946])).
% 1.75/1.92 tff(948,plain,
% 1.75/1.92 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[947])).
% 1.75/1.92 tff(949,plain,
% 1.75/1.92 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.75/1.92 inference(transitivity,[status(thm)],[276, 948, 134])).
% 1.75/1.92 tff(950,plain,
% 1.75/1.92 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[949])).
% 1.75/1.92 tff(951,plain,
% 1.75/1.92 (s(s(s(z))) = s(s(elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[782])).
% 1.75/1.92 tff(952,plain,
% 1.75/1.92 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[951])).
% 1.75/1.92 tff(953,plain,
% 1.75/1.92 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.75/1.92 inference(symmetry,[status(thm)],[952])).
% 1.75/1.92 tff(954,plain,
% 1.75/1.92 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[953])).
% 1.75/1.92 tff(955,plain,
% 1.75/1.92 (s(s(s(s(elem!1)))) = elem!1),
% 1.75/1.92 inference(transitivity,[status(thm)],[954, 281, 950, 129])).
% 1.75/1.92 tff(956,plain,
% 1.75/1.92 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[770])).
% 1.75/1.92 tff(957,plain,
% 1.75/1.92 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[956])).
% 1.75/1.92 tff(958,plain,
% 1.75/1.92 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.75/1.92 inference(commutativity,[status(thm)],[])).
% 1.75/1.92 tff(959,plain,
% 1.75/1.92 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(z)))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[958])).
% 1.75/1.92 tff(960,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.92 tff(961,plain,
% 1.75/1.92 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[960])).
% 1.75/1.92 tff(962,plain,
% 1.75/1.92 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.75/1.92 inference(symmetry,[status(thm)],[961])).
% 1.75/1.92 tff(963,plain,
% 1.75/1.92 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(964,plain,
% 1.75/1.92 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[963, 127])).
% 1.75/1.92 tff(965,plain,
% 1.75/1.92 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.75/1.92 inference(symmetry,[status(thm)],[964])).
% 1.75/1.92 tff(966,plain,
% 1.75/1.92 (s(s(s(elem!1))) = z),
% 1.75/1.92 inference(transitivity,[status(thm)],[965, 962, 304])).
% 1.75/1.92 tff(967,plain,
% 1.75/1.92 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(968,plain,
% 1.75/1.92 (~(s(s(s(elem!1))) = z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[967, 13])).
% 1.75/1.92 tff(969,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[968, 966])).
% 1.75/1.92 tff(970,plain,(~(s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(971,plain,
% 1.75/1.92 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[970, 959])).
% 1.75/1.92 tff(972,plain,
% 1.75/1.92 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[971, 957])).
% 1.75/1.92 tff(973,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[972, 955])).
% 1.75/1.92 tff(974,plain,(b(elem!1, s(s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(z), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(975,plain,
% 1.75/1.92 (b(elem!1, s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[974, 83, 151, 150, 55, 2, 149, 56])).
% 1.75/1.92 tff(976,plain,
% 1.75/1.92 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.92 tff(977,plain,
% 1.75/1.92 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[976])).
% 1.75/1.92 tff(978,plain,
% 1.75/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[620, 977])).
% 1.75/1.92 tff(979,plain,
% 1.75/1.92 ((s(z) = z) <=> (elem!1 = z)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.92 tff(980,plain,
% 1.75/1.92 ((s(z) = z) <=> (z = elem!1)),
% 1.75/1.92 inference(transitivity,[status(thm)],[979, 73])).
% 1.75/1.92 tff(981,plain,
% 1.75/1.92 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[980])).
% 1.75/1.92 tff(982,plain,
% 1.75/1.92 (~(z = elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[36, 981])).
% 1.75/1.92 tff(983,plain,
% 1.75/1.92 (b(z, elem!1)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[102, 982, 56])).
% 1.75/1.92 tff(984,plain,
% 1.75/1.92 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.92 tff(985,plain,
% 1.75/1.92 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[2, 984])).
% 1.75/1.92 tff(986,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(987,plain,
% 1.75/1.92 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(988,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[987])).
% 1.75/1.92 tff(989,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[988, 986])).
% 1.75/1.92 tff(990,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(991,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.75/1.92 tff(992,plain,
% 1.75/1.92 ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[991, 198, 68, 83, 985])).
% 1.75/1.92 tff(993,plain,
% 1.75/1.92 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[992, 983])).
% 1.75/1.92 tff(994,plain,
% 1.75/1.92 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[31, 993])).
% 1.75/1.92 tff(995,plain,
% 1.75/1.92 (r(elem!1, z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[212, 206, 150])).
% 1.75/1.92 tff(996,plain,
% 1.75/1.92 ((s(s(z)) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[825])).
% 1.75/1.92 tff(997,plain,
% 1.75/1.92 ((~(s(s(z)) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[996])).
% 1.75/1.92 tff(998,plain,
% 1.75/1.92 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.92 tff(999,plain,
% 1.75/1.92 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[998])).
% 1.75/1.92 tff(1000,plain,
% 1.75/1.92 (~(s(s(z)) = elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[395, 999])).
% 1.75/1.92 tff(1001,plain,
% 1.75/1.92 (~(s(elem!1) = elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1000, 997])).
% 1.75/1.92 tff(1002,plain,
% 1.75/1.92 (~(s(elem!1) = s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[140, 978])).
% 1.75/1.92 tff(1003,plain,
% 1.75/1.92 (~b(s(s(elem!1)), z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[911, 994, 206, 1002, 83, 983, 985, 330, 1001, 995, 150, 153])).
% 1.75/1.92 tff(1004,plain,
% 1.75/1.92 (r(s(s(elem!1)), z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[801, 1003])).
% 1.75/1.92 tff(1005,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1006,plain,
% 1.75/1.92 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1007,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[1006])).
% 1.75/1.92 tff(1008,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[1007, 1005])).
% 1.75/1.92 tff(1009,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(1010,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 1.75/1.92 tff(1011,plain,
% 1.75/1.92 (~r(s(s(elem!1)), elem!1)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1010, 163, 995, 1004, 994])).
% 1.75/1.92 tff(1012,plain,
% 1.75/1.92 (b(s(s(elem!1)), elem!1)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[602, 1011, 978])).
% 1.75/1.92 tff(1013,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1014,plain,
% 1.75/1.92 (((~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)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1015,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[1014])).
% 1.75/1.92 tff(1016,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.75/1.92 tff(1017,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(1018,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.75/1.92 tff(1019,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1018, 198, 983, 1012, 68, 83])).
% 1.75/1.92 tff(1020,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | r(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(1021,plain,
% 1.75/1.92 (~(s(z) = elem!1)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1020, 975, 83, 177, 150, 55, 56, 2])).
% 1.75/1.92 tff(1022,plain,
% 1.75/1.92 (~(s(s(z)) = s(elem!1))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[227, 1021])).
% 1.75/1.92 tff(1023,plain,
% 1.75/1.92 (~(elem!1 = s(z))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[234, 1022])).
% 1.75/1.92 tff(1024,plain,
% 1.75/1.92 (r(s(z), elem!1)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[217, 1021, 149])).
% 1.75/1.92 tff(1025,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[768, 163, 833, 236, 150, 153])).
% 1.75/1.92 tff(1026,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(1027,plain,
% 1.75/1.92 (~r(elem!1, z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1026, 236, 150, 153])).
% 1.75/1.92 tff(1028,plain,
% 1.75/1.92 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 1.75/1.92 inference(monotonicity,[status(thm)],[80])).
% 1.75/1.92 tff(1029,plain,
% 1.75/1.92 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.92 inference(symmetry,[status(thm)],[1028])).
% 1.75/1.92 tff(1030,plain,
% 1.75/1.92 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[330, 1029])).
% 1.75/1.92 tff(1031,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[244, 1030])).
% 1.75/1.92 tff(1032,plain,((~(elem!1 = z)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(1033,plain,
% 1.75/1.92 (~(elem!1 = z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1032, 244, 179])).
% 1.75/1.92 tff(1034,plain,
% 1.75/1.92 (b(elem!1, z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[187, 1033, 1027])).
% 1.75/1.92 tff(1035,plain,
% 1.75/1.92 (b(elem!1, s(z))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[269, 244, 151, 236, 237, 2])).
% 1.75/1.92 tff(1036,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1037,plain,
% 1.75/1.92 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1038,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[1037])).
% 1.75/1.92 tff(1039,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[1038, 1036])).
% 1.75/1.92 tff(1040,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(1041,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 1.75/1.92 tff(1042,plain,
% 1.75/1.92 (~r(s(s(elem!1)), s(z))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1041, 163, 790, 150, 153])).
% 1.75/1.92 tff(1043,plain,
% 1.75/1.92 (b(s(s(elem!1)), s(z))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[626, 1042])).
% 1.75/1.92 tff(1044,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1045,plain,
% 1.75/1.92 (((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), 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)))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1046,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[1045])).
% 1.75/1.92 tff(1047,plain,
% 1.75/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[1046, 1044])).
% 1.75/1.92 tff(1048,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(1049,plain,
% 1.75/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 1.75/1.92 tff(1050,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1049, 163, 790, 150, 682, 153])).
% 1.75/1.92 tff(1051,plain,((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(1052,plain,
% 1.75/1.92 (~r(s(z), s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1051, 790, 150, 153])).
% 1.75/1.92 tff(1053,plain,
% 1.75/1.92 (b(s(z), s(s(elem!1)))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[642, 1052])).
% 1.75/1.92 tff(1054,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1055,plain,
% 1.75/1.92 (((~b(s(z), s(s(elem!1)))) | (~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(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(1056,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[1055])).
% 1.75/1.92 tff(1057,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[1056, 1054])).
% 1.75/1.92 tff(1058,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(1059,plain,
% 1.75/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 1.75/1.92 tff(1060,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1059, 198, 1053, 68, 1043, 320])).
% 1.75/1.92 tff(1061,plain,((~r(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(1062,plain,
% 1.75/1.92 (~r(s(s(elem!1)), z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[1061, 1035, 68, 150, 153])).
% 1.75/1.92 tff(1063,plain,
% 1.75/1.92 (b(s(s(elem!1)), z)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[801, 1062])).
% 1.75/1.92 tff(1064,plain,
% 1.75/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1065,plain,
% 1.75/1.93 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1066,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1065])).
% 1.75/1.93 tff(1067,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.75/1.93 tff(1068,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1069,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.75/1.93 tff(1070,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1069, 198, 271, 723, 68, 83])).
% 1.75/1.93 tff(1071,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1072,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1071, 1063, 1034, 68, 83])).
% 1.75/1.93 tff(1073,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (elem!1 = s(z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1074,plain,
% 1.75/1.93 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1073, 975, 83, 150, 55, 151, 1024, 1023, 2])).
% 1.75/1.93 tff(1075,plain,
% 1.75/1.93 (~r(elem!1, z)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1026, 1024, 150, 55])).
% 1.75/1.93 tff(1076,plain,
% 1.75/1.93 (~(z = elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[71, 975, 42])).
% 1.75/1.93 tff(1077,plain,
% 1.75/1.93 (z = elem!1),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[80, 73])).
% 1.75/1.93 tff(1078,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3, 1077])).
% 1.75/1.93 tff(1079,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1080,plain,
% 1.75/1.93 (~(elem!1 = z)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1079, 1076])).
% 1.75/1.93 tff(1081,plain,
% 1.75/1.93 (b(elem!1, z)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[187, 1080, 1075])).
% 1.75/1.93 tff(1082,plain,
% 1.75/1.93 (b(z, elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[102, 1076, 56])).
% 1.75/1.93 tff(1083,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[204, 198, 1082, 1081, 1074, 177])).
% 1.75/1.93 tff(1084,plain,((~b(z, s(s(elem!1)))) | r(z, elem!1) | b(z, s(s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1085,plain,
% 1.75/1.93 (~b(z, s(s(elem!1)))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1084, 151, 42, 150, 56, 2, 149])).
% 1.75/1.93 tff(1086,plain,
% 1.75/1.93 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[110, 1085, 56])).
% 1.75/1.93 tff(1087,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1088,plain,
% 1.75/1.93 (s(s(elem!1)) = z),
% 1.75/1.93 inference(symmetry,[status(thm)],[1087])).
% 1.75/1.93 tff(1089,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[108, 1088])).
% 1.75/1.93 tff(1090,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1091,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.75/1.93 tff(1092,plain,
% 1.75/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1093,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1094,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 1.75/1.93 tff(1095,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1094, 26, 1091, 89, 1090])).
% 1.75/1.93 tff(1096,plain,(b(z, s(s(elem!1))) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1097,plain,
% 1.75/1.93 (r(z, s(s(elem!1)))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1096, 1085])).
% 1.75/1.93 tff(1098,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.75/1.93 tff(1099,plain,
% 1.75/1.93 (b(z, s(z)) <=> b(z, elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.93 tff(1100,plain,
% 1.75/1.93 (b(z, elem!1) <=> b(z, s(z))),
% 1.75/1.93 inference(symmetry,[status(thm)],[1099])).
% 1.75/1.93 tff(1101,plain,
% 1.75/1.93 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[976, 113])).
% 1.75/1.93 tff(1102,plain,
% 1.75/1.93 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1101])).
% 1.75/1.93 tff(1103,plain,
% 1.75/1.93 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[620, 1102])).
% 1.75/1.93 tff(1104,plain,
% 1.75/1.93 (r(elem!1, s(s(elem!1)))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[147, 1103, 85])).
% 1.75/1.93 tff(1105,plain,
% 1.75/1.93 (r(z, s(z)) <=> r(z, elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.93 tff(1106,plain,
% 1.75/1.93 (r(z, elem!1) <=> r(z, s(z))),
% 1.75/1.93 inference(symmetry,[status(thm)],[1105])).
% 1.75/1.93 tff(1107,plain,
% 1.75/1.93 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1106])).
% 1.75/1.93 tff(1108,plain,
% 1.75/1.93 (~r(z, s(z))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[56, 1107])).
% 1.75/1.93 tff(1109,plain,
% 1.75/1.93 (b(z, s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[593, 1108])).
% 1.75/1.93 tff(1110,plain,
% 1.75/1.93 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.93 tff(1111,plain,
% 1.75/1.93 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 1.75/1.93 inference(symmetry,[status(thm)],[1110])).
% 1.75/1.93 tff(1112,plain,
% 1.75/1.93 ((s(s(z)) = elem!1) <=> (s(elem!1) = s(z))),
% 1.75/1.93 inference(transitivity,[status(thm)],[996, 1111])).
% 1.75/1.93 tff(1113,plain,
% 1.75/1.93 ((~(s(s(z)) = elem!1)) <=> (~(s(elem!1) = s(z)))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1112])).
% 1.75/1.93 tff(1114,plain,
% 1.75/1.93 (~(s(elem!1) = s(z))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1000, 1113])).
% 1.75/1.93 tff(1115,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.75/1.93 tff(1116,plain,
% 1.75/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1117,plain,
% 1.75/1.93 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1118,plain,
% 1.75/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1117])).
% 1.75/1.93 tff(1119,plain,
% 1.75/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[1118, 1116])).
% 1.75/1.93 tff(1120,plain,
% 1.75/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1121,plain,
% 1.75/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.75/1.93 tff(1122,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1121, 163, 833, 1115, 1098, 405])).
% 1.75/1.93 tff(1123,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1124,plain,
% 1.75/1.93 (~r(s(s(elem!1)), elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1123, 995, 1098, 1104])).
% 1.75/1.93 tff(1125,plain,
% 1.75/1.93 (b(s(s(elem!1)), elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[602, 1124, 978])).
% 1.75/1.93 tff(1126,plain,
% 1.75/1.93 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.93 tff(1127,plain,
% 1.75/1.93 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.75/1.93 inference(symmetry,[status(thm)],[1126])).
% 1.75/1.93 tff(1128,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.75/1.93 tff(1129,plain,
% 1.75/1.93 (b(s(s(elem!1)), s(z))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.75/1.93 tff(1130,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[621, 1129])).
% 1.75/1.93 tff(1131,plain,((~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), s(z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1132,plain,
% 1.75/1.93 (b(s(s(elem!1)), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1131, 1125, 206])).
% 1.75/1.93 tff(1133,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1134,plain,
% 1.75/1.93 (~(s(elem!1) = s(s(elem!1)))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[140, 598])).
% 1.75/1.93 tff(1135,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.75/1.93 tff(1136,plain,
% 1.75/1.93 (s(elem!1) = s(s(elem!1))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1135, 804])).
% 1.75/1.93 tff(1137,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[890, 1136])).
% 1.75/1.93 tff(1138,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1139,plain,
% 1.75/1.93 (~(s(s(elem!1)) = s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1138, 1134])).
% 1.75/1.93 tff(1140,plain,
% 1.75/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1141,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1142,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.75/1.93 tff(1143,plain,
% 1.75/1.93 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1142, 26])).
% 1.75/1.93 tff(1144,plain,
% 1.75/1.93 (b(s(s(elem!1)), s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1143, 1139, 1133])).
% 1.75/1.93 tff(1145,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1146,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1147,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.75/1.93 tff(1148,plain,
% 1.75/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1149,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1150,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 1.75/1.93 tff(1151,plain,
% 1.75/1.93 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1150, 26, 1147])).
% 1.75/1.93 tff(1152,plain,
% 1.75/1.93 (b(s(elem!1), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1151, 820])).
% 1.75/1.93 tff(1153,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.75/1.93 tff(1154,plain,
% 1.75/1.93 (s(elem!1) = s(z)),
% 1.75/1.93 inference(symmetry,[status(thm)],[1153])).
% 1.75/1.93 tff(1155,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[820, 1154])).
% 1.75/1.93 tff(1156,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1157,plain,
% 1.75/1.93 (~(s(z) = s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1156, 820])).
% 1.75/1.93 tff(1158,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1159,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.75/1.93 tff(1160,plain,
% 1.75/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1161,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1162,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.75/1.93 tff(1163,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1162, 26, 1146, 1159, 1158])).
% 1.75/1.93 tff(1164,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1165,plain,
% 1.75/1.93 (b(s(z), s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1164, 1157, 1146])).
% 1.75/1.93 tff(1166,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1167,plain,
% 1.75/1.93 (((~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1168,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1167])).
% 1.75/1.93 tff(1169,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[1168, 1166])).
% 1.75/1.93 tff(1170,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1171,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.75/1.93 tff(1172,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1171, 198, 1145, 722, 1165, 1152])).
% 1.75/1.93 tff(1173,plain,((s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | r(s(z), s(elem!1)) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1174,plain,
% 1.75/1.93 (r(s(elem!1), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1173, 1146, 820, 722, 1145])).
% 1.75/1.93 tff(1175,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.75/1.93 tff(1176,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1177,plain,
% 1.75/1.93 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1178,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1177])).
% 1.75/1.93 tff(1179,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.75/1.93 tff(1180,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1181,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.75/1.93 tff(1182,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1181, 198, 1175, 723, 1145, 722, 595])).
% 1.75/1.93 tff(1183,plain,((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1184,plain,
% 1.75/1.93 (~b(s(elem!1), z)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1183, 723, 1145, 722, 595])).
% 1.75/1.93 tff(1185,assumption,(b(s(z), z)), introduced(assumption)).
% 1.75/1.93 tff(1186,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1187,plain,
% 1.75/1.93 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1188,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1187])).
% 1.75/1.93 tff(1189,plain,
% 1.75/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[1188, 1186])).
% 1.75/1.93 tff(1190,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1191,plain,
% 1.75/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.75/1.93 tff(1192,plain,
% 1.75/1.93 (~b(s(s(elem!1)), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1191, 198, 723, 1185, 595])).
% 1.75/1.93 tff(1193,plain,
% 1.75/1.93 (r(s(s(elem!1)), s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[624, 26, 1192, 620])).
% 1.75/1.93 tff(1194,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.75/1.93 tff(1195,plain,
% 1.75/1.93 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[58])).
% 1.75/1.93 tff(1196,plain,
% 1.75/1.93 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.75/1.93 inference(symmetry,[status(thm)],[1195])).
% 1.75/1.93 tff(1197,plain,
% 1.75/1.93 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[1196])).
% 1.75/1.93 tff(1198,plain,
% 1.75/1.93 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[57])).
% 1.75/1.93 tff(1199,plain,
% 1.75/1.93 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.75/1.93 inference(symmetry,[status(thm)],[1198])).
% 1.75/1.93 tff(1200,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.75/1.93 tff(1201,plain,
% 1.75/1.93 (b(s(elem!1), z)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.75/1.93 tff(1202,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1194, 1201])).
% 1.75/1.93 tff(1203,plain,((~(z = elem!1)) | b(s(elem!1), z) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1204,plain,
% 1.75/1.93 (~b(s(elem!1), elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1203, 57, 1194])).
% 1.75/1.93 tff(1205,plain,
% 1.75/1.93 (~b(s(z), elem!1)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1204, 1197])).
% 1.75/1.93 tff(1206,plain,
% 1.75/1.93 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.75/1.93 inference(monotonicity,[status(thm)],[57])).
% 1.75/1.93 tff(1207,plain,
% 1.75/1.93 (b(s(z), elem!1)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1185, 1206])).
% 1.75/1.93 tff(1208,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1207, 1205])).
% 1.75/1.93 tff(1209,plain,((~(z = elem!1)) | (~b(s(z), z)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(1210,plain,
% 1.75/1.93 (~(z = elem!1)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1209, 1185, 1194])).
% 1.75/1.93 tff(1211,plain,
% 1.75/1.93 (~(s(elem!1) = s(z))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[814, 1210])).
% 1.75/1.93 tff(1212,plain,
% 1.75/1.93 (~(s(z) = s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1156, 1211])).
% 1.75/1.93 tff(1213,plain,
% 1.75/1.93 (b(s(z), s(elem!1))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1164, 1212, 1146])).
% 1.75/1.93 tff(1214,plain,
% 1.75/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(1215,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(1216,plain,
% 1.75/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.75/1.93 tff(1217,plain,
% 1.75/1.93 (b(s(elem!1), z) | r(s(elem!1), z)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[1216, 26, 618])).
% 1.75/1.94 tff(1218,plain,
% 1.75/1.94 (r(s(elem!1), z)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1217, 1194])).
% 1.75/1.94 tff(1219,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.75/1.94 tff(1220,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.75/1.94 tff(1221,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.75/1.94 tff(1222,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1223,plain,
% 1.75/1.94 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), 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)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1224,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1223])).
% 1.75/1.94 tff(1225,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.94 inference(transitivity,[status(thm)],[1224, 1222])).
% 1.75/1.94 tff(1226,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1227,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 1.75/1.94 tff(1228,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1227, 163, 1221, 1220, 1098, 1219])).
% 1.75/1.94 tff(1229,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1230,plain,
% 1.75/1.94 (~r(s(elem!1), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1229, 1193, 1098, 1218])).
% 1.75/1.94 tff(1231,plain,
% 1.75/1.94 (b(s(elem!1), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[901, 1230, 1134])).
% 1.75/1.94 tff(1232,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1233,plain,
% 1.75/1.94 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1234,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1233])).
% 1.75/1.94 tff(1235,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.94 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.75/1.94 tff(1236,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1237,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.75/1.94 tff(1238,plain,
% 1.75/1.94 (~b(s(z), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1237, 198, 723, 1231, 1185, 1213])).
% 1.75/1.94 tff(1239,plain,
% 1.75/1.94 (r(s(z), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[642, 1238])).
% 1.75/1.94 tff(1240,plain,
% 1.75/1.94 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.75/1.94 inference(commutativity,[status(thm)],[])).
% 1.75/1.94 tff(1241,plain,
% 1.75/1.94 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.75/1.94 inference(symmetry,[status(thm)],[1240])).
% 1.75/1.94 tff(1242,plain,
% 1.75/1.94 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1241])).
% 1.75/1.94 tff(1243,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.75/1.94 tff(1244,plain,
% 1.75/1.94 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1243])).
% 1.75/1.94 tff(1245,plain,
% 1.75/1.94 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1246,plain,
% 1.75/1.94 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1245, 127])).
% 1.75/1.94 tff(1247,plain,
% 1.75/1.94 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.75/1.94 inference(symmetry,[status(thm)],[1246])).
% 1.75/1.94 tff(1248,plain,
% 1.75/1.94 (s(s(elem!1)) = elem!1),
% 1.75/1.94 inference(transitivity,[status(thm)],[1247, 1244, 129])).
% 1.75/1.94 tff(1249,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[138, 1248])).
% 1.75/1.94 tff(1250,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1251,plain,
% 1.75/1.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1250, 598])).
% 1.75/1.94 tff(1252,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.75/1.94 tff(1253,plain,
% 1.75/1.94 (s(s(s(elem!1))) = z),
% 1.75/1.94 inference(symmetry,[status(thm)],[1252])).
% 1.75/1.94 tff(1254,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[968, 1253])).
% 1.75/1.94 tff(1255,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1256,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.75/1.94 tff(1257,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.75/1.94 tff(1258,plain,
% 1.75/1.94 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1257])).
% 1.75/1.94 tff(1259,plain,
% 1.75/1.94 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.75/1.94 inference(symmetry,[status(thm)],[1258])).
% 1.75/1.94 tff(1260,plain,
% 1.75/1.94 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.75/1.94 inference(symmetry,[status(thm)],[1257])).
% 1.75/1.94 tff(1261,plain,
% 1.75/1.94 (s(s(s(elem!1))) = s(elem!1)),
% 1.75/1.94 inference(transitivity,[status(thm)],[1260, 1247, 1259, 134])).
% 1.75/1.94 tff(1262,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1256, 1261])).
% 1.75/1.94 tff(1263,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1264,plain,
% 1.75/1.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1263, 1256])).
% 1.75/1.94 tff(1265,plain,
% 1.75/1.94 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.75/1.94 inference(commutativity,[status(thm)],[])).
% 1.75/1.94 tff(1266,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.75/1.94 tff(1267,plain,
% 1.75/1.94 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.75/1.94 tff(1268,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.94 tff(1269,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1268, 1267])).
% 1.75/1.94 tff(1270,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1271,plain,
% 1.75/1.94 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1270, 1264])).
% 1.75/1.94 tff(1272,plain,
% 1.75/1.94 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.94 tff(1273,plain,
% 1.75/1.94 (r(elem!1, s(s(elem!1)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[682, 1272])).
% 1.75/1.94 tff(1274,plain,
% 1.75/1.94 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.75/1.94 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.94 tff(1275,plain,
% 1.75/1.94 (r(s(s(elem!1)), elem!1)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1193, 1274])).
% 1.75/1.94 tff(1276,plain,
% 1.75/1.94 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.75/1.94 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.94 tff(1277,plain,
% 1.75/1.94 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1276])).
% 1.75/1.94 tff(1278,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.75/1.94 tff(1279,plain,
% 1.75/1.94 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1278])).
% 1.75/1.94 tff(1280,plain,
% 1.75/1.94 (s(s(elem!1)) = z),
% 1.75/1.94 inference(transitivity,[status(thm)],[1247, 1279, 304])).
% 1.75/1.94 tff(1281,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[108, 1280])).
% 1.75/1.94 tff(1282,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1283,plain,
% 1.75/1.94 (~(s(s(s(elem!1))) = elem!1)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1282, 1277])).
% 1.75/1.94 tff(1284,plain,
% 1.75/1.94 (b(z, elem!1)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[595, 1099])).
% 1.75/1.94 tff(1285,plain,
% 1.75/1.94 (b(s(z), z) <=> b(elem!1, z)),
% 1.75/1.94 inference(monotonicity,[status(thm)],[206])).
% 1.75/1.94 tff(1286,plain,
% 1.75/1.94 (b(elem!1, z)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1185, 1285])).
% 1.75/1.94 tff(1287,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.75/1.94 tff(1288,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1289,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1290,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.75/1.94 tff(1291,plain,
% 1.75/1.94 (~r(s(s(s(elem!1))), z)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1290, 163, 1115, 1098, 1287])).
% 1.75/1.94 tff(1292,plain,
% 1.75/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1293,plain,
% 1.75/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1294,plain,
% 1.75/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.75/1.94 tff(1295,plain,
% 1.75/1.94 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1294, 26, 968])).
% 1.75/1.94 tff(1296,plain,
% 1.75/1.94 (b(s(s(s(elem!1))), z)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1295, 1291])).
% 1.75/1.94 tff(1297,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.75/1.94 tff(1298,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1299,plain,
% 1.75/1.94 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(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)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1300,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1299])).
% 1.75/1.94 tff(1301,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.75/1.94 tff(1302,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1303,plain,
% 1.75/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.75/1.94 tff(1304,plain,
% 1.75/1.94 (~r(s(s(s(elem!1))), elem!1)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1303, 163, 1115, 405, 1287])).
% 1.75/1.94 tff(1305,plain,
% 1.75/1.94 (((~![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))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1306,plain,
% 1.75/1.94 ((~![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))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1307,plain,
% 1.75/1.94 ((~![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)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.75/1.94 tff(1308,plain,
% 1.75/1.94 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1307, 26])).
% 1.75/1.94 tff(1309,plain,
% 1.75/1.94 (b(s(s(s(elem!1))), elem!1)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1308, 1304, 1297])).
% 1.75/1.94 tff(1310,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.75/1.94 tff(1311,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.75/1.94 tff(1312,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1313,plain,
% 1.75/1.94 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1314,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1313])).
% 1.75/1.94 tff(1315,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.75/1.94 tff(1316,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1317,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.75/1.94 tff(1318,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1317, 198, 95, 271, 1311, 1310])).
% 1.75/1.94 tff(1319,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1320,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1319, 1309, 1296, 271, 95])).
% 1.75/1.94 tff(1321,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(1322,plain,
% 1.75/1.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1321, 1286, 1284, 1283, 1275, 1273, 1098])).
% 1.75/1.94 tff(1323,plain,
% 1.75/1.94 (((~![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))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1324,plain,
% 1.75/1.94 ((~![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))))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1325,plain,
% 1.75/1.94 ((~![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)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.75/1.94 tff(1326,plain,
% 1.75/1.94 ((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)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1325, 26])).
% 1.75/1.94 tff(1327,plain,
% 1.75/1.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1326, 1322, 1271])).
% 1.75/1.94 tff(1328,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.75/1.94 tff(1329,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1330,plain,
% 1.75/1.94 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(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))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1331,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1330])).
% 1.75/1.94 tff(1332,plain,
% 1.75/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.94 inference(transitivity,[status(thm)],[1331, 1329])).
% 1.75/1.94 tff(1333,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1334,plain,
% 1.75/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.75/1.94 tff(1335,plain,
% 1.75/1.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1334, 198, 1145, 1328, 1327])).
% 1.75/1.94 tff(1336,plain,
% 1.75/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1337,plain,
% 1.75/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(1338,plain,
% 1.75/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.75/1.94 tff(1339,plain,
% 1.75/1.94 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1338, 26])).
% 1.75/1.94 tff(1340,plain,
% 1.75/1.94 (r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1339, 1335, 1256])).
% 1.75/1.94 tff(1341,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1342,plain,
% 1.75/1.94 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(1343,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[1342])).
% 1.75/1.94 tff(1344,plain,
% 1.75/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1343, 1341])).
% 1.75/1.95 tff(1345,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1346,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 1.75/1.95 tff(1347,plain,
% 1.75/1.95 (~r(z, s(s(s(elem!1))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1346, 163, 1340, 791, 1221])).
% 1.75/1.95 tff(1348,plain,
% 1.75/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1349,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1350,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.75/1.95 tff(1351,plain,
% 1.75/1.95 (b(z, s(s(s(elem!1))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1350, 26, 1347, 1255])).
% 1.75/1.95 tff(1352,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.75/1.95 tff(1353,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.75/1.95 tff(1354,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1355,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1356,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.75/1.95 tff(1357,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1356, 163, 1353, 791, 1221, 1352])).
% 1.75/1.95 tff(1358,plain,((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1359,plain,
% 1.75/1.95 (~r(s(s(s(elem!1))), z)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1358, 1340, 791, 1221])).
% 1.75/1.95 tff(1360,plain,
% 1.75/1.95 (b(s(s(s(elem!1))), z)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1295, 1359])).
% 1.75/1.95 tff(1361,plain,
% 1.75/1.95 (~b(s(s(s(elem!1))), elem!1)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1319, 1360, 1286, 1284])).
% 1.75/1.95 tff(1362,plain,
% 1.75/1.95 (r(s(s(s(elem!1))), elem!1)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1308, 1361, 1283])).
% 1.75/1.95 tff(1363,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.75/1.95 tff(1364,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.95 tff(1365,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1366,plain,
% 1.75/1.95 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(elem!1, 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)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1367,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[1366])).
% 1.75/1.95 tff(1368,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1367, 1365])).
% 1.75/1.95 tff(1369,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1370,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.75/1.95 tff(1371,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1370, 163, 1115, 1364, 1363, 405])).
% 1.75/1.95 tff(1372,plain,((~r(elem!1, 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))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1373,plain,
% 1.75/1.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1372, 1362, 1273, 1275])).
% 1.75/1.95 tff(1374,plain,
% 1.75/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1375,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1376,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.75/1.95 tff(1377,plain,
% 1.75/1.95 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1376, 26])).
% 1.75/1.95 tff(1378,plain,
% 1.75/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1377, 1373, 1264])).
% 1.75/1.95 tff(1379,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1380,plain,
% 1.75/1.95 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1381,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[1380])).
% 1.75/1.95 tff(1382,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.75/1.95 tff(1383,plain,
% 1.75/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1384,plain,
% 1.75/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.75/1.95 tff(1385,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1384, 198, 1284, 1286, 723, 1378, 1360, 1351])).
% 1.75/1.95 tff(1386,plain,((~(s(z) = elem!1)) | (~b(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1387,plain,
% 1.75/1.95 (~(s(z) = elem!1)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1386, 1231, 791, 1218, 1251, 1145, 723, 1098, 1239, 595, 1185])).
% 1.75/1.95 tff(1388,plain,
% 1.75/1.95 (~(elem!1 = s(z))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1387, 1242])).
% 1.75/1.95 tff(1389,plain,
% 1.75/1.95 (~(elem!1 = z)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1079, 1210])).
% 1.75/1.95 tff(1390,plain,
% 1.75/1.95 (~r(s(elem!1), s(s(elem!1)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1229, 1219, 1098, 1221])).
% 1.75/1.95 tff(1391,plain,
% 1.75/1.95 (b(s(elem!1), s(s(elem!1)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[901, 1390, 1134])).
% 1.75/1.95 tff(1392,plain,
% 1.75/1.95 (s(s(elem!1)) = s(elem!1)),
% 1.75/1.95 inference(monotonicity,[status(thm)],[771])).
% 1.75/1.95 tff(1393,plain,
% 1.75/1.95 (s(s(elem!1)) = elem!1),
% 1.75/1.95 inference(transitivity,[status(thm)],[1392, 771])).
% 1.75/1.95 tff(1394,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[138, 1393])).
% 1.75/1.95 tff(1395,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1396,plain,
% 1.75/1.95 (~(s(elem!1) = elem!1)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1395, 598])).
% 1.75/1.95 tff(1397,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.75/1.95 tff(1398,plain,
% 1.75/1.95 (s(elem!1) = elem!1),
% 1.75/1.95 inference(symmetry,[status(thm)],[1397])).
% 1.75/1.95 tff(1399,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[834, 1398])).
% 1.75/1.95 tff(1400,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1401,plain,
% 1.75/1.95 (~(elem!1 = s(elem!1))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1400, 1396])).
% 1.75/1.95 tff(1402,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1403,plain,
% 1.75/1.95 (((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1404,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[1403])).
% 1.75/1.95 tff(1405,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1404, 1402])).
% 1.75/1.95 tff(1406,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1407,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 1.75/1.95 tff(1408,plain,
% 1.75/1.95 (~r(elem!1, s(elem!1))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1407, 163, 833, 791, 1221])).
% 1.75/1.95 tff(1409,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.75/1.95 tff(1410,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.75/1.95 tff(1411,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.75/1.95 tff(1412,plain,
% 1.75/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1413,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1414,plain,
% 1.75/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.75/1.95 tff(1415,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1414, 26, 1411, 1410, 1409])).
% 1.75/1.95 tff(1416,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1417,plain,
% 1.75/1.95 (b(elem!1, s(elem!1))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1416, 1408, 1401])).
% 1.75/1.95 tff(1418,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.75/1.95 tff(1419,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1420,plain,
% 1.75/1.95 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), 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)))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1421,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[1420])).
% 1.75/1.95 tff(1422,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1421, 1419])).
% 1.75/1.95 tff(1423,plain,
% 1.75/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1424,plain,
% 1.75/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.75/1.95 tff(1425,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1424, 198, 1145, 1328, 68, 1418])).
% 1.75/1.95 tff(1426,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1427,plain,
% 1.75/1.95 (~b(elem!1, s(s(elem!1)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1426, 1417, 1145, 1391])).
% 1.75/1.95 tff(1428,plain,
% 1.75/1.95 (r(elem!1, s(s(elem!1)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[147, 1427, 116])).
% 1.75/1.95 tff(1429,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1430,plain,
% 1.75/1.95 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, 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)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1431,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[1430])).
% 1.75/1.95 tff(1432,plain,
% 1.75/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.75/1.95 inference(transitivity,[status(thm)],[1431, 1429])).
% 1.75/1.95 tff(1433,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(1434,plain,
% 1.75/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.75/1.95 tff(1435,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1434, 163, 833, 1098, 1428, 1219])).
% 1.75/1.95 tff(1436,plain,((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(1437,plain,
% 1.75/1.95 (~r(elem!1, z)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1436, 1193, 1098, 116, 1145, 791, 1218])).
% 1.75/1.95 tff(1438,plain,
% 1.75/1.95 (b(elem!1, z)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[187, 1437, 1389])).
% 1.75/1.95 tff(1439,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1440,plain,
% 1.75/1.95 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(1441,plain,
% 1.75/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1440])).
% 1.75/1.96 tff(1442,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.75/1.96 tff(1443,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1444,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.75/1.96 tff(1445,plain,
% 1.75/1.96 (~b(elem!1, s(z))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1444, 198, 1438, 1185, 595])).
% 1.75/1.96 tff(1446,plain,
% 1.75/1.96 (r(elem!1, s(z))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[242, 1445, 1388])).
% 1.75/1.96 tff(1447,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1448,plain,
% 1.75/1.96 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(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))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1449,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1448])).
% 1.75/1.96 tff(1450,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.75/1.96 tff(1451,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1452,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.75/1.96 tff(1453,plain,
% 1.75/1.96 (~r(s(s(elem!1)), elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1452, 163, 1446, 1239, 1193])).
% 1.75/1.96 tff(1454,plain,
% 1.75/1.96 (b(s(s(elem!1)), elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[602, 1453, 598])).
% 1.75/1.96 tff(1455,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1456,plain,
% 1.75/1.96 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1457,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1456])).
% 1.75/1.96 tff(1458,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.75/1.96 tff(1459,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1460,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.75/1.96 tff(1461,plain,
% 1.75/1.96 (~r(elem!1, s(s(elem!1)))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1460, 163, 1446, 1239, 1193])).
% 1.75/1.96 tff(1462,plain,
% 1.75/1.96 (b(elem!1, s(s(elem!1)))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[147, 1461, 116])).
% 1.75/1.96 tff(1463,plain,
% 1.75/1.96 (~b(elem!1, s(elem!1))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1426, 1462, 1145, 1231])).
% 1.75/1.96 tff(1464,plain,
% 1.75/1.96 (r(elem!1, s(elem!1))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1416, 1463, 1401])).
% 1.75/1.96 tff(1465,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1466,plain,
% 1.75/1.96 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1467,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1466])).
% 1.75/1.96 tff(1468,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1467, 1465])).
% 1.75/1.96 tff(1469,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1470,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.75/1.96 tff(1471,plain,
% 1.75/1.96 (~b(s(elem!1), elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1470, 198, 1454, 1231, 1462])).
% 1.75/1.96 tff(1472,plain,
% 1.75/1.96 (r(s(elem!1), elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[856, 1471, 1396])).
% 1.75/1.96 tff(1473,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.75/1.96 tff(1474,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.75/1.96 tff(1475,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.75/1.96 tff(1476,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1477,plain,
% 1.75/1.96 (((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1478,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1477])).
% 1.75/1.96 tff(1479,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.75/1.96 tff(1480,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1481,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.75/1.96 tff(1482,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1481, 163, 1475, 1474, 791, 1473])).
% 1.75/1.96 tff(1483,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(1484,plain,
% 1.75/1.96 (~r(z, elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1483, 1472, 1464, 791])).
% 1.75/1.96 tff(1485,plain,
% 1.75/1.96 (b(z, elem!1)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[102, 1484, 1210])).
% 1.75/1.96 tff(1486,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1487,plain,
% 1.75/1.96 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1488,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1487])).
% 1.75/1.96 tff(1489,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1488, 1486])).
% 1.75/1.96 tff(1490,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1491,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 1.75/1.96 tff(1492,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1491, 198, 1485, 1438, 1454, 723])).
% 1.75/1.96 tff(1493,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | r(s(z), s(elem!1)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(1494,plain,
% 1.75/1.96 (~b(s(z), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1493, 1146, 791, 1145, 116, 595, 1098, 1184, 723])).
% 1.75/1.96 tff(1495,plain,
% 1.75/1.96 (r(s(z), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[40, 1494])).
% 1.75/1.96 tff(1496,plain,
% 1.75/1.96 (r(s(elem!1), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1217, 1184])).
% 1.75/1.96 tff(1497,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1498,plain,
% 1.75/1.96 (((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1499,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1498])).
% 1.75/1.96 tff(1500,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1499, 1497])).
% 1.75/1.96 tff(1501,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1502,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.75/1.96 tff(1503,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1502, 163, 791, 1496, 1495, 1174])).
% 1.75/1.96 tff(1504,plain,(r(s(z), s(elem!1)) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(1505,plain,
% 1.75/1.96 (r(s(z), s(elem!1))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1504, 723, 1145, 116, 595, 1098, 791, 820, 722])).
% 1.75/1.96 tff(1506,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1507,plain,
% 1.75/1.96 (((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1508,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1507])).
% 1.75/1.96 tff(1509,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.75/1.96 tff(1510,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1511,plain,
% 1.75/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.75/1.96 tff(1512,plain,
% 1.75/1.96 (~r(s(z), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1511, 163, 791, 1496, 1505])).
% 1.75/1.96 tff(1513,plain,
% 1.75/1.96 (b(s(z), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[40, 1512])).
% 1.75/1.96 tff(1514,plain,
% 1.75/1.96 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(1515,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[1514])).
% 1.75/1.96 tff(1516,plain,
% 1.75/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[1515, 1186])).
% 1.75/1.96 tff(1517,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(1518,plain,
% 1.75/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.75/1.96 tff(1519,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1518, 198, 723, 722, 1513, 595])).
% 1.75/1.96 tff(1520,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(1521,plain,
% 1.75/1.96 (~b(s(s(elem!1)), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1520, 1144, 595, 791, 722, 116, 1098, 820])).
% 1.75/1.96 tff(1522,plain,
% 1.75/1.96 (r(s(s(elem!1)), z)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[801, 1521])).
% 1.75/1.96 tff(1523,plain,
% 1.75/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1524,plain,
% 1.75/1.97 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1525,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1524])).
% 1.75/1.97 tff(1526,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1525, 1523])).
% 1.75/1.97 tff(1527,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1528,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.75/1.97 tff(1529,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1528, 163, 791, 790, 1220, 1098])).
% 1.75/1.97 tff(1530,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1531,plain,
% 1.75/1.97 (~r(s(elem!1), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1530, 1522, 1098, 791])).
% 1.75/1.97 tff(1532,plain,
% 1.75/1.97 (b(s(elem!1), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[901, 1531, 1134])).
% 1.75/1.97 tff(1533,plain,
% 1.75/1.97 (~r(s(z), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[796, 150, 791, 790])).
% 1.75/1.97 tff(1534,plain,
% 1.75/1.97 (b(s(z), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[642, 1533])).
% 1.75/1.97 tff(1535,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1536,plain,
% 1.75/1.97 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1537,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1536])).
% 1.75/1.97 tff(1538,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1537, 1535])).
% 1.75/1.97 tff(1539,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1540,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 1.75/1.97 tff(1541,plain,
% 1.75/1.97 (~b(s(elem!1), s(z))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1540, 198, 1328, 1534, 722])).
% 1.75/1.97 tff(1542,plain,
% 1.75/1.97 (r(s(elem!1), s(z))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1150, 26, 820, 1541])).
% 1.75/1.97 tff(1543,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.75/1.97 tff(1544,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.75/1.97 tff(1545,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1546,plain,
% 1.75/1.97 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1547,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1546])).
% 1.75/1.97 tff(1548,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1547, 1545])).
% 1.75/1.97 tff(1549,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1550,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.75/1.97 tff(1551,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1550, 198, 1145, 1328, 1544, 1543])).
% 1.75/1.97 tff(1552,plain,((~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(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1553,plain,
% 1.75/1.97 (~b(s(z), s(elem!1))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1552, 1534, 1328, 1145])).
% 1.75/1.97 tff(1554,plain,
% 1.75/1.97 (r(s(z), s(elem!1))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1164, 1553, 1157])).
% 1.75/1.97 tff(1555,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1556,plain,
% 1.75/1.97 (((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1557,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1556])).
% 1.75/1.97 tff(1558,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1557, 1555])).
% 1.75/1.97 tff(1559,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1560,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 1.75/1.97 tff(1561,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1560, 163, 791, 150, 1554, 1542])).
% 1.75/1.97 tff(1562,plain,((~r(s(z), z)) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1563,plain,
% 1.75/1.97 (~r(s(z), z)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1562, 1532, 820, 791, 722, 1144, 1522])).
% 1.75/1.97 tff(1564,plain,
% 1.75/1.97 (b(s(z), z)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[40, 1563])).
% 1.75/1.97 tff(1565,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1566,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1567,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.75/1.97 tff(1568,plain,
% 1.75/1.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1567, 163, 791, 790, 1352])).
% 1.75/1.97 tff(1569,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.75/1.97 tff(1570,plain,
% 1.75/1.97 (s(s(s(elem!1))) = s(elem!1)),
% 1.75/1.97 inference(symmetry,[status(thm)],[1569])).
% 1.75/1.97 tff(1571,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1256, 1570])).
% 1.75/1.97 tff(1572,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1573,plain,
% 1.75/1.97 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1572, 1256])).
% 1.75/1.97 tff(1574,plain,
% 1.75/1.97 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1270, 1268])).
% 1.75/1.97 tff(1575,plain,
% 1.75/1.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1325, 26, 1574, 1568])).
% 1.75/1.97 tff(1576,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.97 tff(1577,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1578,plain,
% 1.75/1.97 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1579,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1578])).
% 1.75/1.97 tff(1580,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.75/1.97 tff(1581,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1582,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.75/1.97 tff(1583,plain,
% 1.75/1.97 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1582, 163, 791, 790, 1352])).
% 1.75/1.97 tff(1584,plain,
% 1.75/1.97 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1377, 1583, 1268])).
% 1.75/1.97 tff(1585,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(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))))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1586,plain,
% 1.75/1.97 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1587,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(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)))))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1586])).
% 1.75/1.97 tff(1588,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(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))))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1587, 1585])).
% 1.75/1.97 tff(1589,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1590,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 1.75/1.97 tff(1591,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1590, 198, 1584, 1328, 1576, 1575])).
% 1.75/1.97 tff(1592,plain,((~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1593,plain,
% 1.75/1.97 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1592, 790, 1352, 1264, 791, 1328])).
% 1.75/1.97 tff(1594,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.97 tff(1595,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.97 tff(1596,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.97 tff(1597,plain,
% 1.75/1.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1598,plain,
% 1.75/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1599,plain,
% 1.75/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 1.75/1.97 tff(1600,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1599, 26, 1596, 1595, 1594])).
% 1.75/1.97 tff(1601,plain,(b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1602,plain,
% 1.75/1.97 (r(s(elem!1), s(s(s(elem!1))))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1601, 1593, 1573])).
% 1.75/1.97 tff(1603,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.75/1.97 tff(1604,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1605,plain,
% 1.75/1.97 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1606,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1605])).
% 1.75/1.97 tff(1607,plain,
% 1.75/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.75/1.97 tff(1608,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1609,plain,
% 1.75/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.75/1.97 tff(1610,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1609, 163, 1353, 791, 1352, 1603])).
% 1.75/1.97 tff(1611,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(1612,plain,
% 1.75/1.97 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1611, 1602, 791, 1352])).
% 1.75/1.97 tff(1613,plain,
% 1.75/1.97 (b(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1339, 1612, 1256])).
% 1.75/1.97 tff(1614,plain,
% 1.75/1.97 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(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))))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(1615,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[1614])).
% 1.75/1.97 tff(1616,plain,
% 1.75/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.97 inference(transitivity,[status(thm)],[1615, 1329])).
% 1.75/1.97 tff(1617,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(1618,plain,
% 1.75/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.75/1.97 tff(1619,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1618, 198, 1613, 1145, 1328])).
% 1.75/1.98 tff(1620,plain,
% 1.75/1.98 ($false),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1326, 1619, 1568, 1271])).
% 1.75/1.98 tff(1621,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.98 tff(1622,plain,
% 1.75/1.98 (~r(s(s(s(elem!1))), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1621, 1532, 791, 1144, 1522, 1251])).
% 1.75/1.98 tff(1623,plain,
% 1.75/1.98 (b(s(s(s(elem!1))), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1295, 1622])).
% 1.75/1.98 tff(1624,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1625,plain,
% 1.75/1.98 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1626,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1625])).
% 1.75/1.98 tff(1627,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.75/1.98 tff(1628,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1629,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.75/1.98 tff(1630,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1629, 198, 1623, 1564, 595])).
% 1.75/1.98 tff(1631,plain,
% 1.75/1.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1632,plain,
% 1.75/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1633,plain,
% 1.75/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 1.75/1.98 tff(1634,plain,
% 1.75/1.98 (r(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1633, 26, 1282, 1630])).
% 1.75/1.98 tff(1635,plain,
% 1.75/1.98 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.75/1.98 inference(symmetry,[status(thm)],[496])).
% 1.75/1.98 tff(1636,plain,
% 1.75/1.98 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1635])).
% 1.75/1.98 tff(1637,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.75/1.98 tff(1638,plain,
% 1.75/1.98 (~b(s(s(elem!1)), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1520, 1145, 595, 791, 722, 116, 1098, 820])).
% 1.75/1.98 tff(1639,plain,
% 1.75/1.98 (r(s(s(elem!1)), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[801, 1638])).
% 1.75/1.98 tff(1640,plain,
% 1.75/1.98 (~r(s(elem!1), s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1530, 1639, 1098, 791])).
% 1.75/1.98 tff(1641,plain,
% 1.75/1.98 (b(s(elem!1), s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[901, 1640, 1134])).
% 1.75/1.98 tff(1642,plain,
% 1.75/1.98 (~r(s(z), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1562, 1641, 820, 791, 722, 1145, 1639])).
% 1.75/1.98 tff(1643,plain,
% 1.75/1.98 (b(s(z), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[40, 1642])).
% 1.75/1.98 tff(1644,plain,
% 1.75/1.98 (s(elem!1) = s(z)),
% 1.75/1.98 inference(monotonicity,[status(thm)],[80])).
% 1.75/1.98 tff(1645,plain,
% 1.75/1.98 ($false),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[820, 1644])).
% 1.75/1.98 tff(1646,plain,((~(elem!1 = z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.98 tff(1647,plain,
% 1.75/1.98 (~(elem!1 = z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1646, 820])).
% 1.75/1.98 tff(1648,plain,
% 1.75/1.98 (~(z = elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[78, 1647])).
% 1.75/1.98 tff(1649,plain,
% 1.75/1.98 (~r(s(elem!1), s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1530, 790, 1098, 791])).
% 1.75/1.98 tff(1650,plain,
% 1.75/1.98 (b(s(elem!1), s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[901, 1649, 1134])).
% 1.75/1.98 tff(1651,plain,
% 1.75/1.98 (~(s(elem!1) = elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1395, 138])).
% 1.75/1.98 tff(1652,plain,
% 1.75/1.98 (~(elem!1 = s(elem!1))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1400, 1651])).
% 1.75/1.98 tff(1653,plain,
% 1.75/1.98 (~b(elem!1, s(elem!1))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1426, 68, 1145, 1328])).
% 1.75/1.98 tff(1654,plain,
% 1.75/1.98 (r(elem!1, s(elem!1))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1416, 1653, 1652])).
% 1.75/1.98 tff(1655,plain,
% 1.75/1.98 (~r(s(elem!1), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1483, 1654, 1475, 791])).
% 1.75/1.98 tff(1656,plain,
% 1.75/1.98 (b(s(elem!1), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[856, 1655, 1651])).
% 1.75/1.98 tff(1657,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1658,plain,
% 1.75/1.98 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1659,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1658])).
% 1.75/1.98 tff(1660,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1659, 1657])).
% 1.75/1.98 tff(1661,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1662,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 1.75/1.98 tff(1663,plain,
% 1.75/1.98 ($false),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1662, 163, 1475, 1115, 1473, 790])).
% 1.75/1.98 tff(1664,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.98 tff(1665,plain,
% 1.75/1.98 (~r(s(s(elem!1)), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1664, 1654, 790, 1475])).
% 1.75/1.98 tff(1666,plain,
% 1.75/1.98 (b(s(s(elem!1)), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[602, 1665, 138])).
% 1.75/1.98 tff(1667,plain,
% 1.75/1.98 ($false),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1470, 198, 1666, 1328, 1656, 68])).
% 1.75/1.98 tff(1668,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.98 tff(1669,plain,
% 1.75/1.98 (~b(elem!1, s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1668, 1475, 598, 1650, 791, 790, 1145])).
% 1.75/1.98 tff(1670,plain,
% 1.75/1.98 (r(elem!1, s(s(elem!1)))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[147, 1669, 116])).
% 1.75/1.98 tff(1671,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1672,plain,
% 1.75/1.98 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1673,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1672])).
% 1.75/1.98 tff(1674,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1673, 1671])).
% 1.75/1.98 tff(1675,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1676,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 1.75/1.98 tff(1677,plain,
% 1.75/1.98 ($false),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1676, 163, 1475, 790, 1098, 1670])).
% 1.75/1.98 tff(1678,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.98 tff(1679,plain,
% 1.75/1.98 (~r(z, elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1678, 1639, 1098, 116, 791, 1145])).
% 1.75/1.98 tff(1680,plain,
% 1.75/1.98 (b(z, elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[102, 1679, 1648])).
% 1.75/1.98 tff(1681,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1682,plain,
% 1.75/1.98 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1683,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1682])).
% 1.75/1.98 tff(1684,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1683, 1681])).
% 1.75/1.98 tff(1685,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1686,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.75/1.98 tff(1687,plain,
% 1.75/1.98 (~r(elem!1, z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1686, 163, 790, 1098, 405])).
% 1.75/1.98 tff(1688,plain,
% 1.75/1.98 (b(elem!1, z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[187, 1687, 1647])).
% 1.75/1.98 tff(1689,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1690,plain,
% 1.75/1.98 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1691,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1690])).
% 1.75/1.98 tff(1692,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.75/1.98 tff(1693,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1694,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.75/1.98 tff(1695,plain,
% 1.75/1.98 (~b(elem!1, s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1694, 198, 95, 1688, 1185, 595])).
% 1.75/1.98 tff(1696,plain,
% 1.75/1.98 (~r(s(s(s(elem!1))), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1621, 1328, 791, 1145, 790, 1256])).
% 1.75/1.98 tff(1697,plain,
% 1.75/1.98 (b(s(s(s(elem!1))), z)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1295, 1696])).
% 1.75/1.98 tff(1698,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1629, 198, 1697, 1185, 595])).
% 1.75/1.98 tff(1699,plain,
% 1.75/1.98 (r(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1633, 26, 1282, 1698])).
% 1.75/1.98 tff(1700,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1319, 1688, 1697, 95])).
% 1.75/1.98 tff(1701,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.75/1.98 tff(1702,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1319, 271, 1311, 95])).
% 1.75/1.98 tff(1703,plain,
% 1.75/1.98 (~b(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1629, 198, 1311, 1185, 595])).
% 1.75/1.98 tff(1704,plain,
% 1.75/1.98 (r(s(s(s(elem!1))), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1633, 26, 1282, 1703])).
% 1.75/1.98 tff(1705,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1706,plain,
% 1.75/1.98 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1707,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1706])).
% 1.75/1.98 tff(1708,plain,
% 1.75/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1707, 1705])).
% 1.75/1.98 tff(1709,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1710,plain,
% 1.75/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.75/1.98 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.75/1.98 tff(1711,plain,
% 1.75/1.98 (~b(s(elem!1), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1710, 198, 95, 271, 1175, 1185, 595])).
% 1.75/1.98 tff(1712,plain,
% 1.75/1.98 (r(s(elem!1), s(z))),
% 1.75/1.98 inference(unit_resolution,[status(thm)],[1150, 26, 820, 1711])).
% 1.75/1.98 tff(1713,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1714,plain,
% 1.75/1.98 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.98 inference(rewrite,[status(thm)],[])).
% 1.75/1.98 tff(1715,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 1.75/1.98 inference(monotonicity,[status(thm)],[1714])).
% 1.75/1.98 tff(1716,plain,
% 1.75/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 1.75/1.98 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.75/1.98 tff(1717,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.98 inference(quant_inst,[status(thm)],[])).
% 1.75/1.98 tff(1718,plain,
% 1.75/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.75/1.99 tff(1719,plain,
% 1.75/1.99 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1718, 163, 1637, 1712, 1704])).
% 1.75/1.99 tff(1720,plain,
% 1.75/1.99 (b(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1339, 1719, 1256])).
% 1.75/1.99 tff(1721,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1722,plain,
% 1.75/1.99 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1723,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1722])).
% 1.75/1.99 tff(1724,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1723, 1721])).
% 1.75/1.99 tff(1725,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1726,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 1.75/1.99 tff(1727,plain,
% 1.75/1.99 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1726, 198, 1175, 1145, 1311])).
% 1.75/1.99 tff(1728,plain,
% 1.75/1.99 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1727, 1720])).
% 1.75/1.99 tff(1729,plain,
% 1.75/1.99 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1326, 1728, 1271])).
% 1.75/1.99 tff(1730,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1731,plain,
% 1.75/1.99 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1732,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1731])).
% 1.75/1.99 tff(1733,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.75/1.99 tff(1734,plain,
% 1.75/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1735,plain,
% 1.75/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.75/1.99 tff(1736,plain,
% 1.75/1.99 (~r(s(s(s(elem!1))), elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1735, 163, 790, 405, 1729])).
% 1.75/1.99 tff(1737,plain,
% 1.75/1.99 (s(s(s(elem!1))) = elem!1),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1308, 1736, 1702])).
% 1.75/1.99 tff(1738,plain,
% 1.75/1.99 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1737])).
% 1.75/1.99 tff(1739,plain,
% 1.75/1.99 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.99 inference(symmetry,[status(thm)],[1738])).
% 1.75/1.99 tff(1740,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1741,plain,
% 1.75/1.99 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1742,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1741])).
% 1.75/1.99 tff(1743,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1742, 1740])).
% 1.75/1.99 tff(1744,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1745,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.75/1.99 tff(1746,plain,
% 1.75/1.99 (~b(s(elem!1), elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1745, 198, 95, 271, 1175])).
% 1.75/1.99 tff(1747,plain,
% 1.75/1.99 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.75/1.99 inference(monotonicity,[status(thm)],[114])).
% 1.75/1.99 tff(1748,plain,
% 1.75/1.99 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.75/1.99 inference(symmetry,[status(thm)],[1747])).
% 1.75/1.99 tff(1749,plain,
% 1.75/1.99 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1748])).
% 1.75/1.99 tff(1750,plain,
% 1.75/1.99 (~b(s(elem!1), s(s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[850, 1749])).
% 1.75/1.99 tff(1751,plain,
% 1.75/1.99 ($false),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1328, 1750])).
% 1.75/1.99 tff(1752,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.99 tff(1753,plain,
% 1.75/1.99 (~(s(s(elem!1)) = elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1752, 1328, 850])).
% 1.75/1.99 tff(1754,plain,
% 1.75/1.99 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[676, 1753])).
% 1.75/1.99 tff(1755,plain,
% 1.75/1.99 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.75/1.99 inference(commutativity,[status(thm)],[])).
% 1.75/1.99 tff(1756,plain,
% 1.75/1.99 (s(s(elem!1)) = elem!1),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1395, 771])).
% 1.75/1.99 tff(1757,plain,
% 1.75/1.99 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1756])).
% 1.75/1.99 tff(1758,plain,
% 1.75/1.99 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.75/1.99 inference(transitivity,[status(thm)],[1757, 1755])).
% 1.75/1.99 tff(1759,plain,
% 1.75/1.99 ((s(elem!1) = elem!1) <=> (s(s(elem!1)) = s(elem!1))),
% 1.75/1.99 inference(symmetry,[status(thm)],[1758])).
% 1.75/1.99 tff(1760,plain,
% 1.75/1.99 (s(s(elem!1)) = s(elem!1)),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[771, 1759])).
% 1.75/1.99 tff(1761,plain,
% 1.75/1.99 ($false),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1701, 1760])).
% 1.75/1.99 tff(1762,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.99 tff(1763,plain,
% 1.75/1.99 (~(s(elem!1) = elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1762, 1701])).
% 1.75/1.99 tff(1764,plain,
% 1.75/1.99 (~(elem!1 = s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1400, 1763])).
% 1.75/1.99 tff(1765,plain,
% 1.75/1.99 (b(elem!1, s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1416, 1411, 1764])).
% 1.75/1.99 tff(1766,plain,
% 1.75/1.99 (r(s(elem!1), elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[856, 1763, 850])).
% 1.75/1.99 tff(1767,plain,
% 1.75/1.99 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), z))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1199])).
% 1.75/1.99 tff(1768,plain,
% 1.75/1.99 (~b(s(elem!1), z)),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[850, 1767])).
% 1.75/1.99 tff(1769,plain,
% 1.75/1.99 ($false),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1175, 1768])).
% 1.75/1.99 tff(1770,plain,((~(z = elem!1)) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.99 tff(1771,plain,
% 1.75/1.99 (~(z = elem!1)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1770, 1175, 850])).
% 1.75/1.99 tff(1772,plain,
% 1.75/1.99 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1250, 1753])).
% 1.75/1.99 tff(1773,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.75/1.99 tff(1774,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1775,plain,
% 1.75/1.99 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1776,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1775])).
% 1.75/1.99 tff(1777,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.75/1.99 tff(1778,plain,
% 1.75/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1779,plain,
% 1.75/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.75/1.99 tff(1780,plain,
% 1.75/1.99 ($false),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1779, 163, 1474, 791, 790, 1773])).
% 1.75/1.99 tff(1781,plain,((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.99 tff(1782,plain,
% 1.75/1.99 (~r(z, s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1781, 1773, 790, 1474])).
% 1.75/1.99 tff(1783,plain,
% 1.75/1.99 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.75/1.99 inference(commutativity,[status(thm)],[])).
% 1.75/1.99 tff(1784,plain,
% 1.75/1.99 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.75/1.99 inference(symmetry,[status(thm)],[1783])).
% 1.75/1.99 tff(1785,plain,
% 1.75/1.99 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1784])).
% 1.75/1.99 tff(1786,plain,
% 1.75/1.99 (~(z = s(elem!1))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[618, 1785])).
% 1.75/1.99 tff(1787,plain,
% 1.75/1.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1788,plain,
% 1.75/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1789,plain,
% 1.75/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.75/1.99 tff(1790,plain,
% 1.75/1.99 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1789, 26])).
% 1.75/1.99 tff(1791,plain,
% 1.75/1.99 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1790, 1786])).
% 1.75/1.99 tff(1792,plain,
% 1.75/1.99 (b(z, s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1791, 1782])).
% 1.75/1.99 tff(1793,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1794,plain,
% 1.75/1.99 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1795,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1794])).
% 1.75/1.99 tff(1796,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.75/1.99 tff(1797,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1798,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.75/1.99 tff(1799,plain,
% 1.75/1.99 (~b(elem!1, z)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1798, 198, 1175, 1792, 1765])).
% 1.75/1.99 tff(1800,plain,
% 1.75/1.99 (r(elem!1, z)),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[187, 1799, 76])).
% 1.75/1.99 tff(1801,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.75/1.99 tff(1802,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.75/1.99 tff(1803,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1804,plain,
% 1.75/1.99 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))))),
% 1.75/1.99 inference(rewrite,[status(thm)],[])).
% 1.75/1.99 tff(1805,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1)))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1804])).
% 1.75/1.99 tff(1806,plain,
% 1.75/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))))),
% 1.75/1.99 inference(transitivity,[status(thm)],[1805, 1803])).
% 1.75/1.99 tff(1807,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.75/1.99 inference(quant_inst,[status(thm)],[])).
% 1.75/1.99 tff(1808,plain,
% 1.75/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 1.75/1.99 tff(1809,plain,
% 1.75/1.99 ($false),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1808, 198, 1802, 1175, 1311, 1801])).
% 1.75/1.99 tff(1810,plain,((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.99 tff(1811,plain,
% 1.75/1.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.75/1.99 inference(unit_resolution,[status(thm)],[1810, 1792, 1311, 1175])).
% 1.75/1.99 tff(1812,plain,
% 1.75/1.99 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.75/1.99 inference(commutativity,[status(thm)],[])).
% 1.75/1.99 tff(1813,plain,
% 1.75/1.99 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.75/1.99 inference(symmetry,[status(thm)],[1812])).
% 1.75/1.99 tff(1814,plain,
% 1.75/1.99 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.75/1.99 inference(monotonicity,[status(thm)],[1813])).
% 1.75/1.99 tff(1815,plain,
% 1.75/1.99 (~(z = s(s(elem!1)))),
% 1.75/1.99 inference(modus_ponens,[status(thm)],[108, 1814])).
% 1.75/1.99 tff(1816,plain,
% 1.75/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1817,plain,
% 1.75/2.00 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1818,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1817])).
% 1.75/2.00 tff(1819,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1818, 1816])).
% 1.75/2.00 tff(1820,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1821,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 1.75/2.00 tff(1822,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1821, 163, 1475, 833, 790, 405])).
% 1.75/2.00 tff(1823,plain,((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1824,plain,
% 1.75/2.00 (~r(z, elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1823, 405, 790, 833])).
% 1.75/2.00 tff(1825,plain,
% 1.75/2.00 (b(z, elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[102, 1824, 3])).
% 1.75/2.00 tff(1826,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1827,plain,
% 1.75/2.00 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1828,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1827])).
% 1.75/2.00 tff(1829,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1828, 1826])).
% 1.75/2.00 tff(1830,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1831,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.75/2.00 tff(1832,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1831, 198, 95, 1801, 1328, 1418, 83])).
% 1.75/2.00 tff(1833,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1834,plain,
% 1.75/2.00 (~b(z, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1833, 1825, 1418, 1328, 1801])).
% 1.75/2.00 tff(1835,plain,
% 1.75/2.00 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1094, 26, 1834])).
% 1.75/2.00 tff(1836,plain,
% 1.75/2.00 (r(z, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1835, 1815])).
% 1.75/2.00 tff(1837,plain,
% 1.75/2.00 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1838,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1837])).
% 1.75/2.00 tff(1839,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1838, 1681])).
% 1.75/2.00 tff(1840,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1841,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.75/2.00 tff(1842,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1841, 163, 833, 790, 1836, 405])).
% 1.75/2.00 tff(1843,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1844,plain,
% 1.75/2.00 (~r(elem!1, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1843, 1800, 790, 1765, 1328, 1792, 3])).
% 1.75/2.00 tff(1845,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.75/2.00 tff(1846,plain,
% 1.75/2.00 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1250, 138])).
% 1.75/2.00 tff(1847,plain,
% 1.75/2.00 (r(s(s(s(elem!1))), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1339, 1846, 1845])).
% 1.75/2.00 tff(1848,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.75/2.00 tff(1849,plain,
% 1.75/2.00 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1848])).
% 1.75/2.00 tff(1850,plain,
% 1.75/2.00 (r(elem!1, s(elem!1))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1353, 1849])).
% 1.75/2.00 tff(1851,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1411, 1850])).
% 1.75/2.00 tff(1852,plain,((~r(s(s(s(elem!1))), s(elem!1))) | r(elem!1, s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1853,plain,
% 1.75/2.00 (~(s(s(s(elem!1))) = elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1852, 1847, 1411])).
% 1.75/2.00 tff(1854,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.75/2.00 tff(1855,plain,
% 1.75/2.00 (b(s(s(elem!1)), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[602, 138, 1854])).
% 1.75/2.00 tff(1856,plain,
% 1.75/2.00 (~(elem!1 = s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[676, 138])).
% 1.75/2.00 tff(1857,plain,
% 1.75/2.00 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[145, 26, 142])).
% 1.75/2.00 tff(1858,plain,
% 1.75/2.00 (b(elem!1, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1857, 1856])).
% 1.75/2.00 tff(1859,plain,
% 1.75/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1426, 1858, 1765, 1328])).
% 1.75/2.00 tff(1860,plain,
% 1.75/2.00 (r(s(s(elem!1)), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1143, 1859, 1701])).
% 1.75/2.00 tff(1861,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1862,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1863,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.75/2.00 tff(1864,plain,
% 1.75/2.00 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1863, 163, 1847, 1474, 1860])).
% 1.75/2.00 tff(1865,plain,
% 1.75/2.00 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1263, 1846])).
% 1.75/2.00 tff(1866,plain,
% 1.75/2.00 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1270, 1865])).
% 1.75/2.00 tff(1867,plain,
% 1.75/2.00 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1325, 26, 1866, 1864])).
% 1.75/2.00 tff(1868,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1869,plain,
% 1.75/2.00 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), 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))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1870,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1869])).
% 1.75/2.00 tff(1871,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1870, 1868])).
% 1.75/2.00 tff(1872,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1873,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.75/2.00 tff(1874,plain,
% 1.75/2.00 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1873, 198])).
% 1.75/2.00 tff(1875,plain,
% 1.75/2.00 (~b(s(s(s(elem!1))), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1874, 1867, 1858, 1855])).
% 1.75/2.00 tff(1876,plain,
% 1.75/2.00 (r(s(s(s(elem!1))), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1308, 1875, 1853])).
% 1.75/2.00 tff(1877,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1878,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1879,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.75/2.00 tff(1880,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1879, 163, 833, 1847, 1474, 1876])).
% 1.75/2.00 tff(1881,plain,((s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | r(elem!1, s(s(elem!1))) | r(elem!1, s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1882,plain,
% 1.75/2.00 (r(s(s(elem!1)), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1881, 1844, 1474, 1701, 1328, 138, 1411, 1811, 1800])).
% 1.75/2.00 tff(1883,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1884,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1885,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.75/2.00 tff(1886,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1885, 163, 1800, 1882, 1474, 1773])).
% 1.75/2.00 tff(1887,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | r(elem!1, s(elem!1)) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (elem!1 = z) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1888,plain,
% 1.75/2.00 (~r(s(s(elem!1)), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1887, 1771, 1701, 1328, 1753, 1411, 790, 1766, 1647, 1175, 1311])).
% 1.75/2.00 tff(1889,plain,
% 1.75/2.00 (b(s(s(elem!1)), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1143, 1888, 1701])).
% 1.75/2.00 tff(1890,plain,
% 1.75/2.00 (~b(elem!1, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1426, 1889, 1765, 1328])).
% 1.75/2.00 tff(1891,plain,
% 1.75/2.00 (r(elem!1, s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[145, 26, 1890, 1754])).
% 1.75/2.00 tff(1892,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1893,plain,
% 1.75/2.00 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1894,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1893])).
% 1.75/2.00 tff(1895,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1894, 1892])).
% 1.75/2.00 tff(1896,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1897,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.75/2.00 tff(1898,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1897, 163, 1475, 1474, 791, 405])).
% 1.75/2.00 tff(1899,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1900,plain,
% 1.75/2.00 (~r(z, elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1899, 791, 405, 1474])).
% 1.75/2.00 tff(1901,plain,
% 1.75/2.00 (b(z, elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[102, 1900, 3])).
% 1.75/2.00 tff(1902,plain,
% 1.75/2.00 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.75/2.00 inference(commutativity,[status(thm)],[])).
% 1.75/2.00 tff(1903,plain,
% 1.75/2.00 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.75/2.00 inference(symmetry,[status(thm)],[1902])).
% 1.75/2.00 tff(1904,plain,
% 1.75/2.00 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1903])).
% 1.75/2.00 tff(1905,plain,
% 1.75/2.00 (~(s(z) = s(elem!1))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[820, 1904])).
% 1.75/2.00 tff(1906,plain,
% 1.75/2.00 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1907,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1906])).
% 1.75/2.00 tff(1908,plain,
% 1.75/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1907, 1312])).
% 1.75/2.00 tff(1909,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1910,plain,
% 1.75/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.75/2.00 tff(1911,plain,
% 1.75/2.00 (~b(s(s(s(elem!1))), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1910, 198, 95, 271, 1311])).
% 1.75/2.00 tff(1912,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.75/2.00 tff(1913,plain,
% 1.75/2.00 (~(s(s(s(elem!1))) = elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1852, 1353, 1411])).
% 1.75/2.00 tff(1914,plain,
% 1.75/2.00 (r(s(s(s(elem!1))), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1308, 1913, 1912])).
% 1.75/2.00 tff(1915,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1916,plain,
% 1.75/2.00 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/2.00 inference(rewrite,[status(thm)],[])).
% 1.75/2.00 tff(1917,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1916])).
% 1.75/2.00 tff(1918,plain,
% 1.75/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.75/2.00 inference(transitivity,[status(thm)],[1917, 1915])).
% 1.75/2.00 tff(1919,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.75/2.00 inference(quant_inst,[status(thm)],[])).
% 1.75/2.00 tff(1920,plain,
% 1.75/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.75/2.00 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 1.75/2.00 tff(1921,plain,
% 1.75/2.00 ($false),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1920, 163, 1353, 1474, 1914, 405])).
% 1.75/2.00 tff(1922,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.00 tff(1923,plain,
% 1.75/2.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1922, 1911, 405, 1474, 1411])).
% 1.75/2.00 tff(1924,plain,
% 1.75/2.00 (b(s(s(s(elem!1))), s(elem!1))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1339, 1923, 1256])).
% 1.75/2.00 tff(1925,plain,
% 1.75/2.00 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1727, 1924])).
% 1.75/2.00 tff(1926,plain,
% 1.75/2.00 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1325, 26, 1271, 1925])).
% 1.75/2.00 tff(1927,plain,
% 1.75/2.00 (~r(s(s(s(elem!1))), elem!1)),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1735, 163, 790, 405, 1926])).
% 1.75/2.00 tff(1928,plain,
% 1.75/2.00 (s(s(s(elem!1))) = elem!1),
% 1.75/2.00 inference(unit_resolution,[status(thm)],[1308, 1927, 1911])).
% 1.75/2.00 tff(1929,plain,
% 1.75/2.00 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(z))),
% 1.75/2.00 inference(monotonicity,[status(thm)],[1928])).
% 1.75/2.00 tff(1930,plain,
% 1.75/2.00 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = elem!1)),
% 1.75/2.00 inference(transitivity,[status(thm)],[1929, 1240])).
% 1.75/2.01 tff(1931,plain,
% 1.75/2.01 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1930])).
% 1.75/2.01 tff(1932,plain,
% 1.75/2.01 (~(s(z) = elem!1)),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1282, 1931])).
% 1.75/2.01 tff(1933,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1934,plain,
% 1.75/2.01 (((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1935,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1934])).
% 1.75/2.01 tff(1936,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1935, 1933])).
% 1.75/2.01 tff(1937,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1938,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.75/2.01 tff(1939,plain,
% 1.75/2.01 (~r(s(z), elem!1)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1938, 163, 790, 405, 682])).
% 1.75/2.01 tff(1940,plain,
% 1.75/2.01 (~r(s(z), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[796, 682, 790, 791])).
% 1.75/2.01 tff(1941,plain,
% 1.75/2.01 (b(s(z), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[40, 1940])).
% 1.75/2.01 tff(1942,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1943,plain,
% 1.75/2.01 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1944,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1943])).
% 1.75/2.01 tff(1945,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.75/2.01 tff(1946,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1947,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.75/2.01 tff(1948,plain,
% 1.75/2.01 (~b(s(z), elem!1)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1947, 198, 95, 271, 1941])).
% 1.75/2.01 tff(1949,plain,
% 1.75/2.01 ($false),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[217, 1948, 1939, 225])).
% 1.75/2.01 tff(1950,plain,((~r(s(z), s(s(elem!1)))) | (s(z) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.01 tff(1951,plain,
% 1.75/2.01 (~r(s(z), s(s(elem!1)))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1950, 1932, 95, 271, 790, 405, 791])).
% 1.75/2.01 tff(1952,plain,
% 1.75/2.01 (b(s(z), s(s(elem!1)))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[642, 1951])).
% 1.75/2.01 tff(1953,plain,
% 1.75/2.01 (((~b(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1954,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1953])).
% 1.75/2.01 tff(1955,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1954, 1545])).
% 1.75/2.01 tff(1956,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1957,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 1.75/2.01 tff(1958,plain,
% 1.75/2.01 (~b(s(z), s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1957, 198, 1145, 1328, 1952])).
% 1.75/2.01 tff(1959,plain,
% 1.75/2.01 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1162, 26, 1958])).
% 1.75/2.01 tff(1960,plain,
% 1.75/2.01 (r(s(z), s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1959, 1905])).
% 1.75/2.01 tff(1961,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1962,plain,
% 1.75/2.01 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1963,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1962])).
% 1.75/2.01 tff(1964,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1963, 1961])).
% 1.75/2.01 tff(1965,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1966,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 1.75/2.01 tff(1967,plain,
% 1.75/2.01 (~r(s(z), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1966, 163, 1474, 791, 1960])).
% 1.75/2.01 tff(1968,plain,
% 1.75/2.01 (b(s(z), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[40, 1967])).
% 1.75/2.01 tff(1969,plain,
% 1.75/2.01 (~b(s(z), elem!1)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1947, 198, 95, 271, 1968])).
% 1.75/2.01 tff(1970,plain,
% 1.75/2.01 (r(s(z), elem!1)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[217, 1969, 1932])).
% 1.75/2.01 tff(1971,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1972,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1973,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.75/2.01 tff(1974,plain,
% 1.75/2.01 ($false),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1973, 163, 1474, 1970, 405, 1960])).
% 1.75/2.01 tff(1975,plain,((~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.01 tff(1976,plain,
% 1.75/2.01 (~b(elem!1, z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1975, 1901, 405, 1474, 791, 820, 1145, 1328, 790, 1175, 1311, 1256, 1411])).
% 1.75/2.01 tff(1977,plain,
% 1.75/2.01 (r(elem!1, z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[187, 1976, 1647])).
% 1.75/2.01 tff(1978,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1979,plain,
% 1.75/2.01 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1980,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1979])).
% 1.75/2.01 tff(1981,plain,
% 1.75/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1980, 1978])).
% 1.75/2.01 tff(1982,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1983,plain,
% 1.75/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 1.75/2.01 tff(1984,plain,
% 1.75/2.01 ($false),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1983, 163, 1977, 791, 790, 405])).
% 1.75/2.01 tff(1985,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/2.01 tff(1986,plain,
% 1.75/2.01 (~r(z, s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1985, 1891, 790, 1766, 820, 1889, 1328, 1175, 1311, 1772, 1411, 1771])).
% 1.75/2.01 tff(1987,plain,
% 1.75/2.01 (b(z, s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1791, 1986])).
% 1.75/2.01 tff(1988,plain,
% 1.75/2.01 (~r(elem!1, z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1843, 1987, 790, 1765, 1328, 1891, 1771])).
% 1.75/2.01 tff(1989,plain,
% 1.75/2.01 (b(elem!1, z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[187, 1988, 1647])).
% 1.75/2.01 tff(1990,plain,
% 1.75/2.01 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(1991,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.75/2.01 inference(monotonicity,[status(thm)],[1990])).
% 1.75/2.01 tff(1992,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.75/2.01 inference(transitivity,[status(thm)],[1991, 1793])).
% 1.75/2.01 tff(1993,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 1.75/2.01 inference(quant_inst,[status(thm)],[])).
% 1.75/2.01 tff(1994,plain,
% 1.75/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.75/2.01 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.75/2.01 tff(1995,plain,
% 1.75/2.01 ($false),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1994, 198, 1989, 1175, 1987, 1765])).
% 1.75/2.01 tff(1996,plain,((~b(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.75/2.01 tff(1997,plain,
% 1.75/2.01 (~b(s(elem!1), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1996, 820, 1328, 790, 1311, 1411, 1701, 850])).
% 1.75/2.01 tff(1998,plain,
% 1.75/2.01 (r(s(elem!1), z)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1217, 1997])).
% 1.75/2.01 tff(1999,plain,
% 1.75/2.01 (~(z = elem!1)),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[78, 76])).
% 1.75/2.01 tff(2000,plain,
% 1.75/2.01 (~b(s(s(elem!1)), s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1426, 1418, 68, 1328])).
% 1.75/2.01 tff(2001,plain,
% 1.75/2.01 (r(s(s(elem!1)), s(elem!1))),
% 1.75/2.01 inference(unit_resolution,[status(thm)],[1143, 2000, 1701])).
% 1.75/2.01 tff(2002,plain,
% 1.75/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.01 inference(rewrite,[status(thm)],[])).
% 1.75/2.01 tff(2003,plain,
% 1.75/2.01 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2004,plain,
% 1.75/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2003])).
% 1.75/2.02 tff(2005,plain,
% 1.75/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.75/2.02 inference(transitivity,[status(thm)],[2004, 2002])).
% 1.75/2.02 tff(2006,plain,
% 1.75/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, z)))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2007,plain,
% 1.75/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 1.75/2.02 tff(2008,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2007, 198, 271, 1801, 1328, 68, 1418])).
% 1.75/2.02 tff(2009,plain,((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2010,plain,
% 1.75/2.02 (~b(z, s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2009, 1418, 1328, 68, 271])).
% 1.75/2.02 tff(2011,plain,
% 1.75/2.02 (r(z, s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1791, 2010])).
% 1.75/2.02 tff(2012,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1779, 163, 1474, 2011, 790, 2001])).
% 1.75/2.02 tff(2013,plain,((~b(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2014,plain,
% 1.75/2.02 (~b(elem!1, z)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2013, 68, 790, 1328, 1474, 1418, 1701])).
% 1.75/2.02 tff(2015,plain,
% 1.75/2.02 (r(elem!1, z)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[187, 2014, 76])).
% 1.75/2.02 tff(2016,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2017,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2018,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.75/2.02 tff(2019,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2018, 163, 1475, 833, 1474, 1221])).
% 1.75/2.02 tff(2020,plain,((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2021,plain,
% 1.75/2.02 (~r(z, elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2020, 2015, 1474, 1221])).
% 1.75/2.02 tff(2022,plain,
% 1.75/2.02 (~b(s(s(elem!1)), s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1426, 68, 1418, 1328])).
% 1.75/2.02 tff(2023,plain,
% 1.75/2.02 (r(s(s(elem!1)), s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1143, 2022, 1701])).
% 1.75/2.02 tff(2024,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2025,plain,
% 1.75/2.02 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2026,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2025])).
% 1.75/2.02 tff(2027,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.02 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.75/2.02 tff(2028,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2029,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.75/2.02 tff(2030,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2029, 163, 1221, 790, 1773, 1098])).
% 1.75/2.02 tff(2031,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2032,plain,
% 1.75/2.02 (~r(z, s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2031, 1773, 790, 1221])).
% 1.75/2.02 tff(2033,plain,
% 1.75/2.02 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1094, 26, 2032])).
% 1.75/2.02 tff(2034,plain,
% 1.75/2.02 (b(z, s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2033, 1815])).
% 1.75/2.02 tff(2035,plain,
% 1.75/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2036,plain,
% 1.75/2.02 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2037,plain,
% 1.75/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2036])).
% 1.75/2.02 tff(2038,plain,
% 1.75/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.75/2.02 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.75/2.02 tff(2039,plain,
% 1.75/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2040,plain,
% 1.75/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.75/2.02 tff(2041,plain,
% 1.75/2.02 ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2040, 198, 95, 1128, 1328])).
% 1.75/2.02 tff(2042,plain,
% 1.75/2.02 (~b(z, s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2041, 2034])).
% 1.75/2.02 tff(2043,plain,
% 1.75/2.02 (r(z, s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1791, 2042])).
% 1.75/2.02 tff(2044,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1779, 163, 1474, 2043, 790, 1773])).
% 1.75/2.02 tff(2045,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2046,plain,
% 1.75/2.02 (~b(s(s(elem!1)), elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2045, 1773, 790, 1221, 1474, 1328, 95])).
% 1.75/2.02 tff(2047,plain,
% 1.75/2.02 (r(s(s(elem!1)), elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[602, 2046, 138])).
% 1.75/2.02 tff(2048,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1885, 163, 833, 2047, 1474, 1773])).
% 1.75/2.02 tff(2049,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2050,plain,
% 1.75/2.02 (~b(z, elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2049, 2023, 1474, 138, 790, 1221, 1328, 2015])).
% 1.75/2.02 tff(2051,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[102, 2050, 2021, 1999])).
% 1.75/2.02 tff(2052,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = z) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2053,plain,
% 1.75/2.02 (~b(elem!1, s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2052, 1998, 1753, 790, 1766, 1328, 1701, 1647, 1765])).
% 1.75/2.02 tff(2054,plain,
% 1.75/2.02 (r(elem!1, s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[147, 2053, 1754])).
% 1.75/2.02 tff(2055,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2056,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2057,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.75/2.02 tff(2058,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2057, 163, 1475, 1474, 1221, 405])).
% 1.75/2.02 tff(2059,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2060,plain,
% 1.75/2.02 (~r(z, elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2059, 1998, 1766, 2054])).
% 1.75/2.02 tff(2061,plain,
% 1.75/2.02 (b(z, elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[102, 2060, 1648])).
% 1.75/2.02 tff(2062,plain,
% 1.75/2.02 (s(s(s(elem!1))) = s(elem!1)),
% 1.75/2.02 inference(monotonicity,[status(thm)],[114])).
% 1.75/2.02 tff(2063,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1256, 2062])).
% 1.75/2.02 tff(2064,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2065,plain,
% 1.75/2.02 (~(s(s(elem!1)) = elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2064, 1256])).
% 1.75/2.02 tff(2066,plain,
% 1.75/2.02 (~(s(elem!1) = s(s(elem!1)))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[140, 2065])).
% 1.75/2.02 tff(2067,plain,
% 1.75/2.02 (~(s(s(elem!1)) = s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1138, 2066])).
% 1.75/2.02 tff(2068,plain,
% 1.75/2.02 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(z))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[1848])).
% 1.75/2.02 tff(2069,plain,
% 1.75/2.02 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = elem!1)),
% 1.75/2.02 inference(transitivity,[status(thm)],[2068, 1240])).
% 1.75/2.02 tff(2070,plain,
% 1.75/2.02 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2069])).
% 1.75/2.02 tff(2071,plain,
% 1.75/2.02 (~(s(z) = elem!1)),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[1282, 2070])).
% 1.75/2.02 tff(2072,plain,
% 1.75/2.02 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 1.75/2.02 inference(monotonicity,[status(thm)],[1848])).
% 1.75/2.02 tff(2073,plain,
% 1.75/2.02 (b(elem!1, z)),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[1311, 2072])).
% 1.75/2.02 tff(2074,plain,
% 1.75/2.02 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[1848])).
% 1.75/2.02 tff(2075,plain,
% 1.75/2.02 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.75/2.02 inference(symmetry,[status(thm)],[2074])).
% 1.75/2.02 tff(2076,plain,
% 1.75/2.02 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2075])).
% 1.75/2.02 tff(2077,plain,
% 1.75/2.02 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[113])).
% 1.75/2.02 tff(2078,plain,
% 1.75/2.02 (~(elem!1 = s(s(elem!1)))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2065, 2077])).
% 1.75/2.02 tff(2079,plain,
% 1.75/2.02 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.75/2.02 inference(symmetry,[status(thm)],[1849])).
% 1.75/2.02 tff(2080,plain,
% 1.75/2.02 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2079])).
% 1.75/2.02 tff(2081,plain,
% 1.75/2.02 (elem!1 = s(s(s(elem!1)))),
% 1.75/2.02 inference(symmetry,[status(thm)],[1848])).
% 1.75/2.02 tff(2082,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.75/2.02 tff(2083,plain,
% 1.75/2.02 (s(s(z)) = s(s(s(elem!1)))),
% 1.75/2.02 inference(transitivity,[status(thm)],[2082, 2081])).
% 1.75/2.02 tff(2084,plain,
% 1.75/2.02 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2083])).
% 1.75/2.02 tff(2085,plain,
% 1.75/2.02 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.75/2.02 inference(symmetry,[status(thm)],[2084])).
% 1.75/2.02 tff(2086,plain,
% 1.75/2.02 (s(s(elem!1)) = s(z)),
% 1.75/2.02 inference(transitivity,[status(thm)],[1247, 2085, 222])).
% 1.75/2.02 tff(2087,plain,
% 1.75/2.02 ($false),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[620, 2086])).
% 1.75/2.02 tff(2088,plain,((~(s(s(z)) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.75/2.02 tff(2089,plain,
% 1.75/2.02 (~(s(s(z)) = elem!1)),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2088, 1848])).
% 1.75/2.02 tff(2090,plain,
% 1.75/2.02 (~(s(s(z)) = s(elem!1))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[227, 2071])).
% 1.75/2.02 tff(2091,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2092,plain,
% 1.75/2.02 (((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.75/2.02 inference(rewrite,[status(thm)],[])).
% 1.75/2.02 tff(2093,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.75/2.02 inference(monotonicity,[status(thm)],[2092])).
% 1.75/2.02 tff(2094,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.75/2.02 inference(transitivity,[status(thm)],[2093, 2091])).
% 1.75/2.02 tff(2095,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.75/2.02 inference(quant_inst,[status(thm)],[])).
% 1.75/2.02 tff(2096,plain,
% 1.75/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.75/2.02 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.75/2.02 tff(2097,plain,
% 1.75/2.02 (~r(s(elem!1), s(z))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[2096, 163, 1474, 1473, 236])).
% 1.75/2.02 tff(2098,plain,
% 1.75/2.02 (b(s(elem!1), s(z))),
% 1.75/2.02 inference(unit_resolution,[status(thm)],[1150, 26, 820, 2097])).
% 1.75/2.02 tff(2099,plain,
% 1.75/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(2100,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(2101,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.86/2.02 tff(2102,plain,
% 1.86/2.02 (~r(s(z), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2101, 163, 1474, 1473, 236])).
% 1.86/2.02 tff(2103,plain,
% 1.86/2.02 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1162, 26, 2102])).
% 1.86/2.02 tff(2104,plain,
% 1.86/2.02 (b(s(z), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2103, 1905])).
% 1.86/2.02 tff(2105,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.86/2.02 tff(2106,plain,
% 1.86/2.02 (~(s(s(z)) = s(s(elem!1)))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[822, 820])).
% 1.86/2.02 tff(2107,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.86/2.02 tff(2108,plain,
% 1.86/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(2109,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(2110,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.86/2.02 tff(2111,plain,
% 1.86/2.02 (~r(s(s(elem!1)), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2110, 163, 791, 1221, 790])).
% 1.86/2.02 tff(2112,plain,
% 1.86/2.02 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1143, 2111, 1701])).
% 1.86/2.02 tff(2113,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.86/2.02 tff(2114,plain,
% 1.86/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(2115,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(2116,plain,
% 1.86/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 1.86/2.02 tff(2117,plain,
% 1.86/2.02 (~r(s(s(z)), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2116, 163, 1474, 1473, 2113])).
% 1.86/2.02 tff(2118,plain,
% 1.86/2.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(2119,plain,
% 1.86/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(2120,plain,
% 1.86/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 1.86/2.02 tff(2121,plain,
% 1.86/2.02 (b(s(s(z)), s(elem!1))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2120, 26, 232, 2117])).
% 1.86/2.02 tff(2122,plain,
% 1.86/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2123,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2124,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.86/2.03 tff(2125,plain,
% 1.86/2.03 (~r(s(s(z)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2124, 163, 1473, 236, 2113])).
% 1.86/2.03 tff(2126,plain,
% 1.86/2.03 (b(s(s(z)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[485, 26, 395, 2125])).
% 1.86/2.03 tff(2127,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2128,plain,
% 1.86/2.03 (((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2129,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2128])).
% 1.86/2.03 tff(2130,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2129, 2127])).
% 1.86/2.03 tff(2131,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2132,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 1.86/2.03 tff(2133,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2132, 198, 1145, 1328, 2126, 1543, 2107, 2121])).
% 1.86/2.03 tff(2134,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (s(s(z)) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2135,plain,
% 1.86/2.03 (~r(s(s(z)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2134, 2112, 1328, 1543, 2107, 232, 1473, 236, 1474])).
% 1.86/2.03 tff(2136,plain,
% 1.86/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2137,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2138,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.86/2.03 tff(2139,plain,
% 1.86/2.03 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2138, 26])).
% 1.86/2.03 tff(2140,plain,
% 1.86/2.03 (b(s(s(z)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2139, 2135, 2105])).
% 1.86/2.03 tff(2141,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2142,plain,
% 1.86/2.03 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2143,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2142])).
% 1.86/2.03 tff(2144,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2143, 2141])).
% 1.86/2.03 tff(2145,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2146,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 1.86/2.03 tff(2147,plain,
% 1.86/2.03 (~b(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2146, 198, 95, 271, 2140])).
% 1.86/2.03 tff(2148,plain,
% 1.86/2.03 (r(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[344, 26, 46, 2147])).
% 1.86/2.03 tff(2149,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2150,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2151,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 1.86/2.03 tff(2152,plain,
% 1.86/2.03 (~r(s(s(z)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2151, 163, 791, 1221, 2148])).
% 1.86/2.03 tff(2153,plain,
% 1.86/2.03 (b(s(s(z)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2120, 26, 232, 2152])).
% 1.86/2.03 tff(2154,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 1.86/2.03 tff(2155,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2156,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2157,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.86/2.03 tff(2158,plain,
% 1.86/2.03 (~r(s(s(z)), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2157, 163, 791, 790, 2148])).
% 1.86/2.03 tff(2159,plain,
% 1.86/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2160,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2161,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 1.86/2.03 tff(2162,plain,
% 1.86/2.03 (b(s(s(z)), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2161, 26, 2158, 2154])).
% 1.86/2.03 tff(2163,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2164,plain,
% 1.86/2.03 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2165,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2164])).
% 1.86/2.03 tff(2166,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2165, 2163])).
% 1.86/2.03 tff(2167,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2168,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 1.86/2.03 tff(2169,plain,
% 1.86/2.03 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2168, 198, 1128, 1328, 2140])).
% 1.86/2.03 tff(2170,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2169, 2162, 2153])).
% 1.86/2.03 tff(2171,plain,((~r(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2172,plain,
% 1.86/2.03 (~r(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2171, 2104, 1328, 2106, 232, 790, 1221, 95, 271, 2105, 1128, 2098, 1473, 236, 1474, 1701])).
% 1.86/2.03 tff(2173,plain,
% 1.86/2.03 (b(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1791, 2172])).
% 1.86/2.03 tff(2174,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2175,plain,
% 1.86/2.03 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2176,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2175])).
% 1.86/2.03 tff(2177,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2176, 2174])).
% 1.86/2.03 tff(2178,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2179,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 1.86/2.03 tff(2180,plain,
% 1.86/2.03 (~b(z, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2179, 198, 2173, 2104, 2098])).
% 1.86/2.03 tff(2181,plain,
% 1.86/2.03 (r(z, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[593, 2180])).
% 1.86/2.03 tff(2182,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2183,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2184,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.86/2.03 tff(2185,plain,
% 1.86/2.03 (~r(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2184, 163, 1221, 790, 2181])).
% 1.86/2.03 tff(2186,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1143, 2185, 1701])).
% 1.86/2.03 tff(2187,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2188,plain,
% 1.86/2.03 (((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), 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(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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2189,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2188])).
% 1.86/2.03 tff(2190,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2189, 2187])).
% 1.86/2.03 tff(2191,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2192,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 1.86/2.04 tff(2193,plain,
% 1.86/2.04 (~b(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2192, 198, 2186, 1328, 2104, 2098])).
% 1.86/2.04 tff(2194,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[624, 26, 2193, 620])).
% 1.86/2.04 tff(2195,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2196,plain,
% 1.86/2.04 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2197,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2196])).
% 1.86/2.04 tff(2198,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2197, 2195])).
% 1.86/2.04 tff(2199,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2200,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 1.86/2.04 tff(2201,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2200, 163, 236, 790, 2181, 2194])).
% 1.86/2.04 tff(2202,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (s(s(z)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2203,plain,
% 1.86/2.04 (~r(elem!1, s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2202, 1128, 790, 1328, 2067, 1221, 2090, 95, 271, 2089, 236, 1474, 820])).
% 1.86/2.04 tff(2204,plain,
% 1.86/2.04 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2203, 2080])).
% 1.86/2.04 tff(2205,plain,
% 1.86/2.04 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1339, 2204, 1256])).
% 1.86/2.04 tff(2206,plain,
% 1.86/2.04 (b(elem!1, s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2205, 2074])).
% 1.86/2.04 tff(2207,plain,
% 1.86/2.04 (~r(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2045, 1128, 790, 95, 1474, 1328, 1221])).
% 1.86/2.04 tff(2208,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1143, 2207, 2067])).
% 1.86/2.04 tff(2209,plain,
% 1.86/2.04 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2210,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2209])).
% 1.86/2.04 tff(2211,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2210, 1419])).
% 1.86/2.04 tff(2212,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2213,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 1.86/2.04 tff(2214,plain,
% 1.86/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2213, 198, 2208, 1328, 2206])).
% 1.86/2.04 tff(2215,plain,
% 1.86/2.04 ((elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[145, 26, 2214])).
% 1.86/2.04 tff(2216,plain,
% 1.86/2.04 (r(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2215, 2078])).
% 1.86/2.04 tff(2217,plain,
% 1.86/2.04 (~r(s(z), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1973, 163, 1474, 236, 2216])).
% 1.86/2.04 tff(2218,plain,
% 1.86/2.04 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1162, 26, 2217])).
% 1.86/2.04 tff(2219,plain,
% 1.86/2.04 (b(s(z), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2218, 1905])).
% 1.86/2.04 tff(2220,plain,
% 1.86/2.04 (~b(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1550, 198, 2208, 1328, 2219])).
% 1.86/2.04 tff(2221,plain,
% 1.86/2.04 (r(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[640, 26, 2220, 635])).
% 1.86/2.04 tff(2222,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1938, 163, 236, 790, 2216, 2221])).
% 1.86/2.04 tff(2223,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2224,plain,
% 1.86/2.04 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2223, 236, 790, 1328, 820, 1474, 95, 1221, 1848, 1256, 271])).
% 1.86/2.04 tff(2225,plain,
% 1.86/2.04 (r(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[602, 2224, 2065])).
% 1.86/2.04 tff(2226,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2227,plain,
% 1.86/2.04 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2228,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2227])).
% 1.86/2.04 tff(2229,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.86/2.04 tff(2230,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2231,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.86/2.04 tff(2232,plain,
% 1.86/2.04 (~r(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2231, 163, 1474, 236, 405])).
% 1.86/2.04 tff(2233,plain,
% 1.86/2.04 (b(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1150, 26, 820, 2232])).
% 1.86/2.04 tff(2234,plain,
% 1.86/2.04 (~r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[609, 163, 1115, 236, 405])).
% 1.86/2.04 tff(2235,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[624, 26, 620, 2234])).
% 1.86/2.04 tff(2236,plain,
% 1.86/2.04 (~r(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[630, 163, 1115, 236, 405])).
% 1.86/2.04 tff(2237,plain,
% 1.86/2.04 (b(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[640, 26, 2236, 635])).
% 1.86/2.04 tff(2238,plain,
% 1.86/2.04 (((~b(s(s(elem!1)), s(z))) | (~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(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2239,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2238])).
% 1.86/2.04 tff(2240,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2239, 1535])).
% 1.86/2.04 tff(2241,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2242,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.86/2.04 tff(2243,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2242, 198, 1328, 2237, 2235, 2233])).
% 1.86/2.04 tff(2244,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2245,plain,
% 1.86/2.04 (~r(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2244, 236, 820, 1474, 1328, 2225])).
% 1.86/2.04 tff(2246,plain,
% 1.86/2.04 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[145, 26, 2245])).
% 1.86/2.04 tff(2247,plain,
% 1.86/2.04 (b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2246, 2078])).
% 1.86/2.04 tff(2248,plain,
% 1.86/2.04 (~b(elem!1, s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2013, 2247, 790, 1328, 1474, 271, 2067])).
% 1.86/2.04 tff(2249,plain,
% 1.86/2.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2248, 2076])).
% 1.86/2.04 tff(2250,plain,
% 1.86/2.04 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1339, 2249, 1256])).
% 1.86/2.04 tff(2251,plain,
% 1.86/2.04 (r(elem!1, s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1852, 2250, 1848])).
% 1.86/2.04 tff(2252,plain,
% 1.86/2.04 (~r(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2096, 163, 1474, 2251, 236])).
% 1.86/2.04 tff(2253,plain,
% 1.86/2.04 (b(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1150, 26, 820, 2252])).
% 1.86/2.04 tff(2254,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2255,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2256,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 1.86/2.04 tff(2257,plain,
% 1.86/2.04 (~r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2256, 163, 2225, 2251, 236])).
% 1.86/2.04 tff(2258,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[624, 26, 620, 2257])).
% 1.86/2.04 tff(2259,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2260,plain,
% 1.86/2.04 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2261,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2260])).
% 1.86/2.04 tff(2262,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.86/2.04 tff(2263,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2264,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.86/2.04 tff(2265,plain,
% 1.86/2.04 (~r(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2264, 163, 2225, 2251, 236])).
% 1.86/2.04 tff(2266,plain,
% 1.86/2.04 (b(s(z), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[640, 26, 2265, 635])).
% 1.86/2.04 tff(2267,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2242, 198, 1328, 2266, 2258, 2253])).
% 1.86/2.04 tff(2268,plain,((~r(s(z), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2269,plain,
% 1.86/2.04 (~r(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2268, 1848, 820, 1474, 1328, 1256, 790, 2073, 95, 1221])).
% 1.86/2.04 tff(2270,plain,
% 1.86/2.04 (b(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[217, 2269, 2071])).
% 1.86/2.04 tff(2271,plain,
% 1.86/2.04 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2272,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2271])).
% 1.86/2.04 tff(2273,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2272, 1942])).
% 1.86/2.04 tff(2274,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2275,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.86/2.04 tff(2276,plain,
% 1.86/2.04 (~b(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2275, 198, 95, 2073, 2270])).
% 1.86/2.04 tff(2277,plain,
% 1.86/2.04 (r(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[40, 2276])).
% 1.86/2.04 tff(2278,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2279,plain,
% 1.86/2.04 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2280,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2279])).
% 1.86/2.04 tff(2281,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.86/2.04 tff(2282,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2283,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.86/2.04 tff(2284,plain,
% 1.86/2.04 (~r(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2283, 163, 1221, 1098, 150])).
% 1.86/2.04 tff(2285,plain,
% 1.86/2.04 (b(s(elem!1), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1150, 26, 820, 2284])).
% 1.86/2.04 tff(2286,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2287,plain,
% 1.86/2.04 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2288,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2287])).
% 1.86/2.04 tff(2289,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2288, 2286])).
% 1.86/2.04 tff(2290,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2291,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 1.86/2.04 tff(2292,plain,
% 1.86/2.04 (~r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2291, 163, 790, 1098, 150])).
% 1.86/2.04 tff(2293,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[624, 26, 620, 2292])).
% 1.86/2.04 tff(2294,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2295,plain,
% 1.86/2.04 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2296,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2295])).
% 1.86/2.04 tff(2297,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.86/2.04 tff(2298,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2299,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.86/2.04 tff(2300,plain,
% 1.86/2.05 (~r(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2299, 163, 790, 1098, 150])).
% 1.86/2.05 tff(2301,plain,
% 1.86/2.05 (b(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[640, 26, 2300, 635])).
% 1.86/2.05 tff(2302,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2242, 198, 1328, 2301, 2293, 2285])).
% 1.86/2.05 tff(2303,plain,((~r(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2304,plain,
% 1.86/2.05 (~r(z, s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2303, 2277, 820, 790, 1328, 1221])).
% 1.86/2.05 tff(2305,plain,
% 1.86/2.05 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1094, 26, 2304])).
% 1.86/2.05 tff(2306,plain,
% 1.86/2.05 (b(z, s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2305, 1815])).
% 1.86/2.05 tff(2307,plain,
% 1.86/2.05 (~r(s(elem!1), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1502, 163, 791, 1221, 150])).
% 1.86/2.05 tff(2308,plain,
% 1.86/2.05 (b(s(elem!1), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1150, 26, 820, 2307])).
% 1.86/2.05 tff(2309,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2310,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2311,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.86/2.05 tff(2312,plain,
% 1.86/2.05 (~r(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2311, 163, 791, 790, 150])).
% 1.86/2.05 tff(2313,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[624, 26, 620, 2312])).
% 1.86/2.05 tff(2314,plain,
% 1.86/2.05 (~r(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[794, 163, 791, 790, 150])).
% 1.86/2.05 tff(2315,plain,
% 1.86/2.05 (b(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[640, 26, 2314, 635])).
% 1.86/2.05 tff(2316,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2242, 198, 1328, 2315, 2313, 2308])).
% 1.86/2.05 tff(2317,plain,((~r(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2318,plain,
% 1.86/2.05 (~r(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2317, 2277, 820, 790, 1328, 1221])).
% 1.86/2.05 tff(2319,plain,
% 1.86/2.05 (b(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1791, 2318])).
% 1.86/2.05 tff(2320,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2321,plain,
% 1.86/2.05 (((~b(s(elem!1), s(s(elem!1)))) | (~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(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2322,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2321])).
% 1.86/2.05 tff(2323,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2322, 2320])).
% 1.86/2.05 tff(2324,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2325,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.86/2.05 tff(2326,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2325, 198, 1145, 1801, 1328, 83])).
% 1.86/2.05 tff(2327,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2328,plain,
% 1.86/2.05 (~b(s(s(elem!1)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2327, 2319, 1328, 2306])).
% 1.86/2.05 tff(2329,plain,
% 1.86/2.05 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1143, 2328, 2067])).
% 1.86/2.05 tff(2330,plain,
% 1.86/2.05 (~b(elem!1, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1833, 2319, 95, 1328, 2306])).
% 1.86/2.05 tff(2331,plain,
% 1.86/2.05 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2330, 2076])).
% 1.86/2.05 tff(2332,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1339, 2331, 1256])).
% 1.86/2.05 tff(2333,plain,
% 1.86/2.05 (r(elem!1, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1852, 2332, 1848])).
% 1.86/2.05 tff(2334,plain,
% 1.86/2.05 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2045, 2329, 790, 95, 1474, 1328, 1221])).
% 1.86/2.05 tff(2335,plain,
% 1.86/2.05 (r(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[602, 2334, 2065])).
% 1.86/2.05 tff(2336,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2337,plain,
% 1.86/2.05 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2338,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2337])).
% 1.86/2.05 tff(2339,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2338, 2336])).
% 1.86/2.05 tff(2340,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2341,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 1.86/2.05 tff(2342,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2341, 163, 2335, 1474, 2333, 2329])).
% 1.86/2.05 tff(2343,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2344,plain,
% 1.86/2.05 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2343, 2061, 1772, 1766, 1328, 790, 1998, 820, 1311])).
% 1.86/2.05 tff(2345,plain,
% 1.86/2.05 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2045, 1773, 790, 95, 1474, 1328, 1221])).
% 1.86/2.05 tff(2346,plain,
% 1.86/2.05 (r(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[602, 2345, 138])).
% 1.86/2.05 tff(2347,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2348,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2349,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.86/2.05 tff(2350,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2349, 163, 2346, 1474, 1773, 405])).
% 1.86/2.05 tff(2351,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2352,plain,
% 1.86/2.05 (~r(s(s(elem!1)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2351, 2061, 1766, 1753, 790, 1998, 1328, 2054])).
% 1.86/2.05 tff(2353,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1143, 2352, 1701])).
% 1.86/2.05 tff(2354,plain,
% 1.86/2.05 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1922, 1912, 405, 1474, 1411])).
% 1.86/2.05 tff(2355,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1339, 2354, 1256])).
% 1.86/2.05 tff(2356,plain,
% 1.86/2.05 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1618, 198, 2355, 1145, 1328])).
% 1.86/2.05 tff(2357,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1325, 26, 1271, 2356])).
% 1.86/2.05 tff(2358,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1308, 1912, 1297])).
% 1.86/2.05 tff(2359,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1735, 163, 790, 2358, 405, 2357])).
% 1.86/2.05 tff(2360,plain,(b(s(s(s(elem!1))), elem!1) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2361,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2360, 2054, 790, 2353, 1328, 1772, 2344, 1766, 1411])).
% 1.86/2.05 tff(2362,plain,
% 1.86/2.05 (~b(elem!1, z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1319, 2061, 1311, 2361])).
% 1.86/2.05 tff(2363,plain,
% 1.86/2.05 (r(elem!1, z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[187, 2362, 1647])).
% 1.86/2.05 tff(2364,plain,
% 1.86/2.05 (~b(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1843, 2363, 790, 1765, 1328, 2054, 1648])).
% 1.86/2.05 tff(2365,plain,
% 1.86/2.05 (r(z, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1791, 2364])).
% 1.86/2.05 tff(2366,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1983, 163, 2363, 2365, 790, 2054])).
% 1.86/2.05 tff(2367,plain,((s(elem!1) = s(z)) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | r(elem!1, s(elem!1)) | (s(s(elem!1)) = s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2368,plain,
% 1.86/2.05 (r(elem!1, s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2367, 1746, 790, 820, 1328, 1701, 1311])).
% 1.86/2.05 tff(2369,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2368, 1739])).
% 1.86/2.05 tff(2370,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1719, 2369])).
% 1.86/2.05 tff(2371,plain,((~b(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2372,plain,
% 1.86/2.05 (~b(s(elem!1), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2371, 405, 790, 1145, 1697, 1256, 1637, 820, 1328, 1701, 95, 1688, 1185, 595])).
% 1.86/2.05 tff(2373,plain,
% 1.86/2.05 (r(s(elem!1), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1217, 2372])).
% 1.86/2.05 tff(2374,plain,
% 1.86/2.05 (~r(s(s(z)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2151, 163, 791, 1221, 332])).
% 1.86/2.05 tff(2375,assumption,(~b(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.86/2.05 tff(2376,assumption,(~r(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.86/2.05 tff(2377,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2120, 26, 232, 2376, 2375])).
% 1.86/2.05 tff(2378,plain,(b(s(s(z)), s(elem!1)) | (s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2379,plain,
% 1.86/2.05 (b(s(s(z)), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2378, 2374, 232])).
% 1.86/2.05 tff(2380,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2157, 163, 791, 790, 332])).
% 1.86/2.05 tff(2381,plain,
% 1.86/2.05 (b(s(s(z)), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2161, 26, 2380, 2154])).
% 1.86/2.05 tff(2382,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2383,plain,
% 1.86/2.05 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2384,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2383])).
% 1.86/2.05 tff(2385,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2384, 2382])).
% 1.86/2.05 tff(2386,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2387,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 1.86/2.05 tff(2388,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2387, 198, 1145, 1328, 2381, 2379])).
% 1.86/2.05 tff(2389,plain,((~r(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2390,plain,
% 1.86/2.05 (~r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2389, 2090, 1328, 2154, 1145, 791, 790, 1221])).
% 1.86/2.05 tff(2391,plain,
% 1.86/2.05 (b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[345, 2390])).
% 1.86/2.05 tff(2392,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2393,plain,
% 1.86/2.05 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2394,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2393])).
% 1.86/2.05 tff(2395,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2394, 2392])).
% 1.86/2.05 tff(2396,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2397,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 1.86/2.05 tff(2398,plain,
% 1.86/2.05 (~b(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2397, 198, 95, 271, 1185, 595, 2391])).
% 1.86/2.05 tff(2399,plain,
% 1.86/2.05 (r(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[485, 26, 395, 2398])).
% 1.86/2.05 tff(2400,plain,
% 1.86/2.05 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2401,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2400])).
% 1.86/2.05 tff(2402,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2401, 2141])).
% 1.86/2.06 tff(2403,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2404,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.86/2.06 tff(2405,plain,
% 1.86/2.06 (~b(s(s(z)), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2404, 198, 95, 271, 2391])).
% 1.86/2.06 tff(2406,plain,
% 1.86/2.06 (r(s(s(z)), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2139, 2405, 2089])).
% 1.86/2.06 tff(2407,plain,
% 1.86/2.06 (~b(s(z), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1947, 198, 95, 271, 1185])).
% 1.86/2.06 tff(2408,plain,
% 1.86/2.06 (r(s(z), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[217, 2071, 2407])).
% 1.86/2.06 tff(2409,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[479, 163, 2408, 405, 2406, 2399])).
% 1.86/2.06 tff(2410,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2411,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2410, 405, 95, 1688, 1185, 595, 1328, 2106, 1145, 791, 790, 2373])).
% 1.86/2.06 tff(2412,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1308, 2411, 1700])).
% 1.86/2.06 tff(2413,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.86/2.06 tff(2414,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2415,plain,
% 1.86/2.06 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2416,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2415])).
% 1.86/2.06 tff(2417,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2416, 2414])).
% 1.86/2.06 tff(2418,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2419,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 1.86/2.06 tff(2420,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2419, 163, 1363, 259, 1637, 2413])).
% 1.86/2.06 tff(2421,plain,((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2422,plain,
% 1.86/2.06 (~r(elem!1, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2421, 2412, 1637, 1699])).
% 1.86/2.06 tff(2423,plain,
% 1.86/2.06 (elem!1 = s(z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[242, 2422, 1695])).
% 1.86/2.06 tff(2424,plain,
% 1.86/2.06 (s(elem!1) = s(s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2423])).
% 1.86/2.06 tff(2425,plain,
% 1.86/2.06 (s(s(z)) = s(elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[2424])).
% 1.86/2.06 tff(2426,plain,
% 1.86/2.06 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2424])).
% 1.86/2.06 tff(2427,plain,
% 1.86/2.06 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2426])).
% 1.86/2.06 tff(2428,plain,
% 1.86/2.06 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2427])).
% 1.86/2.06 tff(2429,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2428, 2425])).
% 1.86/2.06 tff(2430,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2429])).
% 1.86/2.06 tff(2431,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2428, 2425])).
% 1.86/2.06 tff(2432,plain,
% 1.86/2.06 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2431])).
% 1.86/2.06 tff(2433,plain,
% 1.86/2.06 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2426])).
% 1.86/2.06 tff(2434,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2428, 2433])).
% 1.86/2.06 tff(2435,plain,
% 1.86/2.06 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2434])).
% 1.86/2.06 tff(2436,plain,
% 1.86/2.06 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2423])).
% 1.86/2.06 tff(2437,plain,
% 1.86/2.06 (r(s(z), s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[405, 2436])).
% 1.86/2.06 tff(2438,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2428])).
% 1.86/2.06 tff(2439,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2438])).
% 1.86/2.06 tff(2440,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1699, 2439])).
% 1.86/2.06 tff(2441,plain,
% 1.86/2.06 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[230])).
% 1.86/2.06 tff(2442,plain,
% 1.86/2.06 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2441])).
% 1.86/2.06 tff(2443,plain,
% 1.86/2.06 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2442])).
% 1.86/2.06 tff(2444,plain,
% 1.86/2.06 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2443])).
% 1.86/2.06 tff(2445,plain,
% 1.86/2.06 (r(s(z), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[682, 2444])).
% 1.86/2.06 tff(2446,plain,
% 1.86/2.06 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2442])).
% 1.86/2.06 tff(2447,plain,
% 1.86/2.06 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 1.86/2.06 inference(symmetry,[status(thm)],[2446])).
% 1.86/2.06 tff(2448,plain,
% 1.86/2.06 (r(s(s(s(z))), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[790, 2447])).
% 1.86/2.06 tff(2449,plain,
% 1.86/2.06 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2441])).
% 1.86/2.06 tff(2450,plain,
% 1.86/2.06 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2449])).
% 1.86/2.06 tff(2451,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2450, 2442])).
% 1.86/2.06 tff(2452,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2451])).
% 1.86/2.06 tff(2453,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1287, 2452])).
% 1.86/2.06 tff(2454,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.86/2.06 tff(2455,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2456,plain,
% 1.86/2.06 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2457,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2456])).
% 1.86/2.06 tff(2458,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(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(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2457, 2455])).
% 1.86/2.06 tff(2459,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2460,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 1.86/2.06 tff(2461,plain,
% 1.86/2.06 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2460, 163, 2454])).
% 1.86/2.06 tff(2462,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2461, 2453, 2448, 2445])).
% 1.86/2.06 tff(2463,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2464,plain,
% 1.86/2.06 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2463, 2440, 2437, 2423, 790])).
% 1.86/2.06 tff(2465,plain,
% 1.86/2.06 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1326, 2464, 1271])).
% 1.86/2.06 tff(2466,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2465, 2435])).
% 1.86/2.06 tff(2467,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2433, 2425])).
% 1.86/2.06 tff(2468,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2467])).
% 1.86/2.06 tff(2469,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1145, 2468])).
% 1.86/2.06 tff(2470,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2433])).
% 1.86/2.06 tff(2471,plain,
% 1.86/2.06 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2470])).
% 1.86/2.06 tff(2472,plain,
% 1.86/2.06 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2424])).
% 1.86/2.06 tff(2473,plain,
% 1.86/2.06 (b(s(s(z)), s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1328, 2472])).
% 1.86/2.06 tff(2474,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2473, 2471])).
% 1.86/2.06 tff(2475,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2476,plain,
% 1.86/2.06 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2477,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2476])).
% 1.86/2.06 tff(2478,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2477, 2475])).
% 1.86/2.06 tff(2479,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2480,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 1.86/2.06 tff(2481,plain,
% 1.86/2.06 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2480, 198, 2474])).
% 1.86/2.06 tff(2482,plain,
% 1.86/2.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2481, 2469, 2466])).
% 1.86/2.06 tff(2483,plain,
% 1.86/2.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2482, 2432])).
% 1.86/2.06 tff(2484,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1339, 2483, 1256])).
% 1.86/2.06 tff(2485,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2484, 2430])).
% 1.86/2.06 tff(2486,plain,
% 1.86/2.06 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2424])).
% 1.86/2.06 tff(2487,plain,
% 1.86/2.06 (r(s(s(z)), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2373, 2486])).
% 1.86/2.06 tff(2488,plain,
% 1.86/2.06 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2425])).
% 1.86/2.06 tff(2489,plain,
% 1.86/2.06 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2488])).
% 1.86/2.06 tff(2490,plain,
% 1.86/2.06 (r(s(z), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1637, 2489])).
% 1.86/2.06 tff(2491,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2492,plain,
% 1.86/2.06 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2493,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2492])).
% 1.86/2.06 tff(2494,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2493, 2491])).
% 1.86/2.06 tff(2495,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2496,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.86/2.06 tff(2497,plain,
% 1.86/2.06 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2496, 163, 2490, 2440, 2487])).
% 1.86/2.06 tff(2498,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2497, 2485])).
% 1.86/2.06 tff(2499,plain,((~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2500,plain,
% 1.86/2.06 (~r(elem!1, s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2499, 1637, 1145, 1639, 1251, 1641, 1680, 1643, 595, 791, 820, 1139, 1098])).
% 1.86/2.06 tff(2501,plain,
% 1.86/2.06 (b(elem!1, s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[147, 2500, 116])).
% 1.86/2.06 tff(2502,plain,
% 1.86/2.06 (~r(s(s(s(elem!1))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1621, 1641, 791, 1145, 1639, 1251])).
% 1.86/2.06 tff(2503,plain,
% 1.86/2.06 (b(s(s(s(elem!1))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1295, 2502])).
% 1.86/2.06 tff(2504,plain,
% 1.86/2.06 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1629, 198, 2503, 1643, 595])).
% 1.86/2.06 tff(2505,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1633, 26, 1282, 2504])).
% 1.86/2.06 tff(2506,plain,
% 1.86/2.06 (~(elem!1 = s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1400, 834])).
% 1.86/2.06 tff(2507,plain,
% 1.86/2.06 (r(elem!1, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1416, 1653, 2506])).
% 1.86/2.06 tff(2508,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2509,plain,
% 1.86/2.06 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2510,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2509])).
% 1.86/2.06 tff(2511,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2510, 2508])).
% 1.86/2.06 tff(2512,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2513,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.86/2.06 tff(2514,plain,
% 1.86/2.06 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2513, 198, 95, 1328, 68])).
% 1.86/2.06 tff(2515,plain,
% 1.86/2.06 (~b(s(elem!1), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2514, 1175])).
% 1.86/2.06 tff(2516,plain,
% 1.86/2.06 (r(s(elem!1), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[856, 2515, 834])).
% 1.86/2.06 tff(2517,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2518,plain,
% 1.86/2.06 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2519,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2518])).
% 1.86/2.06 tff(2520,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2519, 2517])).
% 1.86/2.06 tff(2521,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2522,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 1.86/2.06 tff(2523,plain,
% 1.86/2.06 ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2522, 163])).
% 1.86/2.06 tff(2524,plain,
% 1.86/2.06 (~r(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2523, 2516, 2507, 791])).
% 1.86/2.06 tff(2525,plain,
% 1.86/2.06 (b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[187, 2524, 76])).
% 1.86/2.06 tff(2526,plain,
% 1.86/2.06 (~b(s(z), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1947, 198, 95, 2525, 1185])).
% 1.86/2.06 tff(2527,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2528,plain,
% 1.86/2.06 (((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2529,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2528])).
% 1.86/2.06 tff(2530,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2529, 2527])).
% 1.86/2.06 tff(2531,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2532,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 1.86/2.07 tff(2533,plain,
% 1.86/2.07 (~r(s(z), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2532, 163, 2516, 2507, 1637])).
% 1.86/2.07 tff(2534,plain,
% 1.86/2.07 (s(z) = elem!1),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[217, 2533, 2526])).
% 1.86/2.07 tff(2535,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2534])).
% 1.86/2.07 tff(2536,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2413, 2535])).
% 1.86/2.07 tff(2537,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2538,plain,
% 1.86/2.07 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2539,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2538])).
% 1.86/2.07 tff(2540,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.86/2.07 tff(2541,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2542,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.86/2.07 tff(2543,plain,
% 1.86/2.07 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2542, 163, 2516, 2507, 2536])).
% 1.86/2.07 tff(2544,plain,
% 1.86/2.07 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1601, 2543, 1573])).
% 1.86/2.07 tff(2545,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.07 tff(2546,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2547,plain,
% 1.86/2.07 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2548,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2547])).
% 1.86/2.07 tff(2549,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.86/2.07 tff(2550,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2551,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.86/2.07 tff(2552,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2551, 198, 1175, 1311, 1576, 2545])).
% 1.86/2.07 tff(2553,plain,((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2554,plain,
% 1.86/2.07 (~b(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2553, 2544, 1697, 1175])).
% 1.86/2.07 tff(2555,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2556,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2557,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.86/2.07 tff(2558,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2557, 163, 2516, 2507, 2536])).
% 1.86/2.07 tff(2559,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1339, 2558, 1256])).
% 1.86/2.07 tff(2560,plain,
% 1.86/2.07 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1726, 198, 1175, 1145, 1697])).
% 1.86/2.07 tff(2561,plain,
% 1.86/2.07 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2560, 2559])).
% 1.86/2.07 tff(2562,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1326, 2561, 1271])).
% 1.86/2.07 tff(2563,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2564,plain,
% 1.86/2.07 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2565,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2564])).
% 1.86/2.07 tff(2566,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.86/2.07 tff(2567,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2568,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.86/2.07 tff(2569,plain,
% 1.86/2.07 (~r(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2568, 163, 790, 1098, 2562])).
% 1.86/2.07 tff(2570,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1350, 26, 2569, 2554, 1255])).
% 1.86/2.07 tff(2571,plain,((~b(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = z) | (~r(z, s(elem!1))) | (s(elem!1) = elem!1) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2572,plain,
% 1.86/2.07 (~b(s(elem!1), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2571, 1637, 1098, 1145, 1251, 2505, 1639, 1680, 1643, 1647, 791, 1396, 1641, 2501])).
% 1.86/2.07 tff(2573,plain,
% 1.86/2.07 (r(s(elem!1), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1217, 2572])).
% 1.86/2.07 tff(2574,plain,
% 1.86/2.07 (~b(elem!1, s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1426, 2501, 1145, 1641])).
% 1.86/2.07 tff(2575,plain,
% 1.86/2.07 (r(elem!1, s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1416, 2574, 1401])).
% 1.86/2.07 tff(2576,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2577,plain,
% 1.86/2.07 (((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2578,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2577])).
% 1.86/2.07 tff(2579,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2578, 2576])).
% 1.86/2.07 tff(2580,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2581,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.86/2.07 tff(2582,plain,
% 1.86/2.07 (~r(elem!1, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2581, 163, 2575, 2573, 1637])).
% 1.86/2.07 tff(2583,plain,
% 1.86/2.07 (((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2584,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2583])).
% 1.86/2.07 tff(2585,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2584, 1402])).
% 1.86/2.07 tff(2586,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2587,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2586, 2585])).
% 1.86/2.07 tff(2588,plain,
% 1.86/2.07 (~r(elem!1, z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2587, 163, 791, 2575, 2573])).
% 1.86/2.07 tff(2589,plain,
% 1.86/2.07 (b(elem!1, z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[187, 2588, 1647])).
% 1.86/2.07 tff(2590,plain,
% 1.86/2.07 (~b(elem!1, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1694, 198, 1680, 2589, 1643, 595])).
% 1.86/2.07 tff(2591,plain,
% 1.86/2.07 (elem!1 = s(z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[242, 2590, 2582])).
% 1.86/2.07 tff(2592,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.86/2.07 tff(2593,plain,
% 1.86/2.07 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2592])).
% 1.86/2.07 tff(2594,plain,
% 1.86/2.07 (s(s(s(elem!1))) = s(z)),
% 1.86/2.07 inference(transitivity,[status(thm)],[2449, 289, 2593, 222])).
% 1.86/2.07 tff(2595,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1282, 2594])).
% 1.86/2.07 tff(2596,plain,((~(s(s(s(s(s(z))))) = s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2597,plain,
% 1.86/2.07 (~(s(s(s(s(s(z))))) = s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2596, 2591])).
% 1.86/2.07 tff(2598,plain,
% 1.86/2.07 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2597, 1636])).
% 1.86/2.07 tff(2599,plain,
% 1.86/2.07 (s(z) = elem!1),
% 1.86/2.07 inference(symmetry,[status(thm)],[2591])).
% 1.86/2.07 tff(2600,plain,
% 1.86/2.07 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2599])).
% 1.86/2.07 tff(2601,plain,
% 1.86/2.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2600])).
% 1.86/2.07 tff(2602,plain,
% 1.86/2.07 (s(elem!1) = s(s(z))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2591])).
% 1.86/2.07 tff(2603,plain,
% 1.86/2.07 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2602])).
% 1.86/2.07 tff(2604,plain,
% 1.86/2.07 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2603])).
% 1.86/2.07 tff(2605,plain,
% 1.86/2.07 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2604, 2591])).
% 1.86/2.07 tff(2606,plain,
% 1.86/2.07 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.07 inference(symmetry,[status(thm)],[2605])).
% 1.86/2.07 tff(2607,plain,
% 1.86/2.07 (b(s(s(s(z))), elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[722, 2606])).
% 1.86/2.07 tff(2608,plain,
% 1.86/2.07 (b(s(s(s(z))), s(z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2607, 2601])).
% 1.86/2.07 tff(2609,plain,
% 1.86/2.07 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2604])).
% 1.86/2.07 tff(2610,plain,
% 1.86/2.07 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2609])).
% 1.86/2.07 tff(2611,plain,
% 1.86/2.07 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2591])).
% 1.86/2.07 tff(2612,plain,
% 1.86/2.07 (b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2501, 2611])).
% 1.86/2.07 tff(2613,plain,
% 1.86/2.07 (b(s(z), s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2612, 2610])).
% 1.86/2.07 tff(2614,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.07 tff(2615,plain,
% 1.86/2.07 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2614])).
% 1.86/2.07 tff(2616,plain,
% 1.86/2.07 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2615])).
% 1.86/2.07 tff(2617,plain,
% 1.86/2.07 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.07 inference(transitivity,[status(thm)],[965, 2616, 134])).
% 1.86/2.07 tff(2618,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1256, 2617])).
% 1.86/2.07 tff(2619,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2620,plain,
% 1.86/2.07 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2619, 1251])).
% 1.86/2.07 tff(2621,plain,
% 1.86/2.07 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(commutativity,[status(thm)],[])).
% 1.86/2.07 tff(2622,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.86/2.07 tff(2623,plain,
% 1.86/2.07 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.86/2.07 tff(2624,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.86/2.07 tff(2625,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2624, 2623])).
% 1.86/2.07 tff(2626,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,[]))).
% 1.86/2.07 tff(2627,plain,
% 1.86/2.07 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2626, 2620])).
% 1.86/2.07 tff(2628,plain,
% 1.86/2.07 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2604])).
% 1.86/2.07 tff(2629,plain,
% 1.86/2.07 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 1.86/2.07 inference(symmetry,[status(thm)],[2628])).
% 1.86/2.07 tff(2630,plain,
% 1.86/2.07 (r(s(s(s(z))), z)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1639, 2629])).
% 1.86/2.07 tff(2631,plain,
% 1.86/2.07 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2604])).
% 1.86/2.07 tff(2632,plain,
% 1.86/2.07 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2631])).
% 1.86/2.07 tff(2633,plain,
% 1.86/2.07 (r(z, s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1098, 2632])).
% 1.86/2.07 tff(2634,plain,
% 1.86/2.07 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2449])).
% 1.86/2.07 tff(2635,plain,
% 1.86/2.07 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2634])).
% 1.86/2.07 tff(2636,plain,
% 1.86/2.07 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2635, 2442])).
% 1.86/2.07 tff(2637,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2636])).
% 1.86/2.07 tff(2638,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.86/2.07 tff(2639,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2635, 2442])).
% 1.86/2.07 tff(2640,plain,
% 1.86/2.07 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2639])).
% 1.86/2.07 tff(2641,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.86/2.07 tff(2642,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.86/2.07 tff(2643,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2644,plain,
% 1.86/2.07 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2645,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2644])).
% 1.86/2.07 tff(2646,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[2645, 2643])).
% 1.86/2.08 tff(2647,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2648,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.86/2.08 tff(2649,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2648, 198, 1185, 595, 559, 2642, 2641])).
% 1.86/2.08 tff(2650,plain,
% 1.86/2.08 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2649, 2640])).
% 1.86/2.08 tff(2651,plain,
% 1.86/2.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2652,plain,
% 1.86/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2653,plain,
% 1.86/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 1.86/2.08 tff(2654,plain,
% 1.86/2.08 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2653, 26])).
% 1.86/2.08 tff(2655,plain,
% 1.86/2.08 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2654, 2650, 2638])).
% 1.86/2.08 tff(2656,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2655, 2637])).
% 1.86/2.08 tff(2657,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2658,plain,
% 1.86/2.08 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2659,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2658])).
% 1.86/2.08 tff(2660,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[2659, 2657])).
% 1.86/2.08 tff(2661,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2662,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 1.86/2.08 tff(2663,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2662, 198, 1185, 595, 559])).
% 1.86/2.08 tff(2664,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[434, 26, 366, 2663])).
% 1.86/2.08 tff(2665,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.86/2.08 tff(2666,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.86/2.08 tff(2667,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2668,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2669,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.86/2.08 tff(2670,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2669, 163, 2666, 2665, 2664])).
% 1.86/2.08 tff(2671,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2670, 2656])).
% 1.86/2.08 tff(2672,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(2673,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2672, 2591, 2633, 2630, 2627, 1643, 595, 2613, 2608])).
% 1.86/2.08 tff(2674,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[468, 2673, 464])).
% 1.86/2.08 tff(2675,plain,
% 1.86/2.08 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2591])).
% 1.86/2.08 tff(2676,plain,
% 1.86/2.08 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[229])).
% 1.86/2.08 tff(2677,plain,
% 1.86/2.08 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[2676])).
% 1.86/2.08 tff(2678,plain,
% 1.86/2.08 (b(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[722, 2677])).
% 1.86/2.08 tff(2679,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[597, 2678])).
% 1.86/2.08 tff(2680,plain,((~(elem!1 = s(z))) | b(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(2681,plain,
% 1.86/2.08 (b(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2680, 2591, 722])).
% 1.86/2.08 tff(2682,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.86/2.08 tff(2683,plain,
% 1.86/2.08 (~b(s(s(z)), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2146, 198, 95, 271, 2682])).
% 1.86/2.08 tff(2684,plain,
% 1.86/2.08 (r(s(s(z)), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[344, 26, 46, 2683])).
% 1.86/2.08 tff(2685,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2686,plain,
% 1.86/2.08 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2687,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2686])).
% 1.86/2.08 tff(2688,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[2687, 2685])).
% 1.86/2.08 tff(2689,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2690,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.86/2.08 tff(2691,plain,
% 1.86/2.08 (~b(s(s(z)), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2690, 198, 95, 271, 1128, 68, 2682])).
% 1.86/2.08 tff(2692,plain,
% 1.86/2.08 (r(s(s(z)), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2161, 26, 2154, 2691])).
% 1.86/2.08 tff(2693,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2157, 163, 791, 790, 2692, 2684])).
% 1.86/2.08 tff(2694,plain,((~b(s(s(z)), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(z)) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(2695,plain,
% 1.86/2.08 (~b(s(s(z)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2694, 2681, 1639, 2106, 2501, 2589, 1680, 791])).
% 1.86/2.08 tff(2696,plain,
% 1.86/2.08 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2591])).
% 1.86/2.08 tff(2697,plain,
% 1.86/2.08 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[2696])).
% 1.86/2.08 tff(2698,plain,
% 1.86/2.08 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2697])).
% 1.86/2.08 tff(2699,plain,
% 1.86/2.08 (~(s(s(z)) = elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[395, 2698])).
% 1.86/2.08 tff(2700,plain,
% 1.86/2.08 (r(s(s(z)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2139, 2699, 2695])).
% 1.86/2.08 tff(2701,plain,
% 1.86/2.08 (r(s(s(z)), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2700, 2675])).
% 1.86/2.08 tff(2702,plain,
% 1.86/2.08 (s(s(z)) = s(elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[2602])).
% 1.86/2.08 tff(2703,plain,
% 1.86/2.08 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2702])).
% 1.86/2.08 tff(2704,plain,
% 1.86/2.08 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2703])).
% 1.86/2.08 tff(2705,plain,
% 1.86/2.08 (r(s(z), s(s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[1637, 2704])).
% 1.86/2.08 tff(2706,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2707,plain,
% 1.86/2.08 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2708,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2707])).
% 1.86/2.08 tff(2709,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.86/2.08 tff(2710,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2711,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.86/2.08 tff(2712,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2711, 163, 2705, 2701, 2674])).
% 1.86/2.08 tff(2713,plain,
% 1.86/2.08 (((~![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)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2714,plain,
% 1.86/2.08 ((~![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)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2715,plain,
% 1.86/2.08 ((~![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))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.86/2.08 tff(2716,plain,
% 1.86/2.08 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2715, 26, 2712])).
% 1.86/2.08 tff(2717,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2716, 2598])).
% 1.86/2.08 tff(2718,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2719,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2720,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 1.86/2.08 tff(2721,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2720, 163, 2705, 2701, 2674])).
% 1.86/2.08 tff(2722,plain,
% 1.86/2.08 ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[511, 26, 2721])).
% 1.86/2.08 tff(2723,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2722, 2597])).
% 1.86/2.08 tff(2724,plain,
% 1.86/2.08 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2603])).
% 1.86/2.08 tff(2725,plain,
% 1.86/2.08 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2724])).
% 1.86/2.08 tff(2726,plain,
% 1.86/2.08 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2725])).
% 1.86/2.08 tff(2727,plain,
% 1.86/2.08 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2724])).
% 1.86/2.08 tff(2728,plain,
% 1.86/2.08 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2727, 2726])).
% 1.86/2.08 tff(2729,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2728])).
% 1.86/2.08 tff(2730,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2729])).
% 1.86/2.08 tff(2731,plain,
% 1.86/2.08 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1263, 1251])).
% 1.86/2.08 tff(2732,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.08 tff(2733,plain,
% 1.86/2.08 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2732])).
% 1.86/2.08 tff(2734,plain,
% 1.86/2.08 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[1247, 2733, 964])).
% 1.86/2.08 tff(2735,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1268, 2734])).
% 1.86/2.08 tff(2736,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(2737,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2736, 2731])).
% 1.86/2.08 tff(2738,plain,
% 1.86/2.08 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2737, 2730])).
% 1.86/2.08 tff(2739,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2727])).
% 1.86/2.08 tff(2740,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2739])).
% 1.86/2.08 tff(2741,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2505, 2740])).
% 1.86/2.08 tff(2742,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2743,plain,
% 1.86/2.08 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2744,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2743])).
% 1.86/2.08 tff(2745,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.86/2.08 tff(2746,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2747,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.86/2.08 tff(2748,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2747, 163, 2705, 2741, 2674])).
% 1.86/2.08 tff(2749,plain,
% 1.86/2.08 (((~![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)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(2750,plain,
% 1.86/2.08 ((~![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)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(2751,plain,
% 1.86/2.08 ((~![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))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2750, 2749])).
% 1.86/2.08 tff(2752,plain,
% 1.86/2.08 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2751, 26, 2748])).
% 1.86/2.08 tff(2753,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2752, 2738])).
% 1.86/2.08 tff(2754,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2727, 2702])).
% 1.86/2.08 tff(2755,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.08 inference(symmetry,[status(thm)],[2754])).
% 1.86/2.08 tff(2756,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2727, 2702])).
% 1.86/2.08 tff(2757,plain,
% 1.86/2.08 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2756])).
% 1.86/2.08 tff(2758,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2759,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2760,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.86/2.09 tff(2761,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2760, 163, 2705, 2741, 2701])).
% 1.86/2.09 tff(2762,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2761, 2757])).
% 1.86/2.09 tff(2763,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1339, 2762, 1251])).
% 1.86/2.09 tff(2764,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2763, 2755])).
% 1.86/2.09 tff(2765,plain,
% 1.86/2.09 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2702, 2727])).
% 1.86/2.09 tff(2766,plain,
% 1.86/2.09 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[2765])).
% 1.86/2.09 tff(2767,plain,
% 1.86/2.09 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1572, 1251])).
% 1.86/2.09 tff(2768,plain,
% 1.86/2.09 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2702, 2727])).
% 1.86/2.09 tff(2769,plain,
% 1.86/2.09 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2768])).
% 1.86/2.09 tff(2770,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2771,plain,
% 1.86/2.09 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2772,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2771])).
% 1.86/2.09 tff(2773,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.86/2.09 tff(2774,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2775,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.86/2.09 tff(2776,plain,
% 1.86/2.09 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2775, 163, 2705, 2741, 2701])).
% 1.86/2.09 tff(2777,plain,
% 1.86/2.09 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2776, 2769])).
% 1.86/2.09 tff(2778,plain,
% 1.86/2.09 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1601, 2777, 2767])).
% 1.86/2.09 tff(2779,plain,
% 1.86/2.09 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2778, 2766])).
% 1.86/2.09 tff(2780,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2781,plain,
% 1.86/2.09 (((~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(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2782,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2781])).
% 1.86/2.09 tff(2783,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2782, 2780])).
% 1.86/2.09 tff(2784,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2785,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2784, 2783])).
% 1.86/2.09 tff(2786,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2785, 198, 2779, 2764, 2753, 2723, 2717])).
% 1.86/2.09 tff(2787,plain,((~r(s(z), s(elem!1))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2788,plain,
% 1.86/2.09 (~r(s(z), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2787, 1144, 1098, 722, 791, 595, 116, 820])).
% 1.86/2.09 tff(2789,plain,
% 1.86/2.09 (r(s(elem!1), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1173, 2788, 820, 722, 1144])).
% 1.86/2.09 tff(2790,plain,
% 1.86/2.09 (b(s(z), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1164, 2788, 1157])).
% 1.86/2.09 tff(2791,plain,
% 1.86/2.09 (~b(s(z), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1552, 2790, 1532, 1144])).
% 1.86/2.09 tff(2792,plain,
% 1.86/2.09 (r(s(z), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[642, 2791])).
% 1.86/2.09 tff(2793,plain,
% 1.86/2.09 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1270, 2731])).
% 1.86/2.09 tff(2794,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2795,plain,
% 1.86/2.09 (((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2796,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2795])).
% 1.86/2.09 tff(2797,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2796, 2794])).
% 1.86/2.09 tff(2798,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2799,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.86/2.09 tff(2800,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2799, 163, 790, 1287, 682, 2413])).
% 1.86/2.09 tff(2801,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2802,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2801, 1522, 2792, 1634])).
% 1.86/2.09 tff(2803,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1326, 2802, 2793])).
% 1.86/2.09 tff(2804,plain,
% 1.86/2.09 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1334, 198, 1144, 1532, 2803])).
% 1.86/2.09 tff(2805,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1339, 2804, 1251])).
% 1.86/2.09 tff(2806,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2807,plain,
% 1.86/2.09 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2808,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2807])).
% 1.86/2.09 tff(2809,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.86/2.09 tff(2810,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2811,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.86/2.09 tff(2812,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2811, 163, 2805, 2792, 2789, 1634])).
% 1.86/2.09 tff(2813,plain,((elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~b(z, s(z))) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2814,plain,
% 1.86/2.09 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2813, 1132, 1098, 842, 1114, 1103, 1109])).
% 1.86/2.09 tff(2815,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2816,plain,
% 1.86/2.09 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, 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)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2817,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2816])).
% 1.86/2.09 tff(2818,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.86/2.09 tff(2819,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2820,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.86/2.09 tff(2821,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2820, 163, 995, 2814, 1098, 1104])).
% 1.86/2.09 tff(2822,plain,((~(s(z) = elem!1)) | (~r(z, s(s(elem!1)))) | b(elem!1, s(s(elem!1))) | (~r(z, s(s(z)))) | r(z, elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2823,plain,
% 1.86/2.09 (b(elem!1, s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2822, 206, 1098, 55, 56, 150])).
% 1.86/2.09 tff(2824,plain,
% 1.86/2.09 (~(z = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[71, 2823, 42])).
% 1.86/2.09 tff(2825,plain,
% 1.86/2.09 (b(z, elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[102, 2824, 56])).
% 1.86/2.09 tff(2826,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2825, 1100])).
% 1.86/2.09 tff(2827,plain,
% 1.86/2.09 (~(s(elem!1) = s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[814, 2824])).
% 1.86/2.09 tff(2828,plain,
% 1.86/2.09 (r(z, s(elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[55, 841])).
% 1.86/2.09 tff(2829,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.86/2.09 inference(symmetry,[status(thm)],[984])).
% 1.86/2.09 tff(2830,plain,
% 1.86/2.09 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2829])).
% 1.86/2.09 tff(2831,plain,
% 1.86/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[244, 2830])).
% 1.86/2.09 tff(2832,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2, 2831])).
% 1.86/2.09 tff(2833,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2834,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2833, 206, 2])).
% 1.86/2.09 tff(2835,plain,
% 1.86/2.09 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[206])).
% 1.86/2.09 tff(2836,plain,
% 1.86/2.09 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[151, 2835])).
% 1.86/2.09 tff(2837,plain,
% 1.86/2.09 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(commutativity,[status(thm)],[])).
% 1.86/2.09 tff(2838,plain,
% 1.86/2.09 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.86/2.09 inference(symmetry,[status(thm)],[2837])).
% 1.86/2.09 tff(2839,plain,
% 1.86/2.09 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2838])).
% 1.86/2.09 tff(2840,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.09 tff(2841,plain,
% 1.86/2.09 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.86/2.09 inference(symmetry,[status(thm)],[2840])).
% 1.86/2.09 tff(2842,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2841])).
% 1.86/2.09 tff(2843,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2842, 1127])).
% 1.86/2.09 tff(2844,plain,
% 1.86/2.09 (b(s(s(elem!1)), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[831, 2843])).
% 1.86/2.09 tff(2845,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[621, 2844])).
% 1.86/2.09 tff(2846,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2847,plain,
% 1.86/2.09 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2846, 621, 831, 206])).
% 1.86/2.09 tff(2848,plain,
% 1.86/2.09 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2847, 2839])).
% 1.86/2.09 tff(2849,plain,
% 1.86/2.09 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1131, 621, 206])).
% 1.86/2.09 tff(2850,plain,
% 1.86/2.09 (r(s(s(elem!1)), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[602, 2849, 138])).
% 1.86/2.09 tff(2851,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2852,plain,
% 1.86/2.09 (((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2853,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2852])).
% 1.86/2.09 tff(2854,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2853, 2851])).
% 1.86/2.09 tff(2855,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2856,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 1.86/2.09 tff(2857,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2856, 163, 833, 1115, 791, 790])).
% 1.86/2.09 tff(2858,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(2859,plain,
% 1.86/2.09 (~r(s(s(elem!1)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2858, 2850, 833, 791])).
% 1.86/2.09 tff(2860,plain,
% 1.86/2.09 (b(s(s(elem!1)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[801, 2859])).
% 1.86/2.09 tff(2861,plain,
% 1.86/2.09 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[926, 198, 95, 2860, 831, 330])).
% 1.86/2.09 tff(2862,plain,
% 1.86/2.09 ((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)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[941, 26, 2861])).
% 1.86/2.09 tff(2863,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2862, 2848])).
% 1.86/2.09 tff(2864,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2865,plain,
% 1.86/2.09 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(2866,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[2865])).
% 1.86/2.09 tff(2867,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[2866, 2864])).
% 1.86/2.09 tff(2868,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(2869,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[2868, 2867])).
% 1.86/2.09 tff(2870,plain,
% 1.86/2.09 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2869, 163, 2850, 1098, 2863])).
% 1.86/2.09 tff(2871,plain,
% 1.86/2.09 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[31, 2870])).
% 1.86/2.09 tff(2872,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2873,plain,
% 1.86/2.10 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2874,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2873])).
% 1.86/2.10 tff(2875,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[2874, 2872])).
% 1.86/2.10 tff(2876,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(2877,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 1.86/2.10 tff(2878,plain,
% 1.86/2.10 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2877, 198, 2860, 2871, 330])).
% 1.86/2.10 tff(2879,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[934, 26, 2878, 2847])).
% 1.86/2.10 tff(2880,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2881,plain,
% 1.86/2.10 (((~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(s(s(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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2882,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2881])).
% 1.86/2.10 tff(2883,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[2882, 2880])).
% 1.86/2.10 tff(2884,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(2885,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 1.86/2.10 tff(2886,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2885, 163, 2850, 694, 2879, 2863])).
% 1.86/2.10 tff(2887,plain,(b(s(s(elem!1)), s(z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2888,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2887, 2836, 177, 1098, 2825, 2834, 995, 2828, 598, 206])).
% 1.86/2.10 tff(2889,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2813, 2888, 1098, 2828, 2827, 116, 2826])).
% 1.86/2.10 tff(2890,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[825])).
% 1.86/2.10 tff(2891,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(z)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2890])).
% 1.86/2.10 tff(2892,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2889, 2891])).
% 1.86/2.10 tff(2893,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.86/2.10 tff(2894,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.10 tff(2895,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(elem!1)), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2896,plain,
% 1.86/2.10 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(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(s(s(elem!1)), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2897,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(elem!1)), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2896])).
% 1.86/2.10 tff(2898,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(elem!1)), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[2897, 2895])).
% 1.86/2.10 tff(2899,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(2900,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 1.86/2.10 tff(2901,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2900, 163, 1098, 2894, 153, 2893])).
% 1.86/2.10 tff(2902,plain,((~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2903,plain,
% 1.86/2.10 (~r(s(s(z)), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2902, 2892, 55, 1098])).
% 1.86/2.10 tff(2904,plain,
% 1.86/2.10 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[825])).
% 1.86/2.10 tff(2905,plain,
% 1.86/2.10 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2904])).
% 1.86/2.10 tff(2906,plain,
% 1.86/2.10 (r(s(s(z)), s(s(elem!1)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[1220, 2905])).
% 1.86/2.10 tff(2907,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.10 tff(2908,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2907, 2906])).
% 1.86/2.10 tff(2909,plain,((~r(s(elem!1), s(s(elem!1)))) | r(s(s(z)), s(s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2910,plain,
% 1.86/2.10 (~r(s(elem!1), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2909, 2903, 206])).
% 1.86/2.10 tff(2911,plain,
% 1.86/2.10 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[901, 2910, 1134])).
% 1.86/2.10 tff(2912,plain,
% 1.86/2.10 (elem!1 = s(z)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[206, 1241])).
% 1.86/2.10 tff(2913,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[237, 2912])).
% 1.86/2.10 tff(2914,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2915,plain,
% 1.86/2.10 (elem!1 = s(z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2914, 206])).
% 1.86/2.10 tff(2916,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2680, 2888, 2915])).
% 1.86/2.10 tff(2917,plain,
% 1.86/2.10 (~b(s(elem!1), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1470, 198, 2916, 2911, 2823])).
% 1.86/2.10 tff(2918,plain,
% 1.86/2.10 (r(s(elem!1), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[856, 2917, 1396])).
% 1.86/2.10 tff(2919,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2920,plain,
% 1.86/2.10 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2921,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2920])).
% 1.86/2.10 tff(2922,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[2921, 2919])).
% 1.86/2.10 tff(2923,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(2924,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 1.86/2.10 tff(2925,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2924, 163, 2918, 2828, 2889, 1098])).
% 1.86/2.10 tff(2926,plain,((~(s(z) = elem!1)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, elem!1) | b(z, s(s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2927,plain,
% 1.86/2.10 (~(s(z) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2926, 1097, 1086, 151, 56, 42, 150, 2])).
% 1.86/2.10 tff(2928,plain,
% 1.86/2.10 (~(s(s(z)) = s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[227, 2927])).
% 1.86/2.10 tff(2929,plain,
% 1.86/2.10 (~(elem!1 = s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[234, 2928])).
% 1.86/2.10 tff(2930,plain,
% 1.86/2.10 (r(s(z), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[217, 2927, 149])).
% 1.86/2.10 tff(2931,plain,
% 1.86/2.10 (~r(elem!1, z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1026, 2930, 150, 55])).
% 1.86/2.10 tff(2932,plain,
% 1.86/2.10 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(commutativity,[status(thm)],[])).
% 1.86/2.10 tff(2933,plain,
% 1.86/2.10 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2932])).
% 1.86/2.10 tff(2934,plain,
% 1.86/2.10 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2933])).
% 1.86/2.10 tff(2935,plain,
% 1.86/2.10 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[314, 2934])).
% 1.86/2.10 tff(2936,plain,
% 1.86/2.10 (s(elem!1) = s(z)),
% 1.86/2.10 inference(symmetry,[status(thm)],[58])).
% 1.86/2.10 tff(2937,plain,
% 1.86/2.10 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2936])).
% 1.86/2.10 tff(2938,plain,
% 1.86/2.10 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2937])).
% 1.86/2.10 tff(2939,plain,
% 1.86/2.10 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[151, 2938])).
% 1.86/2.10 tff(2940,assumption,(~r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.86/2.10 tff(2941,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2940, 2939])).
% 1.86/2.10 tff(2942,plain,(r(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2943,plain,
% 1.86/2.10 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2942, 57, 151])).
% 1.86/2.10 tff(2944,plain,
% 1.86/2.10 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.10 tff(2945,plain,
% 1.86/2.10 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.10 tff(2946,plain,
% 1.86/2.10 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.86/2.10 inference(symmetry,[status(thm)],[2945])).
% 1.86/2.10 tff(2947,plain,
% 1.86/2.10 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[59])).
% 1.86/2.10 tff(2948,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.86/2.10 inference(symmetry,[status(thm)],[2947])).
% 1.86/2.10 tff(2949,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.86/2.10 inference(transitivity,[status(thm)],[2948, 2946])).
% 1.86/2.10 tff(2950,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1032, 79, 330])).
% 1.86/2.10 tff(2951,plain,
% 1.86/2.10 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[58])).
% 1.86/2.10 tff(2952,plain,
% 1.86/2.10 (r(s(elem!1), elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[236, 2951])).
% 1.86/2.10 tff(2953,plain,
% 1.86/2.10 (r(elem!1, s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[147, 72, 116])).
% 1.86/2.10 tff(2954,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[58])).
% 1.86/2.10 tff(2955,plain,
% 1.86/2.10 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.10 tff(2956,plain,
% 1.86/2.10 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.86/2.10 inference(symmetry,[status(thm)],[2955])).
% 1.86/2.10 tff(2957,plain,
% 1.86/2.10 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 1.86/2.10 inference(transitivity,[status(thm)],[2951, 2956])).
% 1.86/2.10 tff(2958,plain,
% 1.86/2.10 (r(s(elem!1), z)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[236, 2957])).
% 1.86/2.10 tff(2959,plain,
% 1.86/2.10 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[59])).
% 1.86/2.10 tff(2960,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[60])).
% 1.86/2.10 tff(2961,plain,
% 1.86/2.10 ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2960])).
% 1.86/2.10 tff(2962,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2936])).
% 1.86/2.10 tff(2963,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2962])).
% 1.86/2.10 tff(2964,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[2, 2963])).
% 1.86/2.10 tff(2965,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[626, 621])).
% 1.86/2.10 tff(2966,plain,
% 1.86/2.10 (~r(s(elem!1), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1229, 2965, 1098, 1221])).
% 1.86/2.10 tff(2967,plain,
% 1.86/2.10 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[901, 2966, 890])).
% 1.86/2.10 tff(2968,plain,
% 1.86/2.10 (~(s(s(elem!1)) = s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1138, 890])).
% 1.86/2.10 tff(2969,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(symmetry,[status(thm)],[2954])).
% 1.86/2.10 tff(2970,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[1145, 2969])).
% 1.86/2.10 tff(2971,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[621, 2970])).
% 1.86/2.10 tff(2972,plain,((~b(s(s(elem!1)), s(elem!1))) | b(s(s(elem!1)), s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2973,plain,
% 1.86/2.10 (~b(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2972, 621, 57])).
% 1.86/2.10 tff(2974,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1143, 2973, 2968])).
% 1.86/2.10 tff(2975,plain,
% 1.86/2.10 (~r(s(s(elem!1)), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2031, 2974, 1098, 1221])).
% 1.86/2.10 tff(2976,plain,
% 1.86/2.10 (b(s(s(elem!1)), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[801, 2975])).
% 1.86/2.10 tff(2977,plain,
% 1.86/2.10 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.10 tff(2978,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.86/2.10 inference(symmetry,[status(thm)],[2977])).
% 1.86/2.10 tff(2979,plain,
% 1.86/2.10 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2978])).
% 1.86/2.10 tff(2980,plain,
% 1.86/2.10 (~b(s(s(elem!1)), z)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[597, 2979])).
% 1.86/2.10 tff(2981,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[723, 2980])).
% 1.86/2.10 tff(2982,plain,((~(z = elem!1)) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(2983,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2982, 2976, 57])).
% 1.86/2.10 tff(2984,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2985,plain,
% 1.86/2.10 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(2986,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[2985])).
% 1.86/2.10 tff(2987,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[2986, 2984])).
% 1.86/2.10 tff(2988,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(2989,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 1.86/2.11 tff(2990,plain,
% 1.86/2.11 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2989, 198, 2983, 2967, 2950])).
% 1.86/2.11 tff(2991,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2990, 2964])).
% 1.86/2.11 tff(2992,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2991, 2961])).
% 1.86/2.11 tff(2993,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[420, 2992])).
% 1.86/2.11 tff(2994,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2993, 2959])).
% 1.86/2.11 tff(2995,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[59])).
% 1.86/2.11 tff(2996,plain,
% 1.86/2.11 (b(s(s(z)), z)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2983, 2949])).
% 1.86/2.11 tff(2997,plain,
% 1.86/2.11 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.11 tff(2998,plain,
% 1.86/2.11 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(symmetry,[status(thm)],[2997])).
% 1.86/2.11 tff(2999,plain,
% 1.86/2.11 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.11 tff(3000,plain,
% 1.86/2.11 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[2999, 663])).
% 1.86/2.11 tff(3001,plain,
% 1.86/2.11 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3000])).
% 1.86/2.11 tff(3002,plain,
% 1.86/2.11 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[15, 3001])).
% 1.86/2.11 tff(3003,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3004,plain,
% 1.86/2.11 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, 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(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3005,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3004])).
% 1.86/2.11 tff(3006,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3005, 3003])).
% 1.86/2.11 tff(3007,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3008,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.86/2.11 tff(3009,plain,
% 1.86/2.11 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3008, 163, 2974, 405, 2994])).
% 1.86/2.11 tff(3010,plain,
% 1.86/2.11 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[703, 3009, 3002])).
% 1.86/2.11 tff(3011,plain,
% 1.86/2.11 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3010, 2998])).
% 1.86/2.11 tff(3012,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[356, 3011, 2996, 330])).
% 1.86/2.11 tff(3013,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[374, 3012])).
% 1.86/2.11 tff(3014,plain,
% 1.86/2.11 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3013, 2995])).
% 1.86/2.11 tff(3015,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3016,plain,
% 1.86/2.11 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3017,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3016])).
% 1.86/2.11 tff(3018,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3017, 3015])).
% 1.86/2.11 tff(3019,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3020,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.86/2.11 tff(3021,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3020, 163, 2974, 3014, 2994, 2939])).
% 1.86/2.11 tff(3022,plain,(b(s(s(elem!1)), s(z)) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3023,plain,
% 1.86/2.11 (b(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3022, 57, 330, 2953, 151, 2, 1098, 2958, 1134])).
% 1.86/2.11 tff(3024,plain,
% 1.86/2.11 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3023, 2954])).
% 1.86/2.11 tff(3025,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(z))),
% 1.86/2.11 inference(symmetry,[status(thm)],[59])).
% 1.86/2.11 tff(3026,plain,
% 1.86/2.11 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3025])).
% 1.86/2.11 tff(3027,plain,
% 1.86/2.11 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.86/2.11 inference(symmetry,[status(thm)],[3026])).
% 1.86/2.11 tff(3028,plain,
% 1.86/2.11 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3027])).
% 1.86/2.11 tff(3029,plain,
% 1.86/2.11 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[508, 3028])).
% 1.86/2.11 tff(3030,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[2936])).
% 1.86/2.11 tff(3031,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.11 inference(symmetry,[status(thm)],[3030])).
% 1.86/2.11 tff(3032,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[58])).
% 1.86/2.11 tff(3033,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(symmetry,[status(thm)],[3032])).
% 1.86/2.11 tff(3034,plain,
% 1.86/2.11 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3033])).
% 1.86/2.11 tff(3035,plain,
% 1.86/2.11 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.11 tff(3036,plain,
% 1.86/2.11 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3035])).
% 1.86/2.11 tff(3037,plain,
% 1.86/2.11 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[366, 3036])).
% 1.86/2.11 tff(3038,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3039,plain,
% 1.86/2.11 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3040,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3039])).
% 1.86/2.11 tff(3041,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3040, 3038])).
% 1.86/2.11 tff(3042,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3043,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 1.86/2.11 tff(3044,plain,
% 1.86/2.11 (~r(s(elem!1), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3043, 163, 1115, 1474, 405])).
% 1.86/2.11 tff(3045,plain,
% 1.86/2.11 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[901, 3044, 890])).
% 1.86/2.11 tff(3046,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3047,plain,
% 1.86/2.11 (((~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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3048,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3047])).
% 1.86/2.11 tff(3049,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3048, 3046])).
% 1.86/2.11 tff(3050,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3051,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 1.86/2.11 tff(3052,plain,
% 1.86/2.11 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3051, 198, 1145, 3045])).
% 1.86/2.11 tff(3053,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3052, 2964])).
% 1.86/2.11 tff(3054,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3053, 2961])).
% 1.86/2.11 tff(3055,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[420, 3054])).
% 1.86/2.11 tff(3056,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3055, 2959])).
% 1.86/2.11 tff(3057,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3058,plain,
% 1.86/2.11 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, 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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3059,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3058])).
% 1.86/2.11 tff(3060,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.86/2.11 tff(3061,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3062,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.86/2.11 tff(3063,plain,
% 1.86/2.11 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3062, 163, 1115, 405, 3056])).
% 1.86/2.11 tff(3064,plain,
% 1.86/2.11 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[703, 3063, 3002])).
% 1.86/2.11 tff(3065,assumption,(r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.86/2.11 tff(3066,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.86/2.11 tff(3067,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3068,plain,
% 1.86/2.11 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3069,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3068])).
% 1.86/2.11 tff(3070,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3069, 3067])).
% 1.86/2.11 tff(3071,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3072,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 1.86/2.11 tff(3073,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3072, 163, 3066, 680, 3065])).
% 1.86/2.11 tff(3074,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3073, 3034])).
% 1.86/2.11 tff(3075,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[469, 3074])).
% 1.86/2.11 tff(3076,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3075, 3031])).
% 1.86/2.11 tff(3077,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3078,plain,
% 1.86/2.11 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3079,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3078])).
% 1.86/2.12 tff(3080,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3079, 3077])).
% 1.86/2.12 tff(3081,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3082,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.86/2.12 tff(3083,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3082, 198, 1145, 1328, 3076])).
% 1.86/2.12 tff(3084,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3085,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3086,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.86/2.12 tff(3087,plain,
% 1.86/2.12 ((s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3086, 26, 3083])).
% 1.86/2.12 tff(3088,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3087, 3029])).
% 1.86/2.12 tff(3089,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3090,plain,
% 1.86/2.12 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3091,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3090])).
% 1.86/2.12 tff(3092,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3091, 3089])).
% 1.86/2.12 tff(3093,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3094,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 1.86/2.12 tff(3095,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3094, 163, 1115, 3066, 680, 3088])).
% 1.86/2.12 tff(3096,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3097,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3096, 1115, 3056, 57, 1145, 3045, 3065])).
% 1.86/2.12 tff(3098,plain,
% 1.86/2.12 (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))))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[446, 314])).
% 1.86/2.12 tff(3099,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3098, 3097])).
% 1.86/2.12 tff(3100,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3101,plain,
% 1.86/2.12 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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))))), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3102,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3101])).
% 1.86/2.12 tff(3103,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3102, 3100])).
% 1.86/2.12 tff(3104,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3105,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3104, 3103])).
% 1.86/2.12 tff(3106,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3105, 198, 3099, 3064, 831])).
% 1.86/2.12 tff(3107,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[528, 3106, 3037])).
% 1.86/2.12 tff(3108,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.86/2.12 tff(3109,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.86/2.12 tff(3110,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3111,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3112,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 1.86/2.12 tff(3113,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3112, 163, 1474, 405, 3109, 3108])).
% 1.86/2.12 tff(3114,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3115,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3114, 3107, 405, 1474])).
% 1.86/2.12 tff(3116,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3115, 3034])).
% 1.86/2.12 tff(3117,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[469, 3116])).
% 1.86/2.12 tff(3118,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3117, 3031])).
% 1.86/2.12 tff(3119,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3082, 198, 1145, 3045, 3118])).
% 1.86/2.12 tff(3120,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3121,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3122,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3121, 3120])).
% 1.86/2.12 tff(3123,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3122, 163, 1115, 405, 3107])).
% 1.86/2.12 tff(3124,plain,
% 1.86/2.12 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3086, 26, 3123])).
% 1.86/2.12 tff(3125,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3124, 3119, 3029])).
% 1.86/2.12 tff(3126,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3127,plain,
% 1.86/2.12 (~r(s(s(elem!1)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3126, 3024, 57, 2953, 2952, 2950, 2943, 2, 1134])).
% 1.86/2.12 tff(3128,plain,
% 1.86/2.12 (b(s(s(elem!1)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[602, 3127, 598])).
% 1.86/2.12 tff(3129,plain,
% 1.86/2.12 (b(s(s(z)), z)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3128, 2949])).
% 1.86/2.12 tff(3130,plain,
% 1.86/2.12 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[57])).
% 1.86/2.12 tff(3131,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 1.86/2.12 tff(3132,plain,
% 1.86/2.12 (b(z, s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1791, 3131])).
% 1.86/2.12 tff(3133,plain,
% 1.86/2.12 (b(elem!1, s(elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3132, 3130])).
% 1.86/2.12 tff(3134,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3135,plain,
% 1.86/2.12 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3136,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3135])).
% 1.86/2.12 tff(3137,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3136, 3134])).
% 1.86/2.12 tff(3138,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3139,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[3138, 3137])).
% 1.98/2.12 tff(3140,plain,
% 1.98/2.12 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3139, 198, 1128, 3133, 2950])).
% 1.98/2.12 tff(3141,plain,
% 1.98/2.12 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3140, 2964])).
% 1.98/2.12 tff(3142,plain,
% 1.98/2.12 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[3141, 2961])).
% 1.98/2.12 tff(3143,plain,
% 1.98/2.12 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[420, 3142])).
% 1.98/2.12 tff(3144,plain,
% 1.98/2.12 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[3143, 2959])).
% 1.98/2.12 tff(3145,plain,
% 1.98/2.12 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[3030])).
% 1.98/2.12 tff(3146,plain,
% 1.98/2.12 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[3025])).
% 1.98/2.12 tff(3147,plain,
% 1.98/2.12 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.12 inference(symmetry,[status(thm)],[3146])).
% 1.98/2.12 tff(3148,plain,
% 1.98/2.12 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[3147])).
% 1.98/2.12 tff(3149,plain,
% 1.98/2.12 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[369, 3148])).
% 1.98/2.12 tff(3150,plain,
% 1.98/2.12 (b(s(s(elem!1)), z)),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[1128, 2978])).
% 1.98/2.12 tff(3151,plain,
% 1.98/2.12 (r(z, s(elem!1)) <=> r(z, s(z))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[1644])).
% 1.98/2.12 tff(3152,plain,
% 1.98/2.12 (r(z, s(z)) <=> r(z, s(elem!1))),
% 1.98/2.12 inference(symmetry,[status(thm)],[3151])).
% 1.98/2.12 tff(3153,plain,
% 1.98/2.12 (r(z, s(elem!1))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[406, 3152])).
% 1.98/2.12 tff(3154,plain,
% 1.98/2.12 ($false),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3131, 3153])).
% 1.98/2.12 tff(3155,plain,((~(elem!1 = z)) | r(z, s(elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.12 tff(3156,plain,
% 1.98/2.12 (~r(z, s(z))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3155, 3131, 79])).
% 1.98/2.12 tff(3157,plain,
% 1.98/2.12 (b(z, s(z))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[593, 3156])).
% 1.98/2.12 tff(3158,plain,
% 1.98/2.12 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[741, 3157, 722, 330, 3150])).
% 1.98/2.12 tff(3159,plain,
% 1.98/2.12 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[934, 26, 3158, 3149])).
% 1.98/2.12 tff(3160,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(3161,plain,
% 1.98/2.12 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(3162,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[3161])).
% 1.98/2.12 tff(3163,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.12 inference(transitivity,[status(thm)],[3162, 3160])).
% 1.98/2.12 tff(3164,plain,
% 1.98/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.98/2.12 inference(quant_inst,[status(thm)],[])).
% 1.98/2.12 tff(3165,plain,
% 1.98/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 1.98/2.12 tff(3166,plain,
% 1.98/2.12 (~r(s(elem!1), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3165, 163, 3159, 3144, 3065])).
% 1.98/2.12 tff(3167,plain,
% 1.98/2.12 (b(s(elem!1), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[901, 3166, 890])).
% 1.98/2.12 tff(3168,plain,
% 1.98/2.12 (b(s(s(elem!1)), s(elem!1))),
% 1.98/2.12 inference(modus_ponens,[status(thm)],[722, 2954])).
% 1.98/2.12 tff(3169,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.98/2.12 tff(3170,plain,
% 1.98/2.12 ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3082, 198, 1145, 1328])).
% 1.98/2.12 tff(3171,plain,
% 1.98/2.12 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3170, 3169])).
% 1.98/2.12 tff(3172,plain,
% 1.98/2.12 ((s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3086, 26, 3171])).
% 1.98/2.12 tff(3173,plain,
% 1.98/2.12 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.12 inference(unit_resolution,[status(thm)],[3172, 3029])).
% 1.98/2.12 tff(3174,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(3175,plain,
% 1.98/2.12 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.12 inference(rewrite,[status(thm)],[])).
% 1.98/2.12 tff(3176,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 1.98/2.12 inference(monotonicity,[status(thm)],[3175])).
% 1.98/2.12 tff(3177,plain,
% 1.98/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3176, 3174])).
% 1.98/2.13 tff(3178,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3179,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.98/2.13 tff(3180,plain,
% 1.98/2.13 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3179, 163, 405, 681, 3173])).
% 1.98/2.13 tff(3181,plain,
% 1.98/2.13 (b(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[528, 3180, 3037])).
% 1.98/2.13 tff(3182,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3183,plain,
% 1.98/2.13 (((~r(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)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3184,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1))))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3183])).
% 1.98/2.13 tff(3185,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.98/2.13 tff(3186,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3187,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1))))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.98/2.13 tff(3188,plain,
% 1.98/2.13 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3187, 163, 681, 680, 3173])).
% 1.98/2.13 tff(3189,plain,
% 1.98/2.13 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3098, 3188])).
% 1.98/2.13 tff(3190,plain,
% 1.98/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3191,plain,
% 1.98/2.13 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3192,plain,
% 1.98/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3191])).
% 1.98/2.13 tff(3193,plain,
% 1.98/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3192, 3190])).
% 1.98/2.13 tff(3194,plain,
% 1.98/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3195,plain,
% 1.98/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3194, 3193])).
% 1.98/2.13 tff(3196,plain,
% 1.98/2.13 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3195, 198, 1418, 831])).
% 1.98/2.13 tff(3197,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3196, 3189, 3181, 3169])).
% 1.98/2.13 tff(3198,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(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(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3199,plain,
% 1.98/2.13 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3198, 3133, 2950, 3159, 3144, 405, 57, 3168, 3167])).
% 1.98/2.13 tff(3200,plain,
% 1.98/2.13 (~b(s(s(s(s(s(z))))), s(z))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3199, 3145])).
% 1.98/2.13 tff(3201,plain,
% 1.98/2.13 (r(s(s(s(s(s(z))))), s(z))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[469, 3200])).
% 1.98/2.13 tff(3202,plain,
% 1.98/2.13 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[422, 3032])).
% 1.98/2.13 tff(3203,assumption,(~r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.98/2.13 tff(3204,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3203, 3202])).
% 1.98/2.13 tff(3205,plain,((~r(s(s(s(s(s(z))))), s(z))) | r(s(s(s(s(s(z))))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3206,plain,
% 1.98/2.13 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3205, 3201, 57])).
% 1.98/2.13 tff(3207,plain,
% 1.98/2.13 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3114, 3206, 405, 1474])).
% 1.98/2.13 tff(3208,plain,
% 1.98/2.13 (b(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[528, 3207, 3037])).
% 1.98/2.13 tff(3209,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(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)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(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)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3210,plain,
% 1.98/2.13 (((~r(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)))) | (~r(elem!1, 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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3211,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(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)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3210])).
% 1.98/2.13 tff(3212,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(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)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3211, 3209])).
% 1.98/2.13 tff(3213,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3214,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(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)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 1.98/2.13 tff(3215,plain,
% 1.98/2.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3214, 163, 405, 3159, 3144])).
% 1.98/2.13 tff(3216,plain,
% 1.98/2.13 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[703, 3215, 3002])).
% 1.98/2.13 tff(3217,plain,
% 1.98/2.13 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), 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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3218,plain,
% 1.98/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3217])).
% 1.98/2.13 tff(3219,plain,
% 1.98/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3218, 3100])).
% 1.98/2.13 tff(3220,plain,
% 1.98/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3221,plain,
% 1.98/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 1.98/2.13 tff(3222,plain,
% 1.98/2.13 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3221, 198, 3216, 2950, 3208])).
% 1.98/2.13 tff(3223,plain,
% 1.98/2.13 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3098, 3222])).
% 1.98/2.13 tff(3224,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3072, 163, 3223, 3206, 3144, 3065])).
% 1.98/2.13 tff(3225,plain,(r(z, s(elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3226,plain,
% 1.98/2.13 (r(z, s(elem!1))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3225, 2943, 2953, 2952, 57, 1134, 3128, 2, 3023, 330])).
% 1.98/2.13 tff(3227,plain,
% 1.98/2.13 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[80])).
% 1.98/2.13 tff(3228,plain,
% 1.98/2.13 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.98/2.13 inference(symmetry,[status(thm)],[3227])).
% 1.98/2.13 tff(3229,plain,
% 1.98/2.13 (r(elem!1, s(elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[791, 3228])).
% 1.98/2.13 tff(3230,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1411, 3229])).
% 1.98/2.13 tff(3231,plain,((~r(z, s(elem!1))) | r(elem!1, s(elem!1)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3232,plain,
% 1.98/2.13 (r(elem!1, s(elem!1))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3231, 3226, 79])).
% 1.98/2.13 tff(3233,plain,
% 1.98/2.13 (s(elem!1) = s(z)),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[1646, 79])).
% 1.98/2.13 tff(3234,plain,
% 1.98/2.13 (r(z, s(elem!1)) <=> r(z, s(z))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[809])).
% 1.98/2.13 tff(3235,plain,
% 1.98/2.13 (r(z, s(z)) <=> r(z, s(elem!1))),
% 1.98/2.13 inference(symmetry,[status(thm)],[3234])).
% 1.98/2.13 tff(3236,plain,
% 1.98/2.13 ((~r(z, s(z))) <=> (~r(z, s(elem!1)))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3235])).
% 1.98/2.13 tff(3237,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.98/2.13 tff(3238,plain,
% 1.98/2.13 (~r(z, s(elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.98/2.13 tff(3239,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[791, 3238])).
% 1.98/2.13 tff(3240,plain,((~(s(elem!1) = s(z))) | (~r(z, s(elem!1))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3241,plain,
% 1.98/2.13 (r(z, s(z))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3240, 3226, 3233])).
% 1.98/2.13 tff(3242,plain,
% 1.98/2.13 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[2989, 198, 1128, 1328, 2950])).
% 1.98/2.13 tff(3243,plain,
% 1.98/2.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3242, 2964])).
% 1.98/2.13 tff(3244,plain,
% 1.98/2.13 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3243, 2961])).
% 1.98/2.13 tff(3245,plain,
% 1.98/2.13 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[420, 3244])).
% 1.98/2.13 tff(3246,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))), introduced(assumption)).
% 1.98/2.13 tff(3247,plain,
% 1.98/2.13 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.98/2.13 inference(symmetry,[status(thm)],[3246])).
% 1.98/2.13 tff(3248,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[930, 3247])).
% 1.98/2.13 tff(3249,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3250,plain,
% 1.98/2.13 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3249, 3149])).
% 1.98/2.13 tff(3251,plain,
% 1.98/2.13 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[941, 26, 3243, 3250])).
% 1.98/2.13 tff(3252,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3253,plain,
% 1.98/2.13 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, 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(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(rewrite,[status(thm)],[])).
% 1.98/2.13 tff(3254,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.13 inference(monotonicity,[status(thm)],[3253])).
% 1.98/2.13 tff(3255,plain,
% 1.98/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.13 inference(transitivity,[status(thm)],[3254, 3252])).
% 1.98/2.13 tff(3256,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 1.98/2.13 inference(quant_inst,[status(thm)],[])).
% 1.98/2.13 tff(3257,plain,
% 1.98/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3256, 3255])).
% 1.98/2.13 tff(3258,plain,
% 1.98/2.13 ($false),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3257, 163, 1473, 694, 680, 3065])).
% 1.98/2.13 tff(3259,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.13 tff(3260,plain,
% 1.98/2.13 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3259, 3251, 1473, 2943])).
% 1.98/2.13 tff(3261,plain,
% 1.98/2.13 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[703, 3260, 3002])).
% 1.98/2.13 tff(3262,plain,
% 1.98/2.13 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3261, 2998])).
% 1.98/2.13 tff(3263,plain,
% 1.98/2.13 (~r(s(s(s(s(s(z))))), s(z))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[456, 3262, 151, 330, 406, 3245])).
% 1.98/2.13 tff(3264,plain,
% 1.98/2.13 (b(s(s(s(s(s(z))))), s(z))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[469, 3263])).
% 1.98/2.13 tff(3265,plain,
% 1.98/2.13 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[3264, 3031])).
% 1.98/2.13 tff(3266,plain,
% 1.98/2.13 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3082, 198, 1145, 1328, 3265])).
% 1.98/2.13 tff(3267,plain,
% 1.98/2.13 ((s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3086, 26, 3266])).
% 1.98/2.13 tff(3268,plain,
% 1.98/2.13 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[3267, 3029])).
% 1.98/2.13 tff(3269,plain,
% 1.98/2.13 (b(s(s(z)), z)),
% 1.98/2.13 inference(modus_ponens,[status(thm)],[1128, 2949])).
% 1.98/2.13 tff(3270,plain,
% 1.98/2.13 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[356, 3262, 3269, 330])).
% 1.98/2.13 tff(3271,plain,
% 1.98/2.13 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.13 inference(unit_resolution,[status(thm)],[374, 3270])).
% 1.98/2.13 tff(3272,assumption,(r(s(s(z)), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.98/2.13 tff(3273,plain,
% 1.98/2.14 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3272, 2995])).
% 1.98/2.14 tff(3274,plain,
% 1.98/2.14 ($false),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[696, 3273])).
% 1.98/2.14 tff(3275,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.14 tff(3276,plain,
% 1.98/2.14 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3275, 3271, 57])).
% 1.98/2.14 tff(3277,plain,
% 1.98/2.14 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3025])).
% 1.98/2.14 tff(3278,plain,
% 1.98/2.14 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3277, 496])).
% 1.98/2.14 tff(3279,plain,
% 1.98/2.14 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.98/2.14 inference(symmetry,[status(thm)],[3278])).
% 1.98/2.14 tff(3280,plain,
% 1.98/2.14 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3279])).
% 1.98/2.14 tff(3281,plain,
% 1.98/2.14 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[508, 3280])).
% 1.98/2.14 tff(3282,plain,
% 1.98/2.14 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[2936])).
% 1.98/2.14 tff(3283,plain,
% 1.98/2.14 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(symmetry,[status(thm)],[3282])).
% 1.98/2.14 tff(3284,plain,
% 1.98/2.14 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[2936])).
% 1.98/2.14 tff(3285,plain,
% 1.98/2.14 ((~r(s(elem!1), s(s(s(s(s(z))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3284])).
% 1.98/2.14 tff(3286,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3287,plain,
% 1.98/2.14 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3288,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3287])).
% 1.98/2.14 tff(3289,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3288, 3286])).
% 1.98/2.14 tff(3290,plain,
% 1.98/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3291,plain,
% 1.98/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3290, 3289])).
% 1.98/2.14 tff(3292,plain,
% 1.98/2.14 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3291, 163, 3066, 680, 3065])).
% 1.98/2.14 tff(3293,plain,
% 1.98/2.14 (~r(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3292, 3285])).
% 1.98/2.14 tff(3294,plain,
% 1.98/2.14 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.98/2.14 inference(commutativity,[status(thm)],[])).
% 1.98/2.14 tff(3295,plain,
% 1.98/2.14 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3294])).
% 1.98/2.14 tff(3296,plain,
% 1.98/2.14 (~(s(z) = s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[464, 3295])).
% 1.98/2.14 tff(3297,plain,
% 1.98/2.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3298,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3299,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 1.98/2.14 tff(3300,plain,
% 1.98/2.14 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3299, 26])).
% 1.98/2.14 tff(3301,plain,
% 1.98/2.14 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3300, 3296])).
% 1.98/2.14 tff(3302,plain,
% 1.98/2.14 (b(s(z), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3301, 3293])).
% 1.98/2.14 tff(3303,plain,
% 1.98/2.14 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3302, 3283])).
% 1.98/2.14 tff(3304,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3305,plain,
% 1.98/2.14 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3306,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3305])).
% 1.98/2.14 tff(3307,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3306, 3304])).
% 1.98/2.14 tff(3308,plain,
% 1.98/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3309,plain,
% 1.98/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.98/2.14 tff(3310,plain,
% 1.98/2.14 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3309, 198, 1145, 1328, 3169])).
% 1.98/2.14 tff(3311,plain,
% 1.98/2.14 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3310, 3303])).
% 1.98/2.14 tff(3312,plain,
% 1.98/2.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), 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(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3313,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3314,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3313, 3312])).
% 1.98/2.14 tff(3315,plain,
% 1.98/2.14 ((s(s(elem!1)) = s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3314, 26, 3311])).
% 1.98/2.14 tff(3316,plain,
% 1.98/2.14 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3315, 3281])).
% 1.98/2.14 tff(3317,assumption,(b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.98/2.14 tff(3318,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3319,plain,
% 1.98/2.14 (((~b(s(s(s(s(s(z))))), 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(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3320,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(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(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3319])).
% 1.98/2.14 tff(3321,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(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(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3320, 3318])).
% 1.98/2.14 tff(3322,plain,
% 1.98/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(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(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3323,plain,
% 1.98/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 1.98/2.14 tff(3324,plain,
% 1.98/2.14 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3323, 198, 1145, 1328, 3169, 3317])).
% 1.98/2.14 tff(3325,plain,
% 1.98/2.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3324, 3303])).
% 1.98/2.14 tff(3326,plain,
% 1.98/2.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3327,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3328,plain,
% 1.98/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 1.98/2.14 tff(3329,plain,
% 1.98/2.14 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3328, 26, 3325])).
% 1.98/2.14 tff(3330,plain,
% 1.98/2.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3329, 2935])).
% 1.98/2.14 tff(3331,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3332,plain,
% 1.98/2.14 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3333,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3332])).
% 1.98/2.14 tff(3334,plain,
% 1.98/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3333, 3331])).
% 1.98/2.14 tff(3335,plain,
% 1.98/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.98/2.14 inference(quant_inst,[status(thm)],[])).
% 1.98/2.14 tff(3336,plain,
% 1.98/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.98/2.14 inference(modus_ponens,[status(thm)],[3335, 3334])).
% 1.98/2.14 tff(3337,plain,
% 1.98/2.14 ($false),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3336, 163, 3066, 3330, 680, 3316])).
% 1.98/2.14 tff(3338,plain,((~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(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.14 tff(3339,plain,
% 1.98/2.14 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3338, 3265, 57, 1145, 1328, 3251, 2964, 2943])).
% 1.98/2.14 tff(3340,plain,
% 1.98/2.14 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.14 inference(unit_resolution,[status(thm)],[3098, 3339])).
% 1.98/2.14 tff(3341,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3342,plain,
% 1.98/2.14 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.14 inference(rewrite,[status(thm)],[])).
% 1.98/2.14 tff(3343,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.98/2.14 inference(monotonicity,[status(thm)],[3342])).
% 1.98/2.14 tff(3344,plain,
% 1.98/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.14 inference(transitivity,[status(thm)],[3343, 3341])).
% 1.98/2.14 tff(3345,plain,
% 1.98/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3346,plain,
% 1.98/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3345, 3344])).
% 1.98/2.15 tff(3347,plain,
% 1.98/2.15 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3346, 198, 3261, 3265, 2964])).
% 1.98/2.15 tff(3348,plain,
% 1.98/2.15 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3347, 3340])).
% 1.98/2.15 tff(3349,plain,
% 1.98/2.15 (r(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[528, 3348, 3037])).
% 1.98/2.15 tff(3350,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3179, 163, 405, 3349, 3276, 3268])).
% 1.98/2.15 tff(3351,plain,((~b(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3352,plain,
% 1.98/2.15 (~b(s(elem!1), s(s(elem!1)))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3351, 2953, 57, 3024, 151, 330, 3241, 3232, 3128, 2])).
% 1.98/2.15 tff(3353,plain,
% 1.98/2.15 (r(s(elem!1), s(s(elem!1)))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[901, 3352, 1134])).
% 1.98/2.15 tff(3354,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3355,plain,
% 1.98/2.15 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3356,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3355])).
% 1.98/2.15 tff(3357,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3356, 3354])).
% 1.98/2.15 tff(3358,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3359,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3358, 3357])).
% 1.98/2.15 tff(3360,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3359, 163, 1473, 1220, 405, 681])).
% 1.98/2.15 tff(3361,plain,((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3362,plain,
% 1.98/2.15 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3361, 3353, 3232, 2953])).
% 1.98/2.15 tff(3363,plain,
% 1.98/2.15 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3275, 3362, 57])).
% 1.98/2.15 tff(3364,plain,
% 1.98/2.15 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[374, 3363])).
% 1.98/2.15 tff(3365,plain,
% 1.98/2.15 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[356, 3364, 3129, 330])).
% 1.98/2.15 tff(3366,plain,
% 1.98/2.15 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[31, 3365])).
% 1.98/2.15 tff(3367,plain,
% 1.98/2.15 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3366, 2944])).
% 1.98/2.15 tff(3368,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3369,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3370,plain,
% 1.98/2.15 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3371,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3370])).
% 1.98/2.15 tff(3372,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3371, 3369])).
% 1.98/2.15 tff(3373,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3374,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 1.98/2.15 tff(3375,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3374, 163, 1474, 694, 3368, 3065])).
% 1.98/2.15 tff(3376,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3377,plain,
% 1.98/2.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3376, 2952, 3367, 2943])).
% 1.98/2.15 tff(3378,plain,
% 1.98/2.15 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3328, 26, 3377])).
% 1.98/2.15 tff(3379,plain,
% 1.98/2.15 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3378, 2935])).
% 1.98/2.15 tff(3380,assumption,(s(s(elem!1)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.98/2.15 tff(3381,plain,
% 1.98/2.15 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.98/2.15 inference(symmetry,[status(thm)],[3380])).
% 1.98/2.15 tff(3382,plain,
% 1.98/2.15 (s(s(s(s(s(z))))) = s(s(z))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3381, 3025])).
% 1.98/2.15 tff(3383,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[508, 3382])).
% 1.98/2.15 tff(3384,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3385,plain,
% 1.98/2.15 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3384, 57])).
% 1.98/2.15 tff(3386,assumption,(r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3387,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3388,plain,
% 1.98/2.15 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3389,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3388])).
% 1.98/2.15 tff(3390,plain,
% 1.98/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3389, 3387])).
% 1.98/2.15 tff(3391,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3392,plain,
% 1.98/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 1.98/2.15 tff(3393,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3392, 163, 1473, 1220, 405, 3386])).
% 1.98/2.15 tff(3394,plain,((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3395,plain,
% 1.98/2.15 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3394, 3353, 3232, 2953])).
% 1.98/2.15 tff(3396,assumption,(~(s(s(elem!1)) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3397,assumption,(~b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3398,assumption,(~r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3399,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3314, 26, 3398, 3397, 3396])).
% 1.98/2.15 tff(3400,plain,(b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3401,plain,
% 1.98/2.15 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3400, 3395, 3385])).
% 1.98/2.15 tff(3402,plain,
% 1.98/2.15 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[59])).
% 1.98/2.15 tff(3403,plain,
% 1.98/2.15 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3364, 3402])).
% 1.98/2.15 tff(3404,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3405,assumption,(b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.98/2.15 tff(3406,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3407,plain,
% 1.98/2.15 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3408,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3407])).
% 1.98/2.15 tff(3409,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3408, 3406])).
% 1.98/2.15 tff(3410,plain,
% 1.98/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3411,plain,
% 1.98/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 1.98/2.15 tff(3412,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3411, 198, 1145, 721, 3169, 3405, 3404])).
% 1.98/2.15 tff(3413,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3414,plain,
% 1.98/2.15 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3413, 3024, 3403, 3401, 3379])).
% 1.98/2.15 tff(3415,plain,
% 1.98/2.15 (~b(s(s(s(s(s(z))))), s(z))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3414, 3145])).
% 1.98/2.15 tff(3416,plain,
% 1.98/2.15 (r(s(s(s(s(s(z))))), s(z))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[469, 3415])).
% 1.98/2.15 tff(3417,plain,
% 1.98/2.15 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3205, 3416, 57])).
% 1.98/2.15 tff(3418,plain,
% 1.98/2.15 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3114, 3417, 2953, 2952])).
% 1.98/2.15 tff(3419,plain,
% 1.98/2.15 (b(s(s(s(s(s(z))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[528, 3418, 3037])).
% 1.98/2.15 tff(3420,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3421,plain,
% 1.98/2.15 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.15 inference(rewrite,[status(thm)],[])).
% 1.98/2.15 tff(3422,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3421])).
% 1.98/2.15 tff(3423,plain,
% 1.98/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.98/2.15 inference(transitivity,[status(thm)],[3422, 3420])).
% 1.98/2.15 tff(3424,plain,
% 1.98/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.15 inference(quant_inst,[status(thm)],[])).
% 1.98/2.15 tff(3425,plain,
% 1.98/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 1.98/2.15 tff(3426,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3425, 198, 3128, 3419, 3403, 3401, 3379])).
% 1.98/2.15 tff(3427,plain,((~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3428,plain,
% 1.98/2.15 (~(z = elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3427, 177, 151, 2, 1097, 2930, 1086, 42])).
% 1.98/2.15 tff(3429,plain,
% 1.98/2.15 (~(elem!1 = z)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[1079, 3428])).
% 1.98/2.15 tff(3430,plain,
% 1.98/2.15 (b(elem!1, z)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[187, 3429, 2931])).
% 1.98/2.15 tff(3431,plain,
% 1.98/2.15 (b(z, elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[102, 3428, 56])).
% 1.98/2.15 tff(3432,plain,
% 1.98/2.15 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[204, 198, 3431, 3430, 177])).
% 1.98/2.15 tff(3433,plain,
% 1.98/2.15 (b(elem!1, s(z))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[269, 3432, 151, 2930, 2929, 2])).
% 1.98/2.15 tff(3434,plain,
% 1.98/2.15 (~(s(z) = elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[2833, 244, 2])).
% 1.98/2.15 tff(3435,plain,
% 1.98/2.15 (r(s(z), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[217, 3434, 149])).
% 1.98/2.15 tff(3436,plain,
% 1.98/2.15 (~(z = elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[78, 1033])).
% 1.98/2.15 tff(3437,plain,
% 1.98/2.15 (b(z, elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[102, 3436, 56])).
% 1.98/2.15 tff(3438,plain,
% 1.98/2.15 (~(elem!1 = s(s(elem!1)))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[97, 3437, 89])).
% 1.98/2.15 tff(3439,plain,
% 1.98/2.15 (r(elem!1, s(s(elem!1)))),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[147, 3438, 85])).
% 1.98/2.15 tff(3440,plain,
% 1.98/2.15 ($false),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[759, 163, 236, 405, 151, 258])).
% 1.98/2.15 tff(3441,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.15 tff(3442,plain,
% 1.98/2.15 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[3441, 3435, 3439, 151])).
% 1.98/2.15 tff(3443,plain,
% 1.98/2.15 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.98/2.15 inference(unit_resolution,[status(thm)],[256, 3442, 244])).
% 1.98/2.15 tff(3444,plain,
% 1.98/2.15 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = elem!1)),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3443])).
% 1.98/2.15 tff(3445,plain,
% 1.98/2.15 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = elem!1))),
% 1.98/2.15 inference(monotonicity,[status(thm)],[3444])).
% 1.98/2.15 tff(3446,plain,
% 1.98/2.15 (~(s(s(z)) = elem!1)),
% 1.98/2.15 inference(modus_ponens,[status(thm)],[369, 3445])).
% 1.98/2.15 tff(3447,plain,
% 1.98/2.15 (~r(elem!1, z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1026, 3435, 150, 153])).
% 1.98/2.16 tff(3448,plain,
% 1.98/2.16 (b(elem!1, z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[187, 3447, 1033])).
% 1.98/2.16 tff(3449,plain,
% 1.98/2.16 (r(z, s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1096, 89])).
% 1.98/2.16 tff(3450,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.98/2.16 tff(3451,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[479, 163, 236, 405, 2113, 3450])).
% 1.98/2.16 tff(3452,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3453,plain,
% 1.98/2.16 (~r(s(s(z)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3452, 3450, 405, 236])).
% 1.98/2.16 tff(3454,plain,
% 1.98/2.16 (b(s(s(z)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2139, 3453, 2105])).
% 1.98/2.16 tff(3455,plain,
% 1.98/2.16 (~b(s(s(z)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2146, 198, 95, 271, 3454])).
% 1.98/2.16 tff(3456,plain,
% 1.98/2.16 (r(s(s(z)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[345, 3455])).
% 1.98/2.16 tff(3457,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3458,plain,
% 1.98/2.16 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3459,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3458])).
% 1.98/2.16 tff(3460,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.98/2.16 tff(3461,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3462,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.98/2.16 tff(3463,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3462, 163, 1098, 150, 3450, 3456])).
% 1.98/2.16 tff(3464,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3465,plain,
% 1.98/2.16 (~r(s(s(z)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3464, 3437, 150, 3449, 3448, 3446, 3439, 3435])).
% 1.98/2.16 tff(3466,plain,
% 1.98/2.16 (b(s(s(z)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[487, 3465])).
% 1.98/2.16 tff(3467,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1, 327])).
% 1.98/2.16 tff(3468,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3469,plain,
% 1.98/2.16 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3468, 3443, 3437])).
% 1.98/2.16 tff(3470,plain,
% 1.98/2.16 (~r(s(z), s(s(z)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[384, 3469, 153, 150, 3443, 179])).
% 1.98/2.16 tff(3471,plain,
% 1.98/2.16 (b(s(z), s(s(z)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[403, 3470])).
% 1.98/2.16 tff(3472,plain,
% 1.98/2.16 (~(s(elem!1) = s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[814, 3436])).
% 1.98/2.16 tff(3473,plain,
% 1.98/2.16 (~(s(s(z)) = s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[822, 3472])).
% 1.98/2.16 tff(3474,plain,
% 1.98/2.16 (~(s(s(elem!1)) = elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[118, 3438])).
% 1.98/2.16 tff(3475,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3476,plain,
% 1.98/2.16 (((~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(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3477,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3476])).
% 1.98/2.16 tff(3478,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3477, 3475])).
% 1.98/2.16 tff(3479,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3480,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 1.98/2.16 tff(3481,plain,
% 1.98/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3480, 198, 1544, 722, 560])).
% 1.98/2.16 tff(3482,plain,
% 1.98/2.16 (r(s(s(z)), s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2161, 26, 2154, 3481])).
% 1.98/2.16 tff(3483,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3484,plain,
% 1.98/2.16 (((~b(s(s(z)), s(z))) | (~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(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3485,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3484])).
% 1.98/2.16 tff(3486,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3485, 3483])).
% 1.98/2.16 tff(3487,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3488,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 1.98/2.16 tff(3489,plain,
% 1.98/2.16 (~b(s(s(elem!1)), s(s(z)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3488, 198, 722, 560, 407])).
% 1.98/2.16 tff(3490,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.98/2.16 tff(3491,plain,
% 1.98/2.16 (s(s(z)) = s(s(elem!1))),
% 1.98/2.16 inference(symmetry,[status(thm)],[3490])).
% 1.98/2.16 tff(3492,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2154, 3491])).
% 1.98/2.16 tff(3493,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3494,plain,
% 1.98/2.16 (~(s(s(elem!1)) = s(s(z)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3493, 2154])).
% 1.98/2.16 tff(3495,plain,
% 1.98/2.16 (((~![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))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3496,plain,
% 1.98/2.16 ((~![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))))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3497,plain,
% 1.98/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3496, 3495])).
% 1.98/2.16 tff(3498,plain,
% 1.98/2.16 (r(s(s(elem!1)), s(s(z)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3497, 26, 3494, 3489])).
% 1.98/2.16 tff(3499,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2902, 3498, 3482, 153, 1098])).
% 1.98/2.16 tff(3500,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3501,plain,
% 1.98/2.16 (~b(s(s(elem!1)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3500, 1053, 1098, 2154, 153, 407, 560])).
% 1.98/2.16 tff(3502,plain,
% 1.98/2.16 (r(s(s(elem!1)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[626, 3501])).
% 1.98/2.16 tff(3503,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[2291, 163, 790, 1098, 150, 3502])).
% 1.98/2.16 tff(3504,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3505,plain,
% 1.98/2.16 (~r(s(s(elem!1)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3504, 3473, 150, 3449, 153, 3471, 3466])).
% 1.98/2.16 tff(3506,plain,
% 1.98/2.16 (b(s(s(elem!1)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[801, 3505])).
% 1.98/2.16 tff(3507,plain,
% 1.98/2.16 (~b(s(s(elem!1)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1491, 198, 3437, 3448, 3506])).
% 1.98/2.16 tff(3508,plain,
% 1.98/2.16 (r(s(s(elem!1)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[602, 3507, 3474])).
% 1.98/2.16 tff(3509,plain,
% 1.98/2.16 (~r(s(s(elem!1)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[609, 163, 3508, 3435, 3439])).
% 1.98/2.16 tff(3510,plain,
% 1.98/2.16 (b(s(s(elem!1)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[626, 3509])).
% 1.98/2.16 tff(3511,plain,
% 1.98/2.16 (~r(s(z), s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[630, 163, 3508, 3435, 3439])).
% 1.98/2.16 tff(3512,plain,
% 1.98/2.16 (b(s(z), s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[642, 3511])).
% 1.98/2.16 tff(3513,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3500, 3512, 3510, 3449, 3473, 153, 3471, 3466])).
% 1.98/2.16 tff(3514,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(elem!1, s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3515,plain,
% 1.98/2.16 (b(elem!1, s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3514, 3432, 150, 151, 149, 2, 55, 1085, 56])).
% 1.98/2.16 tff(3516,plain,
% 1.98/2.16 (~(s(s(elem!1)) = elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[118, 1086])).
% 1.98/2.16 tff(3517,plain,
% 1.98/2.16 (~(s(elem!1) = elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1395, 3516])).
% 1.98/2.16 tff(3518,plain,
% 1.98/2.16 (~(elem!1 = s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1400, 3517])).
% 1.98/2.16 tff(3519,plain,
% 1.98/2.16 (~(s(elem!1) = s(s(elem!1)))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[140, 3516])).
% 1.98/2.16 tff(3520,plain,
% 1.98/2.16 (b(s(s(elem!1)), s(z))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[626, 2292])).
% 1.98/2.16 tff(3521,plain,
% 1.98/2.16 ($false),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1059, 198, 1053, 68, 3520, 320])).
% 1.98/2.16 tff(3522,plain,((~r(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.16 tff(3523,plain,
% 1.98/2.16 (~r(s(s(elem!1)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3522, 3515, 1097, 3433, 150, 55])).
% 1.98/2.16 tff(3524,plain,
% 1.98/2.16 (b(s(s(elem!1)), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[801, 3523])).
% 1.98/2.16 tff(3525,plain,
% 1.98/2.16 (~(s(s(elem!1)) = s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1138, 3519])).
% 1.98/2.16 tff(3526,plain,
% 1.98/2.16 (~b(s(s(elem!1)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1491, 198, 3431, 3430, 3524])).
% 1.98/2.16 tff(3527,plain,
% 1.98/2.16 (r(s(s(elem!1)), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[602, 3526, 3516])).
% 1.98/2.16 tff(3528,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3529,plain,
% 1.98/2.16 (((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3530,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3529])).
% 1.98/2.16 tff(3531,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3530, 3528])).
% 1.98/2.16 tff(3532,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3533,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1))))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3532, 3531])).
% 1.98/2.16 tff(3534,plain,
% 1.98/2.16 (~r(s(elem!1), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3533, 163, 1115, 1220, 1098])).
% 1.98/2.16 tff(3535,plain,
% 1.98/2.16 (b(s(elem!1), z)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1217, 3534])).
% 1.98/2.16 tff(3536,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3537,plain,
% 1.98/2.16 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3538,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3537])).
% 1.98/2.16 tff(3539,plain,
% 1.98/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.98/2.16 tff(3540,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3541,plain,
% 1.98/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.98/2.16 tff(3542,plain,
% 1.98/2.16 (~r(z, s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3541, 163, 1115, 1220, 1098])).
% 1.98/2.16 tff(3543,plain,
% 1.98/2.16 (b(z, s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1791, 3542])).
% 1.98/2.16 tff(3544,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3545,plain,
% 1.98/2.16 (((~b(s(elem!1), z)) | (~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(z, s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3546,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3545])).
% 1.98/2.16 tff(3547,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3546, 3544])).
% 1.98/2.16 tff(3548,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3549,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[3548, 3547])).
% 1.98/2.16 tff(3550,plain,
% 1.98/2.16 (~b(s(s(elem!1)), s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3549, 198, 1175, 723, 1801])).
% 1.98/2.16 tff(3551,plain,
% 1.98/2.16 (r(s(s(elem!1)), s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1143, 3550, 1701])).
% 1.98/2.16 tff(3552,plain,
% 1.98/2.16 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.98/2.16 inference(symmetry,[status(thm)],[1755])).
% 1.98/2.16 tff(3553,plain,
% 1.98/2.16 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3552])).
% 1.98/2.16 tff(3554,plain,
% 1.98/2.16 (~(elem!1 = s(elem!1))),
% 1.98/2.16 inference(modus_ponens,[status(thm)],[834, 3553])).
% 1.98/2.16 tff(3555,plain,
% 1.98/2.16 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[1414, 26, 1411])).
% 1.98/2.16 tff(3556,plain,
% 1.98/2.16 (b(elem!1, s(elem!1))),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[3555, 3554])).
% 1.98/2.16 tff(3557,plain,
% 1.98/2.16 (b(s(elem!1), elem!1)),
% 1.98/2.16 inference(unit_resolution,[status(thm)],[854, 26, 851, 834])).
% 1.98/2.16 tff(3558,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3559,plain,
% 1.98/2.16 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.98/2.16 inference(rewrite,[status(thm)],[])).
% 1.98/2.16 tff(3560,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.98/2.16 inference(monotonicity,[status(thm)],[3559])).
% 1.98/2.16 tff(3561,plain,
% 1.98/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.98/2.16 inference(transitivity,[status(thm)],[3560, 3558])).
% 1.98/2.16 tff(3562,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.98/2.16 inference(quant_inst,[status(thm)],[])).
% 1.98/2.16 tff(3563,plain,
% 1.98/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3562, 3561])).
% 1.98/2.17 tff(3564,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3563, 198, 95, 1801, 3557, 3556])).
% 1.98/2.17 tff(3565,plain,(r(elem!1, s(elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (s(elem!1) = elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3566,plain,
% 1.98/2.17 (r(elem!1, s(elem!1))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3565, 1801, 851, 834, 95])).
% 1.98/2.17 tff(3567,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3568,plain,
% 1.98/2.17 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3569,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3568])).
% 1.98/2.17 tff(3570,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3569, 3567])).
% 1.98/2.17 tff(3571,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3572,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 1.98/2.17 tff(3573,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3572, 163, 1115, 3566, 3551, 1220])).
% 1.98/2.17 tff(3574,plain,((~b(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3575,plain,
% 1.98/2.17 (r(s(elem!1), elem!1)),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3574, 3543, 1115, 95, 1701, 723, 1220, 834, 3535])).
% 1.98/2.17 tff(3576,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3577,plain,
% 1.98/2.17 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3578,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1)))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3577])).
% 1.98/2.17 tff(3579,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3578, 3576])).
% 1.98/2.17 tff(3580,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3581,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1)))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.98/2.17 tff(3582,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3581, 163, 1115, 1474, 1473, 1220])).
% 1.98/2.17 tff(3583,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3584,plain,
% 1.98/2.17 (~r(elem!1, s(elem!1))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3583, 3575, 1115, 1220])).
% 1.98/2.17 tff(3585,plain,
% 1.98/2.17 (b(elem!1, s(elem!1))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[1416, 3584, 2506])).
% 1.98/2.17 tff(3586,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[1994, 198, 271, 3535, 3543, 3585])).
% 1.98/2.17 tff(3587,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), z)) | (s(elem!1) = elem!1) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3588,plain,
% 1.98/2.17 (~r(s(elem!1), s(s(elem!1)))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3587, 3430, 3527, 3431, 3525, 3524, 3517, 1097])).
% 1.98/2.17 tff(3589,plain,
% 1.98/2.17 (b(s(elem!1), s(s(elem!1)))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[901, 3588, 3519])).
% 1.98/2.17 tff(3590,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3591,plain,
% 1.98/2.17 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3592,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3591])).
% 1.98/2.17 tff(3593,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3592, 3590])).
% 1.98/2.17 tff(3594,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3595,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3594, 3593])).
% 1.98/2.17 tff(3596,plain,
% 1.98/2.17 (~b(elem!1, s(elem!1))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3595, 198, 3430, 3524, 3589, 3515])).
% 1.98/2.17 tff(3597,plain,
% 1.98/2.17 (r(elem!1, s(elem!1))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[1416, 3596, 3518])).
% 1.98/2.17 tff(3598,plain,
% 1.98/2.17 (~r(s(z), s(s(elem!1)))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[2264, 163, 3527, 3597, 2930])).
% 1.98/2.17 tff(3599,plain,
% 1.98/2.17 (b(s(z), s(s(elem!1)))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[642, 3598])).
% 1.98/2.17 tff(3600,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3601,plain,
% 1.98/2.17 (((~b(s(s(elem!1)), z)) | (~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(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3602,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3601])).
% 1.98/2.17 tff(3603,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3602, 3600])).
% 1.98/2.17 tff(3604,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3605,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3604, 3603])).
% 1.98/2.17 tff(3606,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3605, 198, 3430, 3524, 3599, 3515, 3433])).
% 1.98/2.17 tff(3607,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(z), elem!1) | r(z, elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3608,plain,
% 1.98/2.17 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3607, 150, 2, 149, 56, 42])).
% 1.98/2.17 tff(3609,plain,
% 1.98/2.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3610,plain,
% 1.98/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3611,plain,
% 1.98/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 1.98/2.17 tff(3612,plain,
% 1.98/2.17 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3611, 26])).
% 1.98/2.17 tff(3613,plain,
% 1.98/2.17 (b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3612, 312])).
% 1.98/2.17 tff(3614,plain,
% 1.98/2.17 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3613, 3608])).
% 1.98/2.17 tff(3615,assumption,(b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.98/2.17 tff(3616,plain,
% 1.98/2.17 (b(z, elem!1)),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[102, 3, 56])).
% 1.98/2.17 tff(3617,plain,
% 1.98/2.17 (~(elem!1 = z)),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[1079, 3])).
% 1.98/2.17 tff(3618,plain,
% 1.98/2.17 (~(s(elem!1) = s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[814, 3])).
% 1.98/2.17 tff(3619,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3620,plain,
% 1.98/2.17 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3621,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3620])).
% 1.98/2.17 tff(3622,plain,
% 1.98/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3621, 3619])).
% 1.98/2.17 tff(3623,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3624,plain,
% 1.98/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 1.98/2.17 tff(3625,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3624, 198, 560, 3615, 348, 2])).
% 1.98/2.17 tff(3626,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3627,plain,
% 1.98/2.17 (~b(s(s(z)), s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3626, 348, 2, 3615])).
% 1.98/2.17 tff(3628,plain,
% 1.98/2.17 (r(s(s(z)), s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[487, 3627])).
% 1.98/2.17 tff(3629,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3630,plain,
% 1.98/2.17 (((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3631,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3630])).
% 1.98/2.17 tff(3632,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.98/2.17 inference(transitivity,[status(thm)],[3631, 3629])).
% 1.98/2.17 tff(3633,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3634,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 1.98/2.17 tff(3635,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3634, 163, 236, 406, 153, 3450])).
% 1.98/2.17 tff(3636,plain,((~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3637,plain,
% 1.98/2.17 (~r(z, s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3636, 3628, 153, 236])).
% 1.98/2.17 tff(3638,plain,
% 1.98/2.17 (b(z, s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[593, 3637])).
% 1.98/2.17 tff(3639,assumption,(r(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.98/2.17 tff(3640,plain,
% 1.98/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.98/2.17 inference(rewrite,[status(thm)],[])).
% 1.98/2.17 tff(3641,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.98/2.17 inference(quant_inst,[status(thm)],[])).
% 1.98/2.17 tff(3642,plain,
% 1.98/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 1.98/2.17 tff(3643,plain,
% 1.98/2.17 ($false),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3642, 163, 150, 3450, 423, 3639])).
% 1.98/2.17 tff(3644,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.17 tff(3645,plain,
% 1.98/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.98/2.17 inference(unit_resolution,[status(thm)],[3644, 423, 3450, 150])).
% 1.98/2.17 tff(3646,plain,
% 1.98/2.17 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.17 inference(commutativity,[status(thm)],[])).
% 1.98/2.17 tff(3647,plain,
% 1.98/2.17 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.98/2.17 inference(symmetry,[status(thm)],[3646])).
% 1.98/2.17 tff(3648,plain,
% 1.98/2.17 ((~(s(z) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(z)))),
% 1.98/2.17 inference(monotonicity,[status(thm)],[3647])).
% 1.98/2.17 tff(3649,plain,
% 1.98/2.17 (~(s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.98/2.17 inference(modus_ponens,[status(thm)],[312, 3648])).
% 1.98/2.17 tff(3650,plain,
% 1.98/2.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3651,plain,
% 1.98/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3652,plain,
% 1.98/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.98/2.18 tff(3653,plain,
% 1.98/2.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3652, 26])).
% 1.98/2.18 tff(3654,plain,
% 1.98/2.18 (b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3653, 3649])).
% 1.98/2.18 tff(3655,plain,
% 1.98/2.18 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3654, 3645])).
% 1.98/2.18 tff(3656,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3657,plain,
% 1.98/2.18 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3658,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3657])).
% 1.98/2.18 tff(3659,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3658, 3656])).
% 1.98/2.18 tff(3660,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3661,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 1.98/2.18 tff(3662,plain,
% 1.98/2.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3661, 163, 153, 3450, 423])).
% 1.98/2.18 tff(3663,plain,
% 1.98/2.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[31, 3662])).
% 1.98/2.18 tff(3664,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3665,plain,
% 1.98/2.18 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3666,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3665])).
% 1.98/2.18 tff(3667,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3666, 3664])).
% 1.98/2.18 tff(3668,plain,
% 1.98/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3669,plain,
% 1.98/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3668, 3667])).
% 1.98/2.18 tff(3670,plain,
% 1.98/2.18 ($false),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3669, 198, 595, 3615, 3663, 3655])).
% 1.98/2.18 tff(3671,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.18 tff(3672,plain,
% 1.98/2.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3671, 3638, 153, 3615, 150, 3628])).
% 1.98/2.18 tff(3673,plain,
% 1.98/2.18 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[420, 3672])).
% 1.98/2.18 tff(3674,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3675,plain,
% 1.98/2.18 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3676,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3675])).
% 1.98/2.18 tff(3677,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3676, 3674])).
% 1.98/2.18 tff(3678,plain,
% 1.98/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3679,plain,
% 1.98/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 1.98/2.18 tff(3680,plain,
% 1.98/2.18 (~b(s(z), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3679, 198, 3615, 348, 3673, 2])).
% 1.98/2.18 tff(3681,plain,
% 1.98/2.18 (r(s(z), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[403, 3680])).
% 1.98/2.18 tff(3682,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3683,plain,
% 1.98/2.18 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3684,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3683])).
% 1.98/2.18 tff(3685,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3684, 3682])).
% 1.98/2.18 tff(3686,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3687,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.98/2.18 tff(3688,plain,
% 1.98/2.18 ($false),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3687, 163, 150, 3681, 153, 3628])).
% 1.98/2.18 tff(3689,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.18 tff(3690,plain,
% 1.98/2.18 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3689, 3435, 153, 3615, 2, 150])).
% 1.98/2.18 tff(3691,plain,
% 1.98/2.18 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[374, 3690])).
% 1.98/2.18 tff(3692,plain,
% 1.98/2.18 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3468, 1, 95])).
% 1.98/2.18 tff(3693,plain,
% 1.98/2.18 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[256, 3692, 244])).
% 1.98/2.18 tff(3694,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3695,plain,
% 1.98/2.18 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3696,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3695])).
% 1.98/2.18 tff(3697,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3696, 3694])).
% 1.98/2.18 tff(3698,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3699,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3698, 3697])).
% 1.98/2.18 tff(3700,plain,
% 1.98/2.18 ($false),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3699, 163, 153, 3272, 3693, 32])).
% 1.98/2.18 tff(3701,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.18 tff(3702,plain,
% 1.98/2.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3701, 3691, 153, 244, 95])).
% 1.98/2.18 tff(3703,plain,
% 1.98/2.18 (~b(z, s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3669, 198, 3615, 3702, 2])).
% 1.98/2.18 tff(3704,plain,
% 1.98/2.18 (r(z, s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[593, 3703])).
% 1.98/2.18 tff(3705,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3706,plain,
% 1.98/2.18 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3707,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3706])).
% 1.98/2.18 tff(3708,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3707, 3705])).
% 1.98/2.18 tff(3709,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3710,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3709, 3708])).
% 1.98/2.18 tff(3711,plain,
% 1.98/2.18 ($false),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3710, 163, 150, 328, 153, 3272])).
% 1.98/2.18 tff(3712,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.18 tff(3713,plain,
% 1.98/2.18 (~r(s(z), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3712, 3691, 153, 150])).
% 1.98/2.18 tff(3714,plain,
% 1.98/2.18 (b(s(z), s(s(z)))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[403, 3713])).
% 1.98/2.18 tff(3715,plain,
% 1.98/2.18 (~r(s(s(z)), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3636, 3704, 153, 3435])).
% 1.98/2.18 tff(3716,plain,
% 1.98/2.18 (b(s(s(z)), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[487, 3715])).
% 1.98/2.18 tff(3717,plain,
% 1.98/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3718,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.98/2.18 inference(quant_inst,[status(thm)],[])).
% 1.98/2.18 tff(3719,plain,
% 1.98/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.98/2.18 inference(modus_ponens,[status(thm)],[3718, 3717])).
% 1.98/2.18 tff(3720,plain,
% 1.98/2.18 (~r(s(s(elem!1)), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[3719, 163, 790, 150, 406])).
% 1.98/2.18 tff(3721,plain,
% 1.98/2.18 (b(s(s(elem!1)), s(z))),
% 1.98/2.18 inference(unit_resolution,[status(thm)],[626, 3720])).
% 1.98/2.18 tff(3722,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3723,plain,
% 1.98/2.18 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), 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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.18 inference(rewrite,[status(thm)],[])).
% 1.98/2.18 tff(3724,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.98/2.18 inference(monotonicity,[status(thm)],[3723])).
% 1.98/2.18 tff(3725,plain,
% 1.98/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.98/2.18 inference(transitivity,[status(thm)],[3724, 3722])).
% 1.98/2.18 tff(3726,plain,
% 1.98/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3727,plain,
% 1.98/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3726, 3725])).
% 1.98/2.19 tff(3728,plain,
% 1.98/2.19 (~b(s(s(elem!1)), s(s(z)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3727, 198, 1053, 3721, 560, 407])).
% 1.98/2.19 tff(3729,plain,
% 1.98/2.19 (r(s(s(elem!1)), s(s(z)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3497, 26, 3494, 3728])).
% 1.98/2.19 tff(3730,plain,
% 1.98/2.19 (~b(s(s(z)), s(s(elem!1)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3480, 198, 1053, 3721, 560])).
% 1.98/2.19 tff(3731,plain,
% 1.98/2.19 (r(s(s(z)), s(s(elem!1)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[2161, 26, 2154, 3730])).
% 1.98/2.19 tff(3732,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3733,plain,
% 1.98/2.19 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3734,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3733])).
% 1.98/2.19 tff(3735,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3734, 3732])).
% 1.98/2.19 tff(3736,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3737,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 1.98/2.19 tff(3738,plain,
% 1.98/2.19 ($false),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3737, 163, 790, 3731, 153, 3729])).
% 1.98/2.19 tff(3739,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.19 tff(3740,plain,
% 1.98/2.19 (~r(s(s(elem!1)), z)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3739, 3716, 2106, 153, 3714, 150, 3704])).
% 1.98/2.19 tff(3741,plain,
% 1.98/2.19 (b(s(s(elem!1)), z)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[801, 3740])).
% 1.98/2.19 tff(3742,plain,
% 1.98/2.19 (b(elem!1, z)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[187, 3447, 76])).
% 1.98/2.19 tff(3743,plain,
% 1.98/2.19 (~b(s(s(elem!1)), elem!1)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[1491, 198, 95, 3742, 3741])).
% 1.98/2.19 tff(3744,plain,
% 1.98/2.19 (~(s(s(elem!1)) = s(s(z)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3493, 2106])).
% 1.98/2.19 tff(3745,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 1.98/2.19 tff(3746,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3747,plain,
% 1.98/2.19 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3748,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3747])).
% 1.98/2.19 tff(3749,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3748, 3746])).
% 1.98/2.19 tff(3750,plain,
% 1.98/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3751,plain,
% 1.98/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 1.98/2.19 tff(3752,plain,
% 1.98/2.19 ($false),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3751, 198, 560, 407, 3745, 2])).
% 1.98/2.19 tff(3753,plain,((~b(s(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(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.19 tff(3754,plain,
% 1.98/2.19 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3753, 3716, 3714, 2])).
% 1.98/2.19 tff(3755,plain,
% 1.98/2.19 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[420, 3754])).
% 1.98/2.19 tff(3756,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3757,plain,
% 1.98/2.19 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3758,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3757])).
% 1.98/2.19 tff(3759,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3758, 3756])).
% 1.98/2.19 tff(3760,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3761,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 1.98/2.19 tff(3762,plain,
% 1.98/2.19 ($false),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3761, 163, 153, 3272, 423, 152])).
% 1.98/2.19 tff(3763,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.19 tff(3764,plain,
% 1.98/2.19 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3763, 3755, 3691, 153])).
% 1.98/2.19 tff(3765,plain,
% 1.98/2.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[176, 3764])).
% 1.98/2.19 tff(3766,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3767,plain,
% 1.98/2.19 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3768,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3767])).
% 1.98/2.19 tff(3769,plain,
% 1.98/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3768, 3766])).
% 1.98/2.19 tff(3770,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3771,plain,
% 1.98/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3770, 3769])).
% 1.98/2.19 tff(3772,plain,
% 1.98/2.19 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3771, 163, 3691, 3755])).
% 1.98/2.19 tff(3773,plain,
% 1.98/2.19 (s(s(elem!1)) = elem!1),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[140, 130])).
% 1.98/2.19 tff(3774,plain,
% 1.98/2.19 (elem!1 = s(s(elem!1))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[118, 3773])).
% 1.98/2.19 tff(3775,plain,
% 1.98/2.19 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[317, 3774])).
% 1.98/2.19 tff(3776,plain,
% 1.98/2.19 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[256, 3775, 244])).
% 1.98/2.19 tff(3777,plain,
% 1.98/2.19 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[671, 3776, 3774])).
% 1.98/2.19 tff(3778,plain,
% 1.98/2.19 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 1.98/2.19 inference(monotonicity,[status(thm)],[130])).
% 1.98/2.19 tff(3779,plain,
% 1.98/2.19 (b(s(s(elem!1)), z) <=> b(s(elem!1), z)),
% 1.98/2.19 inference(symmetry,[status(thm)],[3778])).
% 1.98/2.19 tff(3780,plain,
% 1.98/2.19 (elem!1 = s(s(elem!1))),
% 1.98/2.19 inference(symmetry,[status(thm)],[3773])).
% 1.98/2.19 tff(3781,plain,
% 1.98/2.19 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3780])).
% 1.98/2.19 tff(3782,plain,
% 1.98/2.19 (b(elem!1, z) <=> b(s(elem!1), z)),
% 1.98/2.19 inference(transitivity,[status(thm)],[3781, 3779])).
% 1.98/2.19 tff(3783,plain,
% 1.98/2.19 (b(s(elem!1), z)),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[271, 3782])).
% 1.98/2.19 tff(3784,plain,
% 1.98/2.19 (~(s(s(z)) = s(elem!1))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[227, 3434])).
% 1.98/2.19 tff(3785,plain,
% 1.98/2.19 (b(z, s(s(elem!1)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[97, 3774, 95])).
% 1.98/2.19 tff(3786,plain,
% 1.98/2.19 (b(s(s(elem!1)), z)),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[271, 3781])).
% 1.98/2.19 tff(3787,plain,
% 1.98/2.19 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.98/2.19 inference(symmetry,[status(thm)],[663])).
% 1.98/2.19 tff(3788,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.98/2.19 tff(3789,plain,
% 1.98/2.19 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3788, 3787])).
% 1.98/2.19 tff(3790,assumption,(~(s(s(s(s(s(s(s(z))))))) = elem!1)), introduced(assumption)).
% 1.98/2.19 tff(3791,plain,
% 1.98/2.19 ($false),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3790, 3789])).
% 1.98/2.19 tff(3792,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,[]))).
% 1.98/2.19 tff(3793,plain,
% 1.98/2.19 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3792, 3775])).
% 1.98/2.19 tff(3794,plain,
% 1.98/2.19 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[698, 696, 3773])).
% 1.98/2.19 tff(3795,plain,
% 1.98/2.19 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[703, 3794, 3793])).
% 1.98/2.19 tff(3796,plain,
% 1.98/2.19 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[711, 3795, 3774])).
% 1.98/2.19 tff(3797,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3798,plain,
% 1.98/2.19 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3799,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3798])).
% 1.98/2.19 tff(3800,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3799, 3797])).
% 1.98/2.19 tff(3801,plain,
% 1.98/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(quant_inst,[status(thm)],[])).
% 1.98/2.19 tff(3802,plain,
% 1.98/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 1.98/2.19 tff(3803,plain,
% 1.98/2.19 (~b(s(s(elem!1)), s(z))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3802, 198, 3615, 2, 3796])).
% 1.98/2.19 tff(3804,plain,
% 1.98/2.19 (r(s(s(elem!1)), s(z))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[626, 3803])).
% 1.98/2.19 tff(3805,plain,
% 1.98/2.19 (s(s(s(elem!1))) = s(elem!1)),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[2064, 3773])).
% 1.98/2.19 tff(3806,assumption,(s(s(s(s(s(z))))) = s(s(elem!1))), introduced(assumption)).
% 1.98/2.19 tff(3807,plain,
% 1.98/2.19 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3806])).
% 1.98/2.19 tff(3808,plain,
% 1.98/2.19 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.98/2.19 inference(transitivity,[status(thm)],[3807, 3805, 130])).
% 1.98/2.19 tff(3809,plain,
% 1.98/2.19 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3808])).
% 1.98/2.19 tff(3810,plain,
% 1.98/2.19 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.98/2.19 inference(symmetry,[status(thm)],[3809])).
% 1.98/2.19 tff(3811,plain,
% 1.98/2.19 (s(elem!1) = s(s(s(elem!1)))),
% 1.98/2.19 inference(symmetry,[status(thm)],[3805])).
% 1.98/2.19 tff(3812,plain,
% 1.98/2.19 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.98/2.19 inference(transitivity,[status(thm)],[136, 3811, 3810])).
% 1.98/2.19 tff(3813,plain,
% 1.98/2.19 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3806])).
% 1.98/2.19 tff(3814,plain,
% 1.98/2.19 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3813])).
% 1.98/2.19 tff(3815,plain,
% 1.98/2.19 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.98/2.19 inference(modus_ponens,[status(thm)],[314, 3814])).
% 1.98/2.19 tff(3816,plain,
% 1.98/2.19 ($false),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3815, 3812])).
% 1.98/2.19 tff(3817,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.98/2.19 tff(3818,plain,
% 1.98/2.19 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.98/2.19 inference(unit_resolution,[status(thm)],[3817, 130])).
% 1.98/2.19 tff(3819,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.98/2.19 tff(3820,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3821,plain,
% 1.98/2.19 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.19 inference(rewrite,[status(thm)],[])).
% 1.98/2.19 tff(3822,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.98/2.19 inference(monotonicity,[status(thm)],[3821])).
% 1.98/2.19 tff(3823,plain,
% 1.98/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.20 inference(transitivity,[status(thm)],[3822, 3820])).
% 1.98/2.20 tff(3824,plain,
% 1.98/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 1.98/2.20 inference(quant_inst,[status(thm)],[])).
% 1.98/2.20 tff(3825,plain,
% 1.98/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.98/2.20 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 1.98/2.20 tff(3826,plain,
% 1.98/2.20 (~b(s(s(s(s(s(z))))), s(z))),
% 1.98/2.20 inference(unit_resolution,[status(thm)],[3825, 198, 3819, 3615, 2])).
% 1.98/2.20 tff(3827,plain,
% 1.98/2.20 (r(s(s(s(s(s(z))))), s(z))),
% 1.98/2.20 inference(unit_resolution,[status(thm)],[469, 3826])).
% 1.98/2.20 tff(3828,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.98/2.20 tff(3829,plain,
% 1.98/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.98/2.20 inference(rewrite,[status(thm)],[])).
% 1.98/2.20 tff(3830,plain,
% 1.98/2.20 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.98/2.20 inference(rewrite,[status(thm)],[])).
% 1.98/2.20 tff(3831,plain,
% 1.98/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.98/2.20 inference(monotonicity,[status(thm)],[3830])).
% 1.98/2.20 tff(3832,plain,
% 1.98/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.98/2.20 inference(transitivity,[status(thm)],[3831, 3829])).
% 1.98/2.20 tff(3833,plain,
% 1.98/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.98/2.20 inference(quant_inst,[status(thm)],[])).
% 1.98/2.20 tff(3834,plain,
% 1.98/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 1.98/2.20 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 1.98/2.20 tff(3835,plain,
% 1.98/2.20 ($false),
% 1.98/2.20 inference(unit_resolution,[status(thm)],[3834, 163, 150, 153, 422, 3828])).
% 2.05/2.20 tff(3836,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3837,plain,
% 2.05/2.20 (~r(s(s(s(s(s(z))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3836, 3827, 153, 150])).
% 2.05/2.20 tff(3838,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.05/2.20 tff(3839,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.05/2.20 tff(3840,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[434, 26, 366, 3839, 3838])).
% 2.05/2.20 tff(3841,plain,(b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3842,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3841, 3837])).
% 2.05/2.20 tff(3843,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3844,plain,
% 2.05/2.20 (((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3845,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3844])).
% 2.05/2.20 tff(3846,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3845, 3843])).
% 2.05/2.20 tff(3847,plain,
% 2.05/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.05/2.20 inference(quant_inst,[status(thm)],[])).
% 2.05/2.20 tff(3848,plain,
% 2.05/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 2.05/2.20 tff(3849,plain,
% 2.05/2.20 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3848, 198, 83, 3819, 721])).
% 2.05/2.20 tff(3850,plain,
% 2.05/2.20 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3849, 3842])).
% 2.05/2.20 tff(3851,plain,
% 2.05/2.20 (~b(s(s(elem!1)), s(z))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3802, 198, 3615, 2, 721])).
% 2.05/2.20 tff(3852,plain,
% 2.05/2.20 (r(s(s(elem!1)), s(z))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[626, 3851])).
% 2.05/2.20 tff(3853,assumption,(r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 2.05/2.20 tff(3854,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3855,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(quant_inst,[status(thm)],[])).
% 2.05/2.20 tff(3856,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3855, 3854])).
% 2.05/2.20 tff(3857,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3856, 163, 150, 1219, 422, 3853])).
% 2.05/2.20 tff(3858,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3859,plain,
% 2.05/2.20 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3858, 3827, 3852, 150])).
% 2.05/2.20 tff(3860,assumption,(~(s(s(s(s(s(z))))) = s(s(elem!1)))), introduced(assumption)).
% 2.05/2.20 tff(3861,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3086, 26, 3860, 3859, 3850])).
% 2.05/2.20 tff(3862,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3863,plain,
% 2.05/2.20 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3862, 3796, 83, 3818, 150, 153, 3615, 2])).
% 2.05/2.20 tff(3864,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3098, 3863])).
% 2.05/2.20 tff(3865,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[136])).
% 2.05/2.20 tff(3866,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(symmetry,[status(thm)],[3865])).
% 2.05/2.20 tff(3867,plain,
% 2.05/2.20 (elem!1 = s(elem!1)),
% 2.05/2.20 inference(transitivity,[status(thm)],[3780, 136])).
% 2.05/2.20 tff(3868,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3867])).
% 2.05/2.20 tff(3869,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3868, 3866])).
% 2.05/2.20 tff(3870,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3867])).
% 2.05/2.20 tff(3871,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.20 inference(symmetry,[status(thm)],[3870])).
% 2.05/2.20 tff(3872,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[136])).
% 2.05/2.20 tff(3873,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.20 inference(transitivity,[status(thm)],[3872, 3871])).
% 2.05/2.20 tff(3874,plain,
% 2.05/2.20 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3873])).
% 2.05/2.20 tff(3875,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3876,plain,
% 2.05/2.20 (((~r(z, 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(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3877,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3876])).
% 2.05/2.20 tff(3878,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3877, 3875])).
% 2.05/2.20 tff(3879,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))),
% 2.05/2.20 inference(quant_inst,[status(thm)],[])).
% 2.05/2.20 tff(3880,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 2.05/2.20 tff(3881,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3880, 163, 3066, 153, 152, 3828])).
% 2.05/2.20 tff(3882,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3883,plain,
% 2.05/2.20 (~r(s(s(s(s(s(z))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3882, 3066, 153, 152])).
% 2.05/2.20 tff(3884,plain,
% 2.05/2.20 (b(s(s(s(s(s(z))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[434, 26, 366, 3883])).
% 2.05/2.20 tff(3885,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3886,plain,
% 2.05/2.20 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3887,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3886])).
% 2.05/2.20 tff(3888,plain,
% 2.05/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3887, 3885])).
% 2.05/2.20 tff(3889,plain,
% 2.05/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.05/2.20 inference(quant_inst,[status(thm)],[])).
% 2.05/2.20 tff(3890,plain,
% 2.05/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3889, 3888])).
% 2.05/2.20 tff(3891,plain,
% 2.05/2.20 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3890, 198, 723, 83, 3884])).
% 2.05/2.20 tff(3892,plain,
% 2.05/2.20 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3891, 3874])).
% 2.05/2.20 tff(3893,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 2.05/2.20 tff(3894,plain,
% 2.05/2.20 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3893, 713])).
% 2.05/2.20 tff(3895,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3894])).
% 2.05/2.20 tff(3896,plain,
% 2.05/2.20 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.20 inference(symmetry,[status(thm)],[3895])).
% 2.05/2.20 tff(3897,plain,
% 2.05/2.20 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3896])).
% 2.05/2.20 tff(3898,plain,
% 2.05/2.20 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[696, 3897])).
% 2.05/2.20 tff(3899,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3066, 3898])).
% 2.05/2.20 tff(3900,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3901,plain,
% 2.05/2.20 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3900, 3066, 696, 3773])).
% 2.05/2.20 tff(3902,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[528, 3901, 3892])).
% 2.05/2.20 tff(3903,plain,
% 2.05/2.20 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3902, 3869])).
% 2.05/2.20 tff(3904,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3905,plain,
% 2.05/2.20 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 2.05/2.20 inference(rewrite,[status(thm)],[])).
% 2.05/2.20 tff(3906,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1))))))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[3905])).
% 2.05/2.20 tff(3907,plain,
% 2.05/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 2.05/2.20 inference(transitivity,[status(thm)],[3906, 3904])).
% 2.05/2.20 tff(3908,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.20 inference(quant_inst,[status(thm)],[])).
% 2.05/2.20 tff(3909,plain,
% 2.05/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.05/2.20 inference(modus_ponens,[status(thm)],[3908, 3907])).
% 2.05/2.20 tff(3910,plain,
% 2.05/2.20 ($false),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3909, 163, 3066, 1219, 680, 3903])).
% 2.05/2.20 tff(3911,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~(s(elem!1) = s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.20 tff(3912,plain,
% 2.05/2.20 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[3911, 3864, 680, 130, 696, 723, 83, 153, 3804])).
% 2.05/2.20 tff(3913,plain,
% 2.05/2.20 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.20 inference(unit_resolution,[status(thm)],[176, 3912])).
% 2.05/2.20 tff(3914,plain,
% 2.05/2.20 (b(z, s(elem!1)) <=> b(z, s(s(elem!1)))),
% 2.05/2.20 inference(monotonicity,[status(thm)],[130])).
% 2.05/2.20 tff(3915,plain,
% 2.05/2.20 (b(z, s(s(elem!1))) <=> b(z, s(elem!1))),
% 2.05/2.20 inference(symmetry,[status(thm)],[3914])).
% 2.05/2.21 tff(3916,plain,
% 2.05/2.21 (b(z, s(elem!1))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[83, 3915])).
% 2.05/2.21 tff(3917,plain,
% 2.05/2.21 (r(s(elem!1), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[130])).
% 2.05/2.21 tff(3918,plain,
% 2.05/2.21 (r(s(s(elem!1)), s(z)) <=> r(s(elem!1), s(z))),
% 2.05/2.21 inference(symmetry,[status(thm)],[3917])).
% 2.05/2.21 tff(3919,plain,
% 2.05/2.21 (r(s(elem!1), s(z))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3804, 3918])).
% 2.05/2.21 tff(3920,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 2.05/2.21 tff(3921,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3922,plain,
% 2.05/2.21 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3923,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1)))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3922])).
% 2.05/2.21 tff(3924,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3923, 3921])).
% 2.05/2.21 tff(3925,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3926,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1)))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3925, 3924])).
% 2.05/2.21 tff(3927,plain,
% 2.05/2.21 (~r(s(s(z)), s(elem!1))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3926, 163, 150, 3450, 3920])).
% 2.05/2.21 tff(3928,plain,
% 2.05/2.21 (b(s(s(z)), s(elem!1))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[2120, 26, 232, 3927])).
% 2.05/2.21 tff(3929,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3930,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3931,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 2.05/2.21 tff(3932,plain,
% 2.05/2.21 (~r(s(s(z)), z)),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3931, 163, 150, 406, 3450])).
% 2.05/2.21 tff(3933,plain,
% 2.05/2.21 (b(s(s(z)), z)),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[345, 3932])).
% 2.05/2.21 tff(3934,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3935,plain,
% 2.05/2.21 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3936,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3935])).
% 2.05/2.21 tff(3937,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3936, 3934])).
% 2.05/2.21 tff(3938,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3939,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3938, 3937])).
% 2.05/2.21 tff(3940,plain,
% 2.05/2.21 ($false),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3939, 198, 1175, 1801, 3933, 3928])).
% 2.05/2.21 tff(3941,plain,((~r(s(s(z)), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.21 tff(3942,plain,
% 2.05/2.21 (~r(z, s(z))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3941, 3628, 150, 3920, 1801, 232, 1175])).
% 2.05/2.21 tff(3943,plain,
% 2.05/2.21 (b(z, s(z))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[593, 3942])).
% 2.05/2.21 tff(3944,plain,
% 2.05/2.21 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3671, 3943, 153, 3615, 150, 3628])).
% 2.05/2.21 tff(3945,plain,
% 2.05/2.21 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[420, 3944])).
% 2.05/2.21 tff(3946,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3947,plain,
% 2.05/2.21 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3948,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3947])).
% 2.05/2.21 tff(3949,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3948, 3946])).
% 2.05/2.21 tff(3950,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3951,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3950, 3949])).
% 2.05/2.21 tff(3952,plain,
% 2.05/2.21 (~b(s(z), s(s(z)))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3951, 198, 3615, 348, 3945])).
% 2.05/2.21 tff(3953,plain,
% 2.05/2.21 (r(s(z), s(s(z)))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[403, 3952])).
% 2.05/2.21 tff(3954,plain,
% 2.05/2.21 (~r(s(s(z)), z)),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[340, 3953, 150, 153])).
% 2.05/2.21 tff(3955,plain,
% 2.05/2.21 (b(s(s(z)), z)),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[345, 3954])).
% 2.05/2.21 tff(3956,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3957,plain,
% 2.05/2.21 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3958,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3957])).
% 2.05/2.21 tff(3959,plain,
% 2.05/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3958, 3956])).
% 2.05/2.21 tff(3960,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3961,plain,
% 2.05/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3960, 3959])).
% 2.05/2.21 tff(3962,plain,
% 2.05/2.21 ($false),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3961, 198, 3943, 3955, 3945, 2, 330])).
% 2.05/2.21 tff(3963,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.21 tff(3964,plain,
% 2.05/2.21 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3963, 3913, 2, 150, 153, 3615, 3919, 3916, 232, 1175])).
% 2.05/2.21 tff(3965,plain,
% 2.05/2.21 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[374, 3964])).
% 2.05/2.21 tff(3966,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3967,plain,
% 2.05/2.21 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3968,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3967])).
% 2.05/2.21 tff(3969,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3968, 3966])).
% 2.05/2.21 tff(3970,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3971,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.21 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 2.05/2.21 tff(3972,plain,
% 2.05/2.21 ($false),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3971, 163, 153, 3272, 33, 680])).
% 2.05/2.21 tff(3973,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.21 tff(3974,plain,
% 2.05/2.21 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3973, 3965, 153, 680])).
% 2.05/2.21 tff(3975,plain,
% 2.05/2.21 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[31, 3974])).
% 2.05/2.21 tff(3976,plain,
% 2.05/2.21 ($false),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[919, 198, 723, 83, 3975, 3913, 3796])).
% 2.05/2.21 tff(3977,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), z)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.21 tff(3978,plain,
% 2.05/2.21 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.21 inference(unit_resolution,[status(thm)],[3977, 723, 83, 153, 680, 2, 150, 3615, 232, 1175, 130])).
% 2.05/2.21 tff(3979,plain,
% 2.05/2.21 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 2.05/2.21 inference(rewrite,[status(thm)],[])).
% 2.05/2.21 tff(3980,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1))))))),
% 2.05/2.21 inference(monotonicity,[status(thm)],[3979])).
% 2.05/2.21 tff(3981,plain,
% 2.05/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1)))))),
% 2.05/2.21 inference(transitivity,[status(thm)],[3980, 3182])).
% 2.05/2.21 tff(3982,plain,
% 2.05/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.21 inference(quant_inst,[status(thm)],[])).
% 2.05/2.21 tff(3983,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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(elem!1))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 2.05/2.22 tff(3984,plain,
% 2.05/2.22 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3983, 163, 3066, 3978, 680])).
% 2.05/2.22 tff(3985,plain,
% 2.05/2.22 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3086, 26, 3818, 3984])).
% 2.05/2.22 tff(3986,plain,
% 2.05/2.22 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.05/2.22 inference(commutativity,[status(thm)],[])).
% 2.05/2.22 tff(3987,plain,
% 2.05/2.22 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[3986])).
% 2.05/2.22 tff(3988,plain,
% 2.05/2.22 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[3818, 3987])).
% 2.05/2.22 tff(3989,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(3990,plain,
% 2.05/2.22 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(3991,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[3990])).
% 2.05/2.22 tff(3992,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.22 inference(transitivity,[status(thm)],[3991, 3989])).
% 2.05/2.22 tff(3993,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(3994,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 2.05/2.22 tff(3995,plain,
% 2.05/2.22 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3994, 163, 3066, 3978, 680])).
% 2.05/2.22 tff(3996,plain,
% 2.05/2.22 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3400, 3995, 3988])).
% 2.05/2.22 tff(3997,plain,
% 2.05/2.22 (s(s(z)) = s(s(elem!1))),
% 2.05/2.22 inference(transitivity,[status(thm)],[2082, 3780])).
% 2.05/2.22 tff(3998,plain,
% 2.05/2.22 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[3997])).
% 2.05/2.22 tff(3999,plain,
% 2.05/2.22 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.05/2.22 inference(symmetry,[status(thm)],[3998])).
% 2.05/2.22 tff(4000,plain,
% 2.05/2.22 (s(s(elem!1)) = s(z)),
% 2.05/2.22 inference(transitivity,[status(thm)],[136, 135, 3999, 222])).
% 2.05/2.22 tff(4001,plain,
% 2.05/2.22 ($false),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[620, 4000])).
% 2.05/2.22 tff(4002,plain,((~(s(s(z)) = elem!1)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.22 tff(4003,plain,
% 2.05/2.22 (~(s(s(z)) = elem!1)),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4002, 130])).
% 2.05/2.22 tff(4004,plain,
% 2.05/2.22 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[713])).
% 2.05/2.22 tff(4005,plain,
% 2.05/2.22 (elem!1 = s(s(elem!1))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[118, 114])).
% 2.05/2.22 tff(4006,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4007,plain,
% 2.05/2.22 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4008,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[4007])).
% 2.05/2.22 tff(4009,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(transitivity,[status(thm)],[4008, 4006])).
% 2.05/2.22 tff(4010,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(4011,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4010, 4009])).
% 2.05/2.22 tff(4012,plain,
% 2.05/2.22 (~r(s(s(z)), s(s(elem!1)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4011, 163, 3272, 152, 681])).
% 2.05/2.22 tff(4013,plain,
% 2.05/2.22 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[90])).
% 2.05/2.22 tff(4014,plain,
% 2.05/2.22 (r(s(s(z)), s(s(elem!1)))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[2113, 4013])).
% 2.05/2.22 tff(4015,plain,
% 2.05/2.22 ($false),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[2907, 4014])).
% 2.05/2.22 tff(4016,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.22 tff(4017,plain,
% 2.05/2.22 (~r(s(s(z)), elem!1)),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4016, 4012, 4005])).
% 2.05/2.22 tff(4018,plain,
% 2.05/2.22 (b(s(s(z)), elem!1)),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[2139, 4017, 2105])).
% 2.05/2.22 tff(4019,plain,
% 2.05/2.22 (b(s(s(z)), s(s(elem!1)))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4018, 4004])).
% 2.05/2.22 tff(4020,plain,
% 2.05/2.22 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3973, 3272, 153, 680])).
% 2.05/2.22 tff(4021,plain,
% 2.05/2.22 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[31, 4020])).
% 2.05/2.22 tff(4022,plain,
% 2.05/2.22 (~b(z, s(z))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[3669, 198, 3615, 4021, 2])).
% 2.05/2.22 tff(4023,plain,
% 2.05/2.22 (r(z, s(z))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[593, 4022])).
% 2.05/2.22 tff(4024,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4025,plain,
% 2.05/2.22 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4026,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[4025])).
% 2.05/2.22 tff(4027,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(transitivity,[status(thm)],[4026, 4024])).
% 2.05/2.22 tff(4028,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(4029,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4028, 4027])).
% 2.05/2.22 tff(4030,plain,
% 2.05/2.22 ($false),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4029, 163, 406, 3272, 332, 152])).
% 2.05/2.22 tff(4031,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.22 tff(4032,plain,
% 2.05/2.22 (~r(s(s(z)), z)),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4031, 4023, 152, 3272])).
% 2.05/2.22 tff(4033,plain,
% 2.05/2.22 (b(s(s(z)), z)),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[345, 4032])).
% 2.05/2.22 tff(4034,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4035,plain,
% 2.05/2.22 (((~b(z, s(s(elem!1)))) | (~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(elem!1)), z)) | (~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)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4036,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[4035])).
% 2.05/2.22 tff(4037,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.05/2.22 inference(transitivity,[status(thm)],[4036, 4034])).
% 2.05/2.22 tff(4038,plain,
% 2.05/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(4039,plain,
% 2.05/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4038, 4037])).
% 2.05/2.22 tff(4040,plain,
% 2.05/2.22 ($false),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4039, 198, 723, 83, 4033, 4019])).
% 2.05/2.22 tff(4041,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.22 tff(4042,plain,
% 2.05/2.22 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4041, 152, 83, 114, 2105, 723, 681, 3615, 2, 153, 680])).
% 2.05/2.22 tff(4043,plain,
% 2.05/2.22 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[374, 4042])).
% 2.05/2.22 tff(4044,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4045,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(4046,plain,
% 2.05/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 2.05/2.22 tff(4047,plain,
% 2.05/2.22 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4046, 163, 150, 3628, 3827])).
% 2.05/2.22 tff(4048,plain,
% 2.05/2.22 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[511, 26, 508, 4047])).
% 2.05/2.22 tff(4049,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.05/2.22 tff(4050,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4051,plain,
% 2.05/2.22 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4052,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[4051])).
% 2.05/2.22 tff(4053,plain,
% 2.05/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(transitivity,[status(thm)],[4052, 4050])).
% 2.05/2.22 tff(4054,plain,
% 2.05/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.22 inference(quant_inst,[status(thm)],[])).
% 2.05/2.22 tff(4055,plain,
% 2.05/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.22 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 2.05/2.22 tff(4056,plain,
% 2.05/2.22 ($false),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4055, 198, 3819, 3615, 348, 3745, 2, 4049])).
% 2.05/2.22 tff(4057,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.22 tff(4058,plain,
% 2.05/2.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[4057, 348, 3615, 3819, 2, 4048])).
% 2.05/2.22 tff(4059,plain,
% 2.05/2.22 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.22 inference(unit_resolution,[status(thm)],[420, 4058])).
% 2.05/2.22 tff(4060,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4061,plain,
% 2.05/2.22 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.05/2.22 inference(rewrite,[status(thm)],[])).
% 2.05/2.22 tff(4062,plain,
% 2.05/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.05/2.22 inference(monotonicity,[status(thm)],[4061])).
% 2.05/2.23 tff(4063,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4062, 4060])).
% 2.05/2.23 tff(4064,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4065,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4064, 4063])).
% 2.05/2.23 tff(4066,plain,
% 2.05/2.23 ($false),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4065, 163, 153, 3628, 4059, 152])).
% 2.05/2.23 tff(4067,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.23 tff(4068,plain,
% 2.05/2.23 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4067, 4043, 152, 3615, 153, 2, 150])).
% 2.05/2.23 tff(4069,plain,
% 2.05/2.23 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3098, 4068])).
% 2.05/2.23 tff(4070,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4071,plain,
% 2.05/2.23 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4072,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4071])).
% 2.05/2.23 tff(4073,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4072, 4070])).
% 2.05/2.23 tff(4074,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4075,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4074, 4073])).
% 2.05/2.23 tff(4076,plain,
% 2.05/2.23 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4075, 163, 4069, 152, 681])).
% 2.05/2.23 tff(4077,plain,
% 2.05/2.23 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3086, 26, 3860, 4076])).
% 2.05/2.23 tff(4078,plain,
% 2.05/2.23 (~r(s(s(s(s(s(z))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3882, 4069, 153, 152])).
% 2.05/2.23 tff(4079,plain,
% 2.05/2.23 (b(s(s(s(s(s(z))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3841, 4078])).
% 2.05/2.23 tff(4080,plain,
% 2.05/2.23 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4081,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4080])).
% 2.05/2.23 tff(4082,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4081, 3885])).
% 2.05/2.23 tff(4083,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4084,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 2.05/2.23 tff(4085,plain,
% 2.05/2.23 ($false),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4084, 198, 723, 83, 4079, 4077])).
% 2.05/2.23 tff(4086,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~(s(s(elem!1)) = elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.23 tff(4087,plain,
% 2.05/2.23 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4086, 723, 83, 3818, 3978, 153, 3615, 2, 150, 3773, 4003, 680])).
% 2.05/2.23 tff(4088,plain,
% 2.05/2.23 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[176, 4087])).
% 2.05/2.23 tff(4089,plain,
% 2.05/2.23 (~b(s(s(s(s(s(z))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4084, 198, 723, 83, 3985])).
% 2.05/2.23 tff(4090,plain,
% 2.05/2.23 (r(s(s(s(s(s(z))))), z)),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3841, 4089])).
% 2.05/2.23 tff(4091,plain,
% 2.05/2.23 (~r(s(s(s(s(s(z))))), s(z))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3836, 4090, 153, 150])).
% 2.05/2.23 tff(4092,plain,
% 2.05/2.23 (b(s(s(s(s(s(z))))), s(z))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[469, 4091])).
% 2.05/2.23 tff(4093,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4094,plain,
% 2.05/2.23 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4095,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4094])).
% 2.05/2.23 tff(4096,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4095, 4093])).
% 2.05/2.23 tff(4097,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4098,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4097, 4096])).
% 2.05/2.23 tff(4099,plain,
% 2.05/2.23 (~b(z, s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4098, 198, 723, 83, 3996, 3985])).
% 2.05/2.23 tff(4100,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.05/2.23 tff(4101,plain,
% 2.05/2.23 (s(s(s(s(s(z))))) = z),
% 2.05/2.23 inference(symmetry,[status(thm)],[4100])).
% 2.05/2.23 tff(4102,plain,
% 2.05/2.23 ($false),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[366, 4101])).
% 2.05/2.23 tff(4103,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.23 tff(4104,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.05/2.23 tff(4105,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.05/2.23 tff(4106,plain,
% 2.05/2.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4107,plain,
% 2.05/2.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4108,plain,
% 2.05/2.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 2.05/2.23 tff(4109,plain,
% 2.05/2.23 ($false),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4108, 26, 4105, 4104, 4103])).
% 2.05/2.23 tff(4110,plain,(r(z, s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.23 tff(4111,plain,
% 2.05/2.23 (r(z, s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4110, 4099])).
% 2.05/2.23 tff(4112,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4113,plain,
% 2.05/2.23 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4114,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4113])).
% 2.05/2.23 tff(4115,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4114, 4112])).
% 2.05/2.23 tff(4116,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4117,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 2.05/2.23 tff(4118,plain,
% 2.05/2.23 (~r(s(z), s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4117, 163, 150, 4111, 4090])).
% 2.05/2.23 tff(4119,plain,
% 2.05/2.23 (b(s(z), s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3301, 4118])).
% 2.05/2.23 tff(4120,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4121,plain,
% 2.05/2.23 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4122,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4121])).
% 2.05/2.23 tff(4123,plain,
% 2.05/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4122, 4120])).
% 2.05/2.23 tff(4124,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4125,plain,
% 2.05/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4124, 4123])).
% 2.05/2.23 tff(4126,plain,
% 2.05/2.23 (~b(s(s(elem!1)), s(z))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4125, 198, 4119, 4092, 3996])).
% 2.05/2.23 tff(4127,plain,
% 2.05/2.23 (r(s(s(elem!1)), s(z))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[626, 4126])).
% 2.05/2.23 tff(4128,plain,
% 2.05/2.23 (r(s(elem!1), s(z))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4127, 3918])).
% 2.05/2.23 tff(4129,plain,
% 2.05/2.23 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[3963, 4128, 2, 150, 153, 3615, 4088, 3916, 232, 1175])).
% 2.05/2.23 tff(4130,plain,
% 2.05/2.23 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[374, 4129])).
% 2.05/2.23 tff(4131,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4132,plain,
% 2.05/2.23 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(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(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4133,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[4132])).
% 2.05/2.23 tff(4134,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(transitivity,[status(thm)],[4133, 4131])).
% 2.05/2.23 tff(4135,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.05/2.23 inference(quant_inst,[status(thm)],[])).
% 2.05/2.23 tff(4136,plain,
% 2.05/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.23 inference(modus_ponens,[status(thm)],[4135, 4134])).
% 2.05/2.23 tff(4137,plain,
% 2.05/2.23 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[4136, 163, 3066, 4130, 680])).
% 2.05/2.23 tff(4138,plain,
% 2.05/2.23 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.05/2.23 inference(unit_resolution,[status(thm)],[2715, 26, 507, 4137])).
% 2.05/2.23 tff(4139,plain,
% 2.05/2.23 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.05/2.23 inference(monotonicity,[status(thm)],[3780])).
% 2.05/2.23 tff(4140,plain,
% 2.05/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.23 inference(rewrite,[status(thm)],[])).
% 2.05/2.23 tff(4141,plain,
% 2.05/2.23 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4142,plain,
% 2.05/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4141])).
% 2.05/2.24 tff(4143,plain,
% 2.05/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4142, 4140])).
% 2.05/2.24 tff(4144,plain,
% 2.05/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.05/2.24 inference(quant_inst,[status(thm)],[])).
% 2.05/2.24 tff(4145,plain,
% 2.05/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4144, 4143])).
% 2.05/2.24 tff(4146,plain,
% 2.05/2.24 (~r(s(s(z)), s(s(elem!1)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4145, 163, 4130, 3978, 680])).
% 2.05/2.24 tff(4147,plain,
% 2.05/2.24 (~r(s(s(z)), elem!1)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4016, 4146, 3774])).
% 2.05/2.24 tff(4148,plain,
% 2.05/2.24 (b(s(s(z)), elem!1)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[2139, 4147, 4003])).
% 2.05/2.24 tff(4149,plain,
% 2.05/2.24 (b(s(s(z)), s(s(elem!1)))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4148, 4139])).
% 2.05/2.24 tff(4150,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4151,plain,
% 2.05/2.24 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4152,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4151])).
% 2.05/2.24 tff(4153,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4152, 4150])).
% 2.05/2.24 tff(4154,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.05/2.24 inference(quant_inst,[status(thm)],[])).
% 2.05/2.24 tff(4155,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 2.05/2.24 tff(4156,plain,
% 2.05/2.24 ($false),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4155, 198, 723, 83, 4149, 4138, 3996, 3985])).
% 2.05/2.24 tff(4157,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(s(elem!1), z)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.24 tff(4158,plain,
% 2.05/2.24 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4157, 3786, 3785, 3777, 2, 150, 153, 3615, 3784, 3783, 130])).
% 2.05/2.24 tff(4159,plain,
% 2.05/2.24 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3098, 4158])).
% 2.05/2.24 tff(4160,plain,
% 2.05/2.24 (~b(s(s(s(s(s(z))))), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3825, 198, 4159, 3615, 2])).
% 2.05/2.24 tff(4161,plain,
% 2.05/2.24 (r(s(s(s(s(s(z))))), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[469, 4160])).
% 2.05/2.24 tff(4162,plain,
% 2.05/2.24 (~r(s(s(s(s(s(z))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3836, 4161, 153, 150])).
% 2.05/2.24 tff(4163,plain,
% 2.05/2.24 (b(s(s(s(s(s(z))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3841, 4162])).
% 2.05/2.24 tff(4164,plain,
% 2.05/2.24 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3977, 3786, 3785, 153, 3777, 2, 150, 3615, 3784, 3783, 130])).
% 2.05/2.24 tff(4165,plain,
% 2.05/2.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4086, 3786, 3785, 3818, 4164, 153, 3615, 2, 150, 3773, 4003, 3777])).
% 2.05/2.24 tff(4166,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[176, 4165])).
% 2.05/2.24 tff(4167,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 2.05/2.24 tff(4168,plain,
% 2.05/2.24 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4169,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4168])).
% 2.05/2.24 tff(4170,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4169, 436])).
% 2.05/2.24 tff(4171,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(quant_inst,[status(thm)],[])).
% 2.05/2.24 tff(4172,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4171, 4170])).
% 2.05/2.24 tff(4173,plain,
% 2.05/2.24 ($false),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4172, 198, 3819, 331, 330, 4167])).
% 2.05/2.24 tff(4174,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.24 tff(4175,plain,
% 2.05/2.24 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4174, 4159, 4166, 4163])).
% 2.05/2.24 tff(4176,plain,
% 2.05/2.24 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[31, 4175])).
% 2.05/2.24 tff(4177,plain,
% 2.05/2.24 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3973, 4176, 153, 3777])).
% 2.05/2.24 tff(4178,plain,
% 2.05/2.24 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[374, 4177])).
% 2.05/2.24 tff(4179,plain,
% 2.05/2.24 (~b(s(s(z)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3626, 4178, 2, 3615])).
% 2.05/2.24 tff(4180,plain,
% 2.05/2.24 (r(s(s(z)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[487, 4179])).
% 2.05/2.24 tff(4181,plain,
% 2.05/2.24 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4046, 163, 150, 4180, 4161])).
% 2.05/2.24 tff(4182,plain,
% 2.05/2.24 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[511, 26, 508, 4181])).
% 2.05/2.24 tff(4183,plain,
% 2.05/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4057, 4182, 3615, 4159, 2, 4178])).
% 2.05/2.24 tff(4184,plain,
% 2.05/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[420, 4183])).
% 2.05/2.24 tff(4185,plain,
% 2.05/2.24 ($false),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3661, 163, 153, 4180, 4176, 4184])).
% 2.05/2.24 tff(4186,plain,((~(s(elem!1) = s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(elem!1, z)) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.24 tff(4187,plain,
% 2.05/2.24 (~(s(elem!1) = s(s(elem!1)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4186, 3742, 3615, 2, 150, 153, 244, 95])).
% 2.05/2.24 tff(4188,plain,
% 2.05/2.24 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3689, 236, 153, 3615, 2, 150])).
% 2.05/2.24 tff(4189,plain,
% 2.05/2.24 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[374, 4188])).
% 2.05/2.24 tff(4190,plain,
% 2.05/2.24 (~r(s(z), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3712, 4189, 153, 150])).
% 2.05/2.24 tff(4191,plain,
% 2.05/2.24 (b(s(z), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[403, 4190])).
% 2.05/2.24 tff(4192,plain,
% 2.05/2.24 (~b(z, s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3669, 198, 3615, 331, 2])).
% 2.05/2.24 tff(4193,plain,
% 2.05/2.24 (r(z, s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[593, 4192])).
% 2.05/2.24 tff(4194,plain,
% 2.05/2.24 (~r(s(s(z)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3636, 4193, 153, 236])).
% 2.05/2.24 tff(4195,plain,
% 2.05/2.24 (b(s(s(z)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[487, 4194])).
% 2.05/2.24 tff(4196,plain,
% 2.05/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3753, 4195, 4191, 2])).
% 2.05/2.24 tff(4197,plain,
% 2.05/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[420, 4196])).
% 2.05/2.24 tff(4198,plain,
% 2.05/2.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
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% 2.05/2.24 tff(4199,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[176, 4198])).
% 2.05/2.24 tff(4200,plain,
% 2.05/2.24 (~r(s(z), s(s(z)))),
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% 2.05/2.24 tff(4201,plain,
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% 2.05/2.24 inference(unit_resolution,[status(thm)],[403, 4200])).
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% 2.05/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
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% 2.05/2.24 tff(4203,plain,
% 2.05/2.24 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
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% 2.05/2.24 tff(4204,plain,
% 2.05/2.24 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3763, 4203, 3272, 153])).
% 2.05/2.24 tff(4205,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(s(z))))))), z)),
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% 2.05/2.24 tff(4206,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 2.05/2.24 tff(4207,plain,
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% 2.05/2.24 inference(unit_resolution,[status(thm)],[801, 4206])).
% 2.05/2.24 tff(4208,plain,
% 2.05/2.24 (~r(s(s(elem!1)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3719, 163, 4207, 150, 406])).
% 2.05/2.24 tff(4209,plain,
% 2.05/2.24 (b(s(s(elem!1)), s(z))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[626, 4208])).
% 2.05/2.24 tff(4210,plain,
% 2.05/2.24 (~r(s(z), s(s(elem!1)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[1051, 4207, 150, 153])).
% 2.05/2.24 tff(4211,plain,
% 2.05/2.24 (b(s(z), s(s(elem!1)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[642, 4210])).
% 2.05/2.24 tff(4212,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4213,plain,
% 2.05/2.24 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4214,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z)))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4213])).
% 2.05/2.24 tff(4215,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4214, 4212])).
% 2.05/2.24 tff(4216,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.24 inference(quant_inst,[status(thm)],[])).
% 2.05/2.24 tff(4217,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4216, 4215])).
% 2.05/2.24 tff(4218,plain,
% 2.05/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4217, 198, 4211, 4209, 2])).
% 2.05/2.24 tff(4219,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), introduced(assumption)).
% 2.05/2.24 tff(4220,plain,
% 2.05/2.24 ($false),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[941, 26, 669, 938, 4219])).
% 2.05/2.24 tff(4221,plain,(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))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.24 tff(4222,plain,
% 2.05/2.24 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4221, 4218, 669])).
% 2.05/2.24 tff(4223,plain,
% 2.05/2.24 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[3249, 4222])).
% 2.05/2.24 tff(4224,plain,
% 2.05/2.24 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4223])).
% 2.05/2.24 tff(4225,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(elem!1)), z)),
% 2.05/2.24 inference(symmetry,[status(thm)],[4224])).
% 2.05/2.24 tff(4226,plain,
% 2.05/2.24 (b(s(s(elem!1)), z)),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[330, 4225])).
% 2.05/2.24 tff(4227,plain,
% 2.05/2.24 ($false),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4206, 4226])).
% 2.05/2.24 tff(4228,plain,(b(s(s(elem!1)), z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.24 tff(4229,plain,
% 2.05/2.24 (b(s(s(elem!1)), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4228, 669, 4193, 2, 150, 4205, 153])).
% 2.05/2.24 tff(4230,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4231,plain,
% 2.05/2.24 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(rewrite,[status(thm)],[])).
% 2.05/2.24 tff(4232,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4231])).
% 2.05/2.24 tff(4233,plain,
% 2.05/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4232, 4230])).
% 2.05/2.24 tff(4234,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.05/2.24 inference(quant_inst,[status(thm)],[])).
% 2.05/2.24 tff(4235,plain,
% 2.05/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.24 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 2.05/2.24 tff(4236,plain,
% 2.05/2.24 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4235, 198, 95, 271, 4229, 331, 4205])).
% 2.05/2.24 tff(4237,plain,
% 2.05/2.24 ((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))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[934, 26, 4236])).
% 2.05/2.24 tff(4238,plain,
% 2.05/2.24 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4237, 696])).
% 2.05/2.24 tff(4239,plain,
% 2.05/2.24 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4238])).
% 2.05/2.24 tff(4240,plain,
% 2.05/2.24 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[135, 4239, 275])).
% 2.05/2.24 tff(4241,plain,
% 2.05/2.24 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4240])).
% 2.05/2.24 tff(4242,plain,
% 2.05/2.24 (elem!1 = inj_0(s(elem!1))),
% 2.05/2.24 inference(symmetry,[status(thm)],[129])).
% 2.05/2.24 tff(4243,plain,
% 2.05/2.24 (elem!1 = s(s(s(s(s(z)))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4242, 4241, 280])).
% 2.05/2.24 tff(4244,plain,
% 2.05/2.24 (b(elem!1, z) <=> b(s(s(s(s(s(z))))), z)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4243])).
% 2.05/2.24 tff(4245,plain,
% 2.05/2.24 (b(s(s(s(s(s(z))))), z) <=> b(elem!1, z)),
% 2.05/2.24 inference(symmetry,[status(thm)],[4244])).
% 2.05/2.24 tff(4246,plain,
% 2.05/2.24 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(elem!1, z))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4245])).
% 2.05/2.24 tff(4247,plain,
% 2.05/2.24 (b(s(s(elem!1)), z)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4228, 4193, 669, 2, 150, 330, 153])).
% 2.05/2.24 tff(4248,plain,
% 2.05/2.24 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[4235, 198, 95, 271, 4247, 331, 330])).
% 2.05/2.24 tff(4249,plain,
% 2.05/2.24 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[934, 26, 696, 4248])).
% 2.05/2.24 tff(4250,plain,
% 2.05/2.24 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4249])).
% 2.05/2.24 tff(4251,plain,
% 2.05/2.24 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.05/2.24 inference(symmetry,[status(thm)],[4249])).
% 2.05/2.24 tff(4252,plain,
% 2.05/2.24 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4249])).
% 2.05/2.24 tff(4253,plain,
% 2.05/2.24 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.05/2.24 inference(symmetry,[status(thm)],[4252])).
% 2.05/2.24 tff(4254,plain,
% 2.05/2.24 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.05/2.24 inference(transitivity,[status(thm)],[276, 4253, 134])).
% 2.05/2.24 tff(4255,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4254, 4251])).
% 2.05/2.24 tff(4256,plain,
% 2.05/2.24 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4255])).
% 2.05/2.24 tff(4257,plain,
% 2.05/2.24 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(elem!1), z)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4254])).
% 2.05/2.24 tff(4258,plain,
% 2.05/2.24 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 2.05/2.24 inference(symmetry,[status(thm)],[4257])).
% 2.05/2.24 tff(4259,plain,
% 2.05/2.24 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(elem!1), z)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4254])).
% 2.05/2.24 tff(4260,plain,
% 2.05/2.24 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(elem!1), z))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4259])).
% 2.05/2.24 tff(4261,plain,
% 2.05/2.24 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[135, 4252, 275])).
% 2.05/2.24 tff(4262,plain,
% 2.05/2.24 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4261])).
% 2.05/2.24 tff(4263,plain,
% 2.05/2.24 (elem!1 = s(s(s(s(s(z)))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4242, 4262, 280])).
% 2.05/2.24 tff(4264,plain,
% 2.05/2.24 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4263])).
% 2.05/2.24 tff(4265,plain,
% 2.05/2.24 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4249])).
% 2.05/2.24 tff(4266,plain,
% 2.05/2.24 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4265, 4264])).
% 2.05/2.24 tff(4267,plain,
% 2.05/2.24 (~b(s(s(elem!1)), elem!1)),
% 2.05/2.24 inference(unit_resolution,[status(thm)],[1491, 198, 95, 271, 4247])).
% 2.05/2.24 tff(4268,plain,
% 2.05/2.24 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.05/2.24 inference(monotonicity,[status(thm)],[4249])).
% 2.05/2.24 tff(4269,plain,
% 2.05/2.24 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.05/2.24 inference(transitivity,[status(thm)],[4268, 663])).
% 2.05/2.24 tff(4270,plain,
% 2.05/2.24 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 2.05/2.25 inference(symmetry,[status(thm)],[4269])).
% 2.05/2.25 tff(4271,plain,
% 2.05/2.25 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.05/2.25 inference(symmetry,[status(thm)],[4262])).
% 2.05/2.25 tff(4272,plain,
% 2.05/2.25 (s(s(s(s(s(z))))) = elem!1),
% 2.05/2.25 inference(transitivity,[status(thm)],[281, 4271, 129])).
% 2.05/2.25 tff(4273,plain,
% 2.05/2.25 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4272])).
% 2.05/2.25 tff(4274,plain,
% 2.05/2.25 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 2.05/2.25 inference(transitivity,[status(thm)],[4273, 4270])).
% 2.05/2.25 tff(4275,plain,
% 2.05/2.25 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4274])).
% 2.05/2.25 tff(4276,plain,
% 2.05/2.25 (~(s(s(elem!1)) = elem!1)),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[314, 4275])).
% 2.05/2.25 tff(4277,plain,
% 2.05/2.25 (r(s(s(elem!1)), elem!1)),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[602, 4276, 4267])).
% 2.05/2.25 tff(4278,plain,
% 2.05/2.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4277, 4266])).
% 2.05/2.25 tff(4279,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4280,plain,
% 2.05/2.25 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(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(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4281,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4280])).
% 2.05/2.25 tff(4282,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(transitivity,[status(thm)],[4281, 4279])).
% 2.05/2.25 tff(4283,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4284,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 2.05/2.25 tff(4285,plain,
% 2.05/2.25 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4284, 163, 3066, 3272, 4278])).
% 2.05/2.25 tff(4286,plain,
% 2.05/2.25 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[2715, 26, 507, 4285])).
% 2.05/2.25 tff(4287,plain,
% 2.05/2.25 (b(elem!1, z) <=> b(s(s(s(s(s(z))))), z)),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4263])).
% 2.05/2.25 tff(4288,plain,
% 2.05/2.25 (b(s(s(s(s(s(z))))), z)),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[271, 4287])).
% 2.05/2.25 tff(4289,plain,
% 2.05/2.25 (b(z, elem!1) <=> b(z, s(s(s(s(s(z))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4263])).
% 2.05/2.25 tff(4290,plain,
% 2.05/2.25 (b(z, s(s(s(s(s(z))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[95, 4289])).
% 2.05/2.25 tff(4291,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4292,plain,
% 2.05/2.25 (((~b(z, s(s(s(s(s(z))))))) | (~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(s(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))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4293,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~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(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4292])).
% 2.05/2.25 tff(4294,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~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(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 2.05/2.25 inference(transitivity,[status(thm)],[4293, 4291])).
% 2.05/2.25 tff(4295,plain,
% 2.05/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~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(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4296,plain,
% 2.05/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4295, 4294])).
% 2.05/2.25 tff(4297,plain,
% 2.05/2.25 (~b(s(s(z)), z)),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4296, 198, 4290, 4288, 4286])).
% 2.05/2.25 tff(4298,plain,
% 2.05/2.25 (r(s(s(z)), z)),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[345, 4297])).
% 2.05/2.25 tff(4299,plain,
% 2.05/2.25 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[2840])).
% 2.05/2.25 tff(4300,plain,
% 2.05/2.25 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.05/2.25 inference(symmetry,[status(thm)],[4299])).
% 2.05/2.25 tff(4301,plain,
% 2.05/2.25 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.05/2.25 inference(transitivity,[status(thm)],[276, 4300, 134])).
% 2.05/2.25 tff(4302,plain,
% 2.05/2.25 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), s(elem!1))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4301])).
% 2.05/2.25 tff(4303,plain,
% 2.05/2.25 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(symmetry,[status(thm)],[4302])).
% 2.05/2.25 tff(4304,plain,
% 2.05/2.25 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(elem!1))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4301])).
% 2.05/2.25 tff(4305,plain,
% 2.05/2.25 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4304])).
% 2.05/2.25 tff(4306,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 2.05/2.25 tff(4307,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4308,plain,
% 2.05/2.25 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4309,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4308])).
% 2.05/2.25 tff(4310,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(transitivity,[status(thm)],[4309, 4307])).
% 2.05/2.25 tff(4311,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4312,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 2.05/2.25 tff(4313,plain,
% 2.05/2.25 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4312, 163, 406, 332])).
% 2.05/2.25 tff(4314,plain,
% 2.05/2.25 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4313, 4306])).
% 2.05/2.25 tff(4315,plain,
% 2.05/2.25 (~r(s(s(z)), s(elem!1))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4314, 4305])).
% 2.05/2.25 tff(4316,plain,
% 2.05/2.25 (b(s(s(z)), s(elem!1))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[2378, 4315, 232])).
% 2.05/2.25 tff(4317,plain,
% 2.05/2.25 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4316, 4303])).
% 2.05/2.25 tff(4318,plain,
% 2.05/2.25 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), s(elem!1))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4301])).
% 2.05/2.25 tff(4319,plain,
% 2.05/2.25 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(symmetry,[status(thm)],[4318])).
% 2.05/2.25 tff(4320,plain,
% 2.05/2.25 (r(s(z), s(s(s(s(s(s(z))))))) <=> r(s(z), s(elem!1))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4301])).
% 2.05/2.25 tff(4321,plain,
% 2.05/2.25 ((~r(s(z), s(s(s(s(s(s(z)))))))) <=> (~r(s(z), s(elem!1)))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4320])).
% 2.05/2.25 tff(4322,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4323,plain,
% 2.05/2.25 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4324,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4323])).
% 2.05/2.25 tff(4325,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(transitivity,[status(thm)],[4324, 4322])).
% 2.05/2.25 tff(4326,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4327,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 2.05/2.25 tff(4328,plain,
% 2.05/2.25 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4327, 163, 150, 406])).
% 2.05/2.25 tff(4329,plain,
% 2.05/2.25 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4328, 4306])).
% 2.05/2.25 tff(4330,plain,
% 2.05/2.25 (~r(s(z), s(elem!1))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4329, 4321])).
% 2.05/2.25 tff(4331,plain,
% 2.05/2.25 (b(s(z), s(elem!1))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[1164, 4330, 1157])).
% 2.05/2.25 tff(4332,plain,
% 2.05/2.25 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4331, 4319])).
% 2.05/2.25 tff(4333,plain,
% 2.05/2.25 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4301])).
% 2.05/2.25 tff(4334,plain,
% 2.05/2.25 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.05/2.25 inference(symmetry,[status(thm)],[4333])).
% 2.05/2.25 tff(4335,plain,
% 2.05/2.25 ((~(s(elem!1) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4334])).
% 2.05/2.25 tff(4336,plain,
% 2.05/2.25 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[820, 4335])).
% 2.05/2.25 tff(4337,plain,
% 2.05/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4338,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4339,plain,
% 2.05/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 2.05/2.25 tff(4340,plain,
% 2.05/2.25 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4339, 163, 150, 406])).
% 2.05/2.25 tff(4341,plain,
% 2.05/2.25 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4340, 4306])).
% 2.05/2.25 tff(4342,plain,
% 2.05/2.25 (((~![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)))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4343,plain,
% 2.05/2.25 ((~![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)))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4344,plain,
% 2.05/2.25 ((~![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))),
% 2.05/2.25 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 2.05/2.25 tff(4345,plain,
% 2.05/2.25 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4344, 26, 4341])).
% 2.05/2.25 tff(4346,plain,
% 2.05/2.25 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.05/2.25 inference(unit_resolution,[status(thm)],[4345, 4336])).
% 2.05/2.25 tff(4347,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4348,plain,
% 2.05/2.25 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(rewrite,[status(thm)],[])).
% 2.05/2.25 tff(4349,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.05/2.25 inference(monotonicity,[status(thm)],[4348])).
% 2.05/2.25 tff(4350,plain,
% 2.05/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.05/2.25 inference(transitivity,[status(thm)],[4349, 4347])).
% 2.05/2.25 tff(4351,plain,
% 2.05/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.05/2.25 inference(quant_inst,[status(thm)],[])).
% 2.05/2.25 tff(4352,plain,
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% 2.05/2.25 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 2.05/2.25 tff(4353,plain,
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% 2.05/2.25 tff(4355,plain,
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% 2.05/2.25 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
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% 2.05/2.25 inference(monotonicity,[status(thm)],[4360])).
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% 2.05/2.26 inference(modus_ponens,[status(thm)],[4363, 4362])).
% 2.05/2.26 tff(4365,plain,
% 2.05/2.26 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4364, 198, 331, 330])).
% 2.05/2.26 tff(4366,plain,
% 2.05/2.26 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4365, 4358])).
% 2.05/2.26 tff(4367,plain,
% 2.05/2.26 (~b(s(elem!1), s(s(elem!1)))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4366, 4256])).
% 2.05/2.26 tff(4368,plain,
% 2.05/2.26 (r(s(elem!1), s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[901, 4367, 890])).
% 2.05/2.26 tff(4369,plain,
% 2.05/2.26 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4368, 4250])).
% 2.05/2.26 tff(4370,plain,
% 2.05/2.26 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4263])).
% 2.05/2.26 tff(4371,plain,
% 2.05/2.26 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(symmetry,[status(thm)],[4370])).
% 2.05/2.26 tff(4372,plain,
% 2.05/2.26 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[3066, 4371])).
% 2.05/2.26 tff(4373,plain,
% 2.05/2.26 (~(s(elem!1) = elem!1)),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[1762, 2968])).
% 2.05/2.26 tff(4374,plain,
% 2.05/2.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4254, 4272])).
% 2.05/2.26 tff(4375,plain,
% 2.05/2.26 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4374])).
% 2.05/2.26 tff(4376,plain,
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% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4377,plain,
% 2.05/2.26 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4378,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4377])).
% 2.05/2.26 tff(4379,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4378, 4376])).
% 2.05/2.26 tff(4380,plain,
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% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4381,plain,
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% 2.05/2.26 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 2.05/2.26 tff(4382,plain,
% 2.05/2.26 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4381, 198, 331, 330, 4290, 4288])).
% 2.05/2.26 tff(4383,plain,
% 2.05/2.26 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4382, 4358])).
% 2.05/2.26 tff(4384,plain,
% 2.05/2.26 (~b(s(elem!1), elem!1)),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4383, 4375])).
% 2.05/2.26 tff(4385,plain,
% 2.05/2.26 (r(s(elem!1), elem!1)),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[856, 4384, 4373])).
% 2.05/2.26 tff(4386,plain,
% 2.05/2.26 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[3376, 4385, 4278, 4372])).
% 2.05/2.26 tff(4387,plain,
% 2.05/2.26 ($false),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4386, 4369])).
% 2.05/2.26 tff(4388,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(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))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.26 tff(4389,plain,
% 2.05/2.26 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4388, 696, 331, 560, 820, 232, 150, 890, 3272, 271, 95, 4205, 669, 2, 153, 3615])).
% 2.05/2.26 tff(4390,plain,
% 2.05/2.26 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[3098, 4389])).
% 2.05/2.26 tff(4391,plain,
% 2.05/2.26 (~b(s(s(s(s(s(z))))), z)),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4174, 4390, 4205, 331])).
% 2.05/2.26 tff(4392,plain,
% 2.05/2.26 (~b(elem!1, z)),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4391, 4246])).
% 2.05/2.26 tff(4393,plain,
% 2.05/2.26 ($false),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[271, 4392])).
% 2.05/2.26 tff(4394,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.26 tff(4395,plain,
% 2.05/2.26 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4394, 669, 331, 4195, 820, 232, 150, 890, 4189, 95, 271, 2, 153, 3615])).
% 2.05/2.26 tff(4396,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4397,plain,
% 2.05/2.26 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4398,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4397])).
% 2.05/2.26 tff(4399,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4398, 4396])).
% 2.05/2.26 tff(4400,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4401,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 2.05/2.26 tff(4402,plain,
% 2.05/2.26 (~r(s(s(elem!1)), s(s(z)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4401, 163, 4189, 4197, 4395])).
% 2.05/2.26 tff(4403,plain,
% 2.05/2.26 (b(s(s(elem!1)), s(s(z)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[3497, 26, 4402, 3744])).
% 2.05/2.26 tff(4404,plain,
% 2.05/2.26 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4405,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4404])).
% 2.05/2.26 tff(4406,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4405, 3483])).
% 2.05/2.26 tff(4407,plain,
% 2.05/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4408,plain,
% 2.05/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 2.05/2.26 tff(4409,plain,
% 2.05/2.26 (~b(s(s(elem!1)), s(z))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4408, 198, 4195, 4191, 4403])).
% 2.05/2.26 tff(4410,plain,
% 2.05/2.26 (r(s(s(elem!1)), s(z))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[626, 4409])).
% 2.05/2.26 tff(4411,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4412,plain,
% 2.05/2.26 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4413,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4412])).
% 2.05/2.26 tff(4414,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4413, 4411])).
% 2.05/2.26 tff(4415,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4416,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 2.05/2.26 tff(4417,plain,
% 2.05/2.26 (~r(z, s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4416, 163, 236, 4193, 4410])).
% 2.05/2.26 tff(4418,plain,
% 2.05/2.26 (b(z, s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[1096, 4417])).
% 2.05/2.26 tff(4419,plain,
% 2.05/2.26 (b(s(s(elem!1)), z)),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4228, 669, 4193, 2, 150, 4199, 153])).
% 2.05/2.26 tff(4420,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4421,plain,
% 2.05/2.26 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4422,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4421])).
% 2.05/2.26 tff(4423,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4422, 4420])).
% 2.05/2.26 tff(4424,plain,
% 2.05/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4425,plain,
% 2.05/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4424, 4423])).
% 2.05/2.26 tff(4426,plain,
% 2.05/2.26 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4425, 198, 95, 271, 4419, 4418, 4199])).
% 2.05/2.26 tff(4427,plain,
% 2.05/2.26 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4221, 4426, 669])).
% 2.05/2.26 tff(4428,plain,
% 2.05/2.26 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(elem!1)))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4427])).
% 2.05/2.26 tff(4429,plain,
% 2.05/2.26 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.26 inference(symmetry,[status(thm)],[4428])).
% 2.05/2.26 tff(4430,plain,
% 2.05/2.26 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4429])).
% 2.05/2.26 tff(4431,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4432,plain,
% 2.05/2.26 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(rewrite,[status(thm)],[])).
% 2.05/2.26 tff(4433,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.26 inference(monotonicity,[status(thm)],[4432])).
% 2.05/2.26 tff(4434,plain,
% 2.05/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.26 inference(transitivity,[status(thm)],[4433, 4431])).
% 2.05/2.26 tff(4435,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.05/2.26 inference(quant_inst,[status(thm)],[])).
% 2.05/2.26 tff(4436,plain,
% 2.05/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.26 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 2.05/2.26 tff(4437,plain,
% 2.05/2.26 (~r(s(s(z)), s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[4436, 163, 4189, 4197, 4395])).
% 2.05/2.26 tff(4438,plain,
% 2.05/2.26 (b(s(s(z)), s(s(elem!1)))),
% 2.05/2.26 inference(unit_resolution,[status(thm)],[2161, 26, 4437, 2106])).
% 2.05/2.26 tff(4439,plain,
% 2.05/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4440,plain,
% 2.05/2.27 (((~b(s(s(elem!1)), s(s(z)))) | (~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(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4441,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4440])).
% 2.05/2.27 tff(4442,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.05/2.27 inference(transitivity,[status(thm)],[4441, 4439])).
% 2.05/2.27 tff(4443,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.05/2.27 inference(quant_inst,[status(thm)],[])).
% 2.05/2.27 tff(4444,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4443, 4442])).
% 2.05/2.27 tff(4445,plain,
% 2.05/2.27 (~b(s(z), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4444, 198, 4191, 4438, 4403])).
% 2.05/2.27 tff(4446,plain,
% 2.05/2.27 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4445, 4430])).
% 2.05/2.27 tff(4447,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3615, 4446])).
% 2.05/2.27 tff(4448,plain,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4449,plain,
% 2.05/2.27 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4448, 3742, 95, 3615, 3435, 3702, 820, 3784, 150, 4187, 2, 153])).
% 2.05/2.27 tff(4450,plain,
% 2.05/2.27 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[2840])).
% 2.05/2.27 tff(4451,plain,
% 2.05/2.27 (r(s(s(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(elem!1)))),
% 2.05/2.27 inference(symmetry,[status(thm)],[4450])).
% 2.05/2.27 tff(4452,plain,
% 2.05/2.27 ((~r(s(s(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(elem!1))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4451])).
% 2.05/2.27 tff(4453,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.05/2.27 tff(4454,plain,
% 2.05/2.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4453, 4452])).
% 2.05/2.27 tff(4455,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[680, 4454])).
% 2.05/2.27 tff(4456,plain,((~(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)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4457,plain,
% 2.05/2.27 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4456, 4449, 3772])).
% 2.05/2.27 tff(4458,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4459,plain,
% 2.05/2.27 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4460,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4459])).
% 2.05/2.27 tff(4461,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(transitivity,[status(thm)],[4460, 4458])).
% 2.05/2.27 tff(4462,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.05/2.27 inference(quant_inst,[status(thm)],[])).
% 2.05/2.27 tff(4463,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4462, 4461])).
% 2.05/2.27 tff(4464,plain,
% 2.05/2.27 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4463, 198, 4211, 4209, 3615, 2])).
% 2.05/2.27 tff(4465,plain,
% 2.05/2.27 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[934, 26, 696, 4464])).
% 2.05/2.27 tff(4466,plain,
% 2.05/2.27 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4465])).
% 2.05/2.27 tff(4467,plain,
% 2.05/2.27 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(elem!1)), z)),
% 2.05/2.27 inference(symmetry,[status(thm)],[4466])).
% 2.05/2.27 tff(4468,plain,
% 2.05/2.27 (b(s(s(elem!1)), z)),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[330, 4467])).
% 2.05/2.27 tff(4469,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4206, 4468])).
% 2.05/2.27 tff(4470,plain,(b(s(s(elem!1)), z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4471,plain,
% 2.05/2.27 (b(s(s(elem!1)), z)),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4470, 696, 330, 3615, 2, 150, 4193, 153])).
% 2.05/2.27 tff(4472,plain,
% 2.05/2.27 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4235, 198, 95, 271, 4471, 331, 330])).
% 2.05/2.27 tff(4473,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[934, 26, 696, 4472, 930])).
% 2.05/2.27 tff(4474,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4475,plain,
% 2.05/2.27 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4474, 4457, 95, 3742, 3702, 3765, 3615, 2, 150, 153])).
% 2.05/2.27 tff(4476,plain,
% 2.05/2.27 (~r(s(s(elem!1)), s(s(z)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4401, 163, 3691, 3755, 4475])).
% 2.05/2.27 tff(4477,plain,
% 2.05/2.27 (b(s(s(elem!1)), s(s(z)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3497, 26, 4476, 3744])).
% 2.05/2.27 tff(4478,plain,
% 2.05/2.27 (~b(s(s(elem!1)), s(z))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4408, 198, 3716, 3714, 4477])).
% 2.05/2.27 tff(4479,plain,
% 2.05/2.27 (r(s(s(elem!1)), s(z))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[626, 4478])).
% 2.05/2.27 tff(4480,plain,
% 2.05/2.27 (~r(z, s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4416, 163, 3435, 3704, 4479])).
% 2.05/2.27 tff(4481,plain,
% 2.05/2.27 (b(z, s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[1096, 4480])).
% 2.05/2.27 tff(4482,plain,
% 2.05/2.27 (~b(elem!1, s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[1071, 4481, 3742, 3741])).
% 2.05/2.27 tff(4483,plain,
% 2.05/2.27 (r(elem!1, s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[147, 1856, 85])).
% 2.05/2.27 tff(4484,plain,
% 2.05/2.27 (r(s(s(elem!1)), elem!1)),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[602, 138, 597])).
% 2.05/2.27 tff(4485,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[609, 163, 4484, 236, 4483, 1219])).
% 2.05/2.27 tff(4486,plain,((s(s(elem!1)) = elem!1) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | b(elem!1, s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4487,plain,
% 2.05/2.27 (s(s(elem!1)) = elem!1),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4486, 3435, 4479, 4482, 3743])).
% 2.05/2.27 tff(4488,plain,
% 2.05/2.27 (elem!1 = s(s(elem!1))),
% 2.05/2.27 inference(symmetry,[status(thm)],[4487])).
% 2.05/2.27 tff(4489,plain,
% 2.05/2.27 (~b(s(s(s(s(s(z))))), z)),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4174, 3819, 330, 331])).
% 2.05/2.27 tff(4490,plain,
% 2.05/2.27 (r(s(s(s(s(s(z))))), z)),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3841, 4489])).
% 2.05/2.27 tff(4491,plain,
% 2.05/2.27 (~r(s(s(s(s(s(z))))), s(z))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3836, 4490, 153, 150])).
% 2.05/2.27 tff(4492,plain,
% 2.05/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[469, 4491])).
% 2.05/2.27 tff(4493,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3825, 198, 3819, 3615, 2, 4492])).
% 2.05/2.27 tff(4494,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.27 tff(4495,plain,
% 2.05/2.27 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4494, 3765, 2, 153, 150, 3615, 3702])).
% 2.05/2.27 tff(4496,plain,
% 2.05/2.27 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3098, 4495])).
% 2.05/2.27 tff(4497,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4498,plain,
% 2.05/2.27 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4499,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4498])).
% 2.05/2.27 tff(4500,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(transitivity,[status(thm)],[4499, 4497])).
% 2.05/2.27 tff(4501,plain,
% 2.05/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.05/2.27 inference(quant_inst,[status(thm)],[])).
% 2.05/2.27 tff(4502,plain,
% 2.05/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 2.05/2.27 tff(4503,plain,
% 2.05/2.27 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4502, 163, 4496, 3691, 3755])).
% 2.05/2.27 tff(4504,plain,
% 2.05/2.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[511, 26, 508, 4503])).
% 2.05/2.27 tff(4505,plain,
% 2.05/2.27 (~r(s(s(z)), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4436, 163, 3691, 3755, 4475])).
% 2.05/2.27 tff(4506,plain,
% 2.05/2.27 (b(s(s(z)), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[2161, 26, 4505, 2106])).
% 2.05/2.27 tff(4507,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4508,plain,
% 2.05/2.27 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4509,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4508])).
% 2.05/2.27 tff(4510,plain,
% 2.05/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.27 inference(transitivity,[status(thm)],[4509, 4507])).
% 2.05/2.27 tff(4511,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.05/2.27 inference(quant_inst,[status(thm)],[])).
% 2.05/2.27 tff(4512,plain,
% 2.05/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4511, 4510])).
% 2.05/2.27 tff(4513,plain,
% 2.05/2.27 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4512, 198, 3716, 3714, 4506, 4504, 4477])).
% 2.05/2.27 tff(4514,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4515,plain,
% 2.05/2.27 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(rewrite,[status(thm)],[])).
% 2.05/2.27 tff(4516,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4515])).
% 2.05/2.27 tff(4517,plain,
% 2.05/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.27 inference(transitivity,[status(thm)],[4516, 4514])).
% 2.05/2.27 tff(4518,plain,
% 2.05/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.27 inference(quant_inst,[status(thm)],[])).
% 2.05/2.27 tff(4519,plain,
% 2.05/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.27 inference(modus_ponens,[status(thm)],[4518, 4517])).
% 2.05/2.27 tff(4520,plain,
% 2.05/2.27 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4519, 163, 4496, 3755, 4475])).
% 2.05/2.27 tff(4521,plain,
% 2.05/2.27 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3086, 26, 4520])).
% 2.05/2.27 tff(4522,plain,
% 2.05/2.27 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[4521, 4513])).
% 2.05/2.27 tff(4523,plain,
% 2.05/2.27 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4522])).
% 2.05/2.27 tff(4524,plain,
% 2.05/2.27 (s(s(s(s(z)))) = s(elem!1)),
% 2.05/2.27 inference(transitivity,[status(thm)],[289, 4523, 134])).
% 2.05/2.27 tff(4525,plain,
% 2.05/2.27 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4524])).
% 2.05/2.27 tff(4526,plain,
% 2.05/2.27 (s(s(s(z))) = s(s(elem!1))),
% 2.05/2.27 inference(transitivity,[status(thm)],[294, 4525, 129, 4488])).
% 2.05/2.27 tff(4527,plain,
% 2.05/2.27 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.05/2.27 inference(monotonicity,[status(thm)],[4526])).
% 2.05/2.27 tff(4528,plain,
% 2.05/2.27 (s(s(z)) = s(elem!1)),
% 2.05/2.27 inference(transitivity,[status(thm)],[299, 4527, 134])).
% 2.05/2.27 tff(4529,plain,
% 2.05/2.27 ($false),
% 2.05/2.27 inference(unit_resolution,[status(thm)],[3784, 4528])).
% 2.05/2.27 tff(4530,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4531,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4530, 95, 153, 150, 3615, 2, 3618, 3617, 149])).
% 2.05/2.28 tff(4532,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4533,plain,
% 2.05/2.28 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4534,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4533])).
% 2.05/2.28 tff(4535,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.28 inference(transitivity,[status(thm)],[4534, 4532])).
% 2.05/2.28 tff(4536,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 2.05/2.28 inference(quant_inst,[status(thm)],[])).
% 2.05/2.28 tff(4537,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 2.05/2.28 tff(4538,plain,
% 2.05/2.28 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4537, 198, 95, 3615, 4531])).
% 2.05/2.28 tff(4539,plain,
% 2.05/2.28 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4538, 595])).
% 2.05/2.28 tff(4540,plain,
% 2.05/2.28 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[31, 4539])).
% 2.05/2.28 tff(4541,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4542,plain,
% 2.05/2.28 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4543,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4542])).
% 2.05/2.28 tff(4544,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(transitivity,[status(thm)],[4543, 4541])).
% 2.05/2.28 tff(4545,plain,
% 2.05/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 2.05/2.28 inference(quant_inst,[status(thm)],[])).
% 2.05/2.28 tff(4546,plain,
% 2.05/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4545, 4544])).
% 2.05/2.28 tff(4547,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4546, 163, 153, 3272, 33, 152])).
% 2.05/2.28 tff(4548,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4549,plain,
% 2.05/2.28 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4548, 4540, 153, 152])).
% 2.05/2.28 tff(4550,plain,
% 2.05/2.28 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[374, 4549])).
% 2.05/2.28 tff(4551,plain,
% 2.05/2.28 (~r(s(z), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3689, 4550, 153, 3615, 2, 150])).
% 2.05/2.28 tff(4552,plain,
% 2.05/2.28 (s(z) = elem!1),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[217, 4551, 149])).
% 2.05/2.28 tff(4553,plain,
% 2.05/2.28 (s(s(z)) = s(elem!1)),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4552])).
% 2.05/2.28 tff(4554,plain,
% 2.05/2.28 (s(elem!1) = s(s(z))),
% 2.05/2.28 inference(symmetry,[status(thm)],[4553])).
% 2.05/2.28 tff(4555,plain,
% 2.05/2.28 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4554])).
% 2.05/2.28 tff(4556,plain,
% 2.05/2.28 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(symmetry,[status(thm)],[4555])).
% 2.05/2.28 tff(4557,plain,
% 2.05/2.28 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4550, 4556])).
% 2.05/2.28 tff(4558,plain,
% 2.05/2.28 (~(s(elem!1) = elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[778, 4552, 3])).
% 2.05/2.28 tff(4559,plain,
% 2.05/2.28 (~(elem!1 = s(elem!1))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[1400, 4558])).
% 2.05/2.28 tff(4560,plain,
% 2.05/2.28 (~b(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3626, 4550, 2, 3615])).
% 2.05/2.28 tff(4561,plain,
% 2.05/2.28 (elem!1 = s(z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[2914, 4552])).
% 2.05/2.28 tff(4562,plain,
% 2.05/2.28 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[229])).
% 2.05/2.28 tff(4563,plain,
% 2.05/2.28 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.05/2.28 inference(symmetry,[status(thm)],[4562])).
% 2.05/2.28 tff(4564,plain,
% 2.05/2.28 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[230])).
% 2.05/2.28 tff(4565,plain,
% 2.05/2.28 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 2.05/2.28 inference(symmetry,[status(thm)],[4564])).
% 2.05/2.28 tff(4566,plain,
% 2.05/2.28 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 2.05/2.28 inference(transitivity,[status(thm)],[4565, 4563])).
% 2.05/2.28 tff(4567,plain,
% 2.05/2.28 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), elem!1))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4566])).
% 2.05/2.28 tff(4568,plain,
% 2.05/2.28 (~b(s(elem!1), elem!1)),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[482, 4567])).
% 2.05/2.28 tff(4569,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[1200, 4568])).
% 2.05/2.28 tff(4570,plain,(b(s(s(z)), s(z)) | (~b(s(elem!1), elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4571,plain,
% 2.05/2.28 (~b(s(elem!1), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4570, 4561, 4560])).
% 2.05/2.28 tff(4572,plain,
% 2.05/2.28 (r(s(elem!1), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[856, 4571, 4558])).
% 2.05/2.28 tff(4573,plain,
% 2.05/2.28 (r(elem!1, z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[212, 4552, 150])).
% 2.05/2.28 tff(4574,plain,
% 2.05/2.28 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4553])).
% 2.05/2.28 tff(4575,plain,
% 2.05/2.28 (r(z, s(elem!1))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[153, 4574])).
% 2.05/2.28 tff(4576,plain,
% 2.05/2.28 (~r(elem!1, s(elem!1))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[2523, 4575, 4573, 4572])).
% 2.05/2.28 tff(4577,plain,
% 2.05/2.28 (b(elem!1, s(elem!1))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[1416, 4576, 4559])).
% 2.05/2.28 tff(4578,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4553])).
% 2.05/2.28 tff(4579,plain,
% 2.05/2.28 (r(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[487, 4560])).
% 2.05/2.28 tff(4580,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3671, 4579, 153, 3615, 150, 595])).
% 2.05/2.28 tff(4581,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[420, 4580])).
% 2.05/2.28 tff(4582,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4581, 4578])).
% 2.05/2.28 tff(4583,plain,
% 2.05/2.28 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4552])).
% 2.05/2.28 tff(4584,plain,
% 2.05/2.28 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[3615, 4583])).
% 2.05/2.28 tff(4585,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4586,plain,
% 2.05/2.28 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4587,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4586])).
% 2.05/2.28 tff(4588,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(transitivity,[status(thm)],[4587, 4585])).
% 2.05/2.28 tff(4589,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(quant_inst,[status(thm)],[])).
% 2.05/2.28 tff(4590,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 2.05/2.28 tff(4591,plain,
% 2.05/2.28 ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4590, 198, 4584, 4582])).
% 2.05/2.28 tff(4592,plain,
% 2.05/2.28 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4591, 4577])).
% 2.05/2.28 tff(4593,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4592, 4557])).
% 2.05/2.28 tff(4594,plain,((~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | (~r(s(z), z)) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4595,plain,
% 2.05/2.28 (~b(z, s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4594, 152, 3615, 3, 150, 149, 2, 153, 95])).
% 2.05/2.28 tff(4596,plain,
% 2.05/2.28 (r(z, s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[593, 4595])).
% 2.05/2.28 tff(4597,plain,
% 2.05/2.28 (b(z, s(z))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[95, 1100])).
% 2.05/2.28 tff(4598,assumption,(~b(z, s(z))), introduced(assumption)).
% 2.05/2.28 tff(4599,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4598, 4597])).
% 2.05/2.28 tff(4600,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4601,plain,
% 2.05/2.28 (~(s(z) = elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4600, 4595, 95])).
% 2.05/2.28 tff(4602,plain,
% 2.05/2.28 (r(s(z), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[217, 4601, 149])).
% 2.05/2.28 tff(4603,plain,
% 2.05/2.28 (~r(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3636, 4602, 153, 4596])).
% 2.05/2.28 tff(4604,plain,
% 2.05/2.28 (b(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[487, 4603])).
% 2.05/2.28 tff(4605,plain,
% 2.05/2.28 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3689, 4602, 153, 3615, 2, 150])).
% 2.05/2.28 tff(4606,plain,
% 2.05/2.28 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[374, 4605])).
% 2.05/2.28 tff(4607,plain,
% 2.05/2.28 (~r(s(z), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3712, 4606, 153, 150])).
% 2.05/2.28 tff(4608,plain,
% 2.05/2.28 (b(s(z), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[403, 4607])).
% 2.05/2.28 tff(4609,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3763, 4606, 152, 153])).
% 2.05/2.28 tff(4610,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[420, 4609])).
% 2.05/2.28 tff(4611,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3753, 4610, 4608, 4604, 2])).
% 2.05/2.28 tff(4612,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (~b(z, elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4613,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4612, 3616, 153, 150, 3615, 149, 2, 3])).
% 2.05/2.28 tff(4614,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[176, 4613])).
% 2.05/2.28 tff(4615,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4530, 3616, 153, 150, 3615, 2, 3618, 3617, 149])).
% 2.05/2.28 tff(4616,plain,
% 2.05/2.28 (~r(s(z), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3689, 348, 153, 3615, 2, 150])).
% 2.05/2.28 tff(4617,plain,
% 2.05/2.28 (s(z) = elem!1),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[217, 4616, 149])).
% 2.05/2.28 tff(4618,plain,
% 2.05/2.28 (s(s(z)) = s(elem!1)),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4617])).
% 2.05/2.28 tff(4619,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4618])).
% 2.05/2.28 tff(4620,plain,
% 2.05/2.28 (b(z, s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4600, 4617, 95])).
% 2.05/2.28 tff(4621,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3671, 4620, 153, 3615, 150, 3628])).
% 2.05/2.28 tff(4622,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[420, 4621])).
% 2.05/2.28 tff(4623,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4622, 4619])).
% 2.05/2.28 tff(4624,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4612, 95, 153, 150, 3615, 149, 2, 3])).
% 2.05/2.28 tff(4625,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[176, 4624])).
% 2.05/2.28 tff(4626,plain,
% 2.05/2.28 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4618])).
% 2.05/2.28 tff(4627,plain,
% 2.05/2.28 (r(elem!1, z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[212, 4617, 150])).
% 2.05/2.28 tff(4628,plain,
% 2.05/2.28 (~(s(elem!1) = elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[778, 4617, 3])).
% 2.05/2.28 tff(4629,plain,
% 2.05/2.28 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4538, 4620])).
% 2.05/2.28 tff(4630,plain,
% 2.05/2.28 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[31, 4629])).
% 2.05/2.28 tff(4631,plain,
% 2.05/2.28 (~r(s(s(z)), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[876, 4630, 4628, 4531, 4617, 4627, 150, 153])).
% 2.05/2.28 tff(4632,plain,
% 2.05/2.28 (b(s(s(z)), z)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[345, 4631])).
% 2.05/2.28 tff(4633,plain,
% 2.05/2.28 (b(s(elem!1), z)),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4632, 4626])).
% 2.05/2.28 tff(4634,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[885, 198, 95, 4633, 4531, 4625, 4623])).
% 2.05/2.28 tff(4635,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4636,plain,
% 2.05/2.28 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4635, 3616, 150, 153, 3615, 3, 149, 2])).
% 2.05/2.28 tff(4637,plain,
% 2.05/2.28 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[374, 4636])).
% 2.05/2.28 tff(4638,plain,
% 2.05/2.28 (~r(s(z), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3712, 4637, 153, 150])).
% 2.05/2.28 tff(4639,plain,
% 2.05/2.28 (b(s(z), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[403, 4638])).
% 2.05/2.28 tff(4640,plain,
% 2.05/2.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3671, 595, 153, 3615, 150, 3450])).
% 2.05/2.28 tff(4641,plain,
% 2.05/2.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[420, 4640])).
% 2.05/2.28 tff(4642,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4643,plain,
% 2.05/2.28 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4644,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4643])).
% 2.05/2.28 tff(4645,plain,
% 2.05/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.05/2.28 inference(transitivity,[status(thm)],[4644, 4642])).
% 2.05/2.28 tff(4646,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.05/2.28 inference(quant_inst,[status(thm)],[])).
% 2.05/2.28 tff(4647,plain,
% 2.05/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 2.05/2.28 tff(4648,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4647, 198, 595, 407, 4641, 2, 330])).
% 2.05/2.28 tff(4649,plain,((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4650,plain,
% 2.05/2.28 (~b(z, s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4649, 3450, 2, 330, 153, 3615, 150, 407])).
% 2.05/2.28 tff(4651,plain,
% 2.05/2.28 (~(s(z) = elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4600, 4650, 95])).
% 2.05/2.28 tff(4652,plain,
% 2.05/2.28 (r(z, s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[593, 4650])).
% 2.05/2.28 tff(4653,plain,
% 2.05/2.28 (~r(s(z), elem!1)),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3636, 4652, 153, 3450])).
% 2.05/2.28 tff(4654,plain,
% 2.05/2.28 ($false),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[217, 4653, 4651, 149])).
% 2.05/2.28 tff(4655,plain,((~r(s(s(z)), s(z))) | b(s(z), elem!1) | (~r(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.28 tff(4656,plain,
% 2.05/2.28 (~r(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4655, 3616, 153, 149, 2, 4614, 3615, 150, 4639])).
% 2.05/2.28 tff(4657,plain,
% 2.05/2.28 (b(s(s(z)), s(z))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[487, 4656])).
% 2.05/2.28 tff(4658,plain,
% 2.05/2.28 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[3753, 4657, 4639, 2])).
% 2.05/2.28 tff(4659,plain,
% 2.05/2.28 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[420, 4658])).
% 2.05/2.28 tff(4660,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4661,plain,
% 2.05/2.28 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(rewrite,[status(thm)],[])).
% 2.05/2.28 tff(4662,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.28 inference(monotonicity,[status(thm)],[4661])).
% 2.05/2.28 tff(4663,plain,
% 2.05/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(transitivity,[status(thm)],[4662, 4660])).
% 2.05/2.28 tff(4664,plain,
% 2.05/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.28 inference(quant_inst,[status(thm)],[])).
% 2.05/2.28 tff(4665,plain,
% 2.05/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.28 inference(modus_ponens,[status(thm)],[4664, 4663])).
% 2.05/2.28 tff(4666,plain,
% 2.05/2.28 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.28 inference(unit_resolution,[status(thm)],[4665, 163, 153, 4637, 4659])).
% 2.05/2.29 tff(4667,plain,
% 2.05/2.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[31, 4666])).
% 2.05/2.29 tff(4668,plain,
% 2.05/2.29 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4537, 198, 3616, 3615, 4615])).
% 2.05/2.29 tff(4669,plain,
% 2.05/2.29 (~b(z, s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4668, 4667])).
% 2.05/2.29 tff(4670,plain,
% 2.05/2.29 (~(s(z) = elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4600, 4669, 3616])).
% 2.05/2.29 tff(4671,plain,
% 2.05/2.29 (r(s(z), elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[217, 4670, 149])).
% 2.05/2.29 tff(4672,plain,
% 2.05/2.29 (~r(elem!1, z)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1026, 4671, 150, 153])).
% 2.05/2.29 tff(4673,plain,
% 2.05/2.29 (b(elem!1, z)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[187, 4672, 3617])).
% 2.05/2.29 tff(4674,plain,
% 2.05/2.29 (((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4675,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4674])).
% 2.05/2.29 tff(4676,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4675, 199])).
% 2.05/2.29 tff(4677,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.05/2.29 inference(quant_inst,[status(thm)],[])).
% 2.05/2.29 tff(4678,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4677, 4676])).
% 2.05/2.29 tff(4679,plain,
% 2.05/2.29 ($false),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4678, 198, 3616, 4673, 4615, 4614])).
% 2.05/2.29 tff(4680,plain,((z = elem!1) | (~r(s(z), z)) | (~r(z, s(s(z)))) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.05/2.29 tff(4681,plain,
% 2.05/2.29 (z = elem!1),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4680, 150, 55, 149, 3614, 2, 56])).
% 2.05/2.29 tff(4682,plain,
% 2.05/2.29 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3384, 4681])).
% 2.05/2.29 tff(4683,plain,
% 2.05/2.29 (s(z) = s(elem!1)),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4681])).
% 2.05/2.29 tff(4684,plain,
% 2.05/2.29 (s(s(z)) = s(s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4683])).
% 2.05/2.29 tff(4685,plain,
% 2.05/2.29 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4684])).
% 2.05/2.29 tff(4686,plain,
% 2.05/2.29 (~b(elem!1, s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[71, 4681, 42])).
% 2.05/2.29 tff(4687,plain,
% 2.05/2.29 (elem!1 = z),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[78, 4681])).
% 2.05/2.29 tff(4688,plain,
% 2.05/2.29 (~b(z, s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[87, 4687, 4686])).
% 2.05/2.29 tff(4689,plain,
% 2.05/2.29 (r(z, s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1096, 4688])).
% 2.05/2.29 tff(4690,plain,
% 2.05/2.29 (~(s(z) = elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[2822, 4689, 4686, 55, 56, 150])).
% 2.05/2.29 tff(4691,plain,
% 2.05/2.29 (r(s(z), elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[217, 4690, 149])).
% 2.05/2.29 tff(4692,plain,
% 2.05/2.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3689, 4691, 55, 3614, 2, 150])).
% 2.05/2.29 tff(4693,plain,
% 2.05/2.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[374, 4692])).
% 2.05/2.29 tff(4694,plain,
% 2.05/2.29 (~r(s(z), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3712, 4693, 55, 150])).
% 2.05/2.29 tff(4695,plain,
% 2.05/2.29 (b(s(z), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[403, 4694])).
% 2.05/2.29 tff(4696,plain,
% 2.05/2.29 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[2936])).
% 2.05/2.29 tff(4697,plain,
% 2.05/2.29 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4696])).
% 2.05/2.29 tff(4698,plain,
% 2.05/2.29 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[3615, 4697])).
% 2.05/2.29 tff(4699,assumption,(~b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.05/2.29 tff(4700,plain,
% 2.05/2.29 ($false),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4699, 4698])).
% 2.05/2.29 tff(4701,plain,(b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.29 tff(4702,plain,
% 2.05/2.29 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4701, 3614, 4681])).
% 2.05/2.29 tff(4703,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.05/2.29 tff(4704,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[58])).
% 2.05/2.29 tff(4705,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[2, 4704])).
% 2.05/2.29 tff(4706,plain,
% 2.05/2.29 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4548, 152, 153, 3272])).
% 2.05/2.29 tff(4707,plain,
% 2.05/2.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[31, 4706])).
% 2.05/2.29 tff(4708,plain,
% 2.05/2.29 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4707, 2997])).
% 2.05/2.29 tff(4709,plain,
% 2.05/2.29 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[58])).
% 2.05/2.29 tff(4710,plain,
% 2.05/2.29 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[57])).
% 2.05/2.29 tff(4711,plain,
% 2.05/2.29 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4710, 4709])).
% 2.05/2.29 tff(4712,plain,
% 2.05/2.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3763, 152, 3272, 153])).
% 2.05/2.29 tff(4713,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[420, 4712])).
% 2.05/2.29 tff(4714,plain,
% 2.05/2.29 (~b(s(s(z)), s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3753, 4713, 407, 2])).
% 2.05/2.29 tff(4715,plain,
% 2.05/2.29 (r(s(s(z)), s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[487, 4714])).
% 2.05/2.29 tff(4716,plain,
% 2.05/2.29 (~r(z, s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3636, 4715, 153, 236])).
% 2.05/2.29 tff(4717,plain,
% 2.05/2.29 (b(z, s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[593, 4716])).
% 2.05/2.29 tff(4718,plain,
% 2.05/2.29 (b(elem!1, s(elem!1))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4717, 4711])).
% 2.05/2.29 tff(4719,plain,
% 2.05/2.29 ($false),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4590, 198, 4718, 4708, 4705, 4703])).
% 2.05/2.29 tff(4720,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.29 tff(4721,plain,
% 2.05/2.29 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4720, 4702, 4681, 55, 4691, 4695, 2, 4693])).
% 2.05/2.29 tff(4722,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[176, 4721])).
% 2.05/2.29 tff(4723,plain,
% 2.05/2.29 (~r(z, s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3636, 3450, 153, 236])).
% 2.05/2.29 tff(4724,plain,
% 2.05/2.29 (~b(z, s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4649, 3450, 2, 330, 153, 3615, 150, 4191])).
% 2.05/2.29 tff(4725,plain,
% 2.05/2.29 ($false),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[593, 4724, 4723])).
% 2.05/2.29 tff(4726,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.29 tff(4727,plain,
% 2.05/2.29 (~r(s(s(z)), s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4726, 4722, 2, 55, 3614, 150, 4691])).
% 2.05/2.29 tff(4728,plain,
% 2.05/2.29 (b(s(s(z)), s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[487, 4727])).
% 2.05/2.29 tff(4729,plain,
% 2.05/2.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3753, 4728, 4695, 2])).
% 2.05/2.29 tff(4730,plain,
% 2.05/2.29 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[420, 4729])).
% 2.05/2.29 tff(4731,plain,
% 2.05/2.29 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4730, 4685])).
% 2.05/2.29 tff(4732,plain,
% 2.05/2.29 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3275, 4693, 4681])).
% 2.05/2.29 tff(4733,plain,
% 2.05/2.29 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3973, 4731, 55, 4693])).
% 2.05/2.29 tff(4734,plain,
% 2.05/2.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[31, 4733])).
% 2.05/2.29 tff(4735,plain,
% 2.05/2.29 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4494, 4734, 2, 55, 150, 3614, 4722])).
% 2.05/2.29 tff(4736,plain,
% 2.05/2.29 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3098, 4735])).
% 2.05/2.29 tff(4737,plain,
% 2.05/2.29 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3994, 163, 4736, 4732, 4731])).
% 2.05/2.29 tff(4738,plain,
% 2.05/2.29 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3400, 4737, 4682])).
% 2.05/2.29 tff(4739,plain,
% 2.05/2.29 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.05/2.29 inference(commutativity,[status(thm)],[])).
% 2.05/2.29 tff(4740,plain,
% 2.05/2.29 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4739])).
% 2.05/2.29 tff(4741,plain,
% 2.05/2.29 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4681])).
% 2.05/2.29 tff(4742,plain,
% 2.05/2.29 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4741, 4740])).
% 2.05/2.29 tff(4743,plain,
% 2.05/2.29 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4742])).
% 2.05/2.29 tff(4744,plain,
% 2.05/2.29 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[366, 4743])).
% 2.05/2.29 tff(4745,plain,
% 2.05/2.29 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4683])).
% 2.05/2.29 tff(4746,plain,
% 2.05/2.29 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4745])).
% 2.05/2.29 tff(4747,plain,
% 2.05/2.29 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4746])).
% 2.05/2.29 tff(4748,plain,
% 2.05/2.29 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3983, 163, 4736, 4732, 4731])).
% 2.05/2.29 tff(4749,plain,
% 2.05/2.29 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 2.05/2.29 inference(symmetry,[status(thm)],[3986])).
% 2.05/2.29 tff(4750,plain,
% 2.05/2.29 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4749])).
% 2.05/2.29 tff(4751,plain,
% 2.05/2.29 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4682, 4750])).
% 2.05/2.29 tff(4752,plain,
% 2.05/2.29 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3086, 26, 4751, 4748])).
% 2.05/2.29 tff(4753,plain,
% 2.05/2.29 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4683, 4684])).
% 2.05/2.29 tff(4754,plain,
% 2.05/2.29 (b(s(elem!1), s(s(elem!1)))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4695, 4753])).
% 2.05/2.29 tff(4755,plain,
% 2.05/2.29 (~(elem!1 = s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[110, 4688, 56])).
% 2.05/2.29 tff(4756,plain,
% 2.05/2.29 (~(s(s(elem!1)) = elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[118, 4755])).
% 2.05/2.29 tff(4757,plain,
% 2.05/2.29 (~(s(elem!1) = s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[140, 4756])).
% 2.05/2.29 tff(4758,plain,
% 2.05/2.29 (~(s(s(elem!1)) = s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1138, 4757])).
% 2.05/2.29 tff(4759,plain,
% 2.05/2.29 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[58])).
% 2.05/2.29 tff(4760,plain,
% 2.05/2.29 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4759])).
% 2.05/2.29 tff(4761,plain,
% 2.05/2.29 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[59])).
% 2.05/2.29 tff(4762,plain,
% 2.05/2.29 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4761])).
% 2.05/2.29 tff(4763,plain,
% 2.05/2.29 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4762, 4760])).
% 2.05/2.29 tff(4764,plain,
% 2.05/2.29 (r(s(s(z)), s(z))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[1773, 4763])).
% 2.05/2.29 tff(4765,plain,
% 2.05/2.29 ($false),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[481, 4764])).
% 2.05/2.29 tff(4766,plain,((~r(s(s(elem!1)), s(elem!1))) | r(s(s(z)), s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.05/2.29 tff(4767,plain,
% 2.05/2.29 (~r(s(s(elem!1)), s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4766, 4727, 4681])).
% 2.05/2.29 tff(4768,plain,
% 2.05/2.29 (b(s(s(elem!1)), s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1143, 4767, 4758])).
% 2.05/2.29 tff(4769,plain,
% 2.05/2.29 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4770,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4769])).
% 2.05/2.29 tff(4771,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4770, 3077])).
% 2.05/2.29 tff(4772,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.05/2.29 inference(quant_inst,[status(thm)],[])).
% 2.05/2.29 tff(4773,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4772, 4771])).
% 2.05/2.29 tff(4774,plain,
% 2.05/2.29 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4773, 198, 4768, 4754, 4752])).
% 2.05/2.29 tff(4775,plain,
% 2.05/2.29 (~b(s(s(s(s(s(z))))), s(z))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4774, 4747])).
% 2.05/2.29 tff(4776,plain,
% 2.05/2.29 (r(s(s(s(s(s(z))))), s(z))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[469, 4775])).
% 2.05/2.29 tff(4777,plain,
% 2.05/2.29 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3205, 4776, 4681])).
% 2.05/2.29 tff(4778,plain,
% 2.05/2.29 (~(s(elem!1) = elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1395, 4756])).
% 2.05/2.29 tff(4779,plain,
% 2.05/2.29 (~(elem!1 = s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1400, 4778])).
% 2.05/2.29 tff(4780,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4683])).
% 2.05/2.29 tff(4781,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[2, 4780])).
% 2.05/2.29 tff(4782,plain,
% 2.05/2.29 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1032, 4722, 4687])).
% 2.05/2.29 tff(4783,plain,
% 2.05/2.29 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4681])).
% 2.05/2.29 tff(4784,plain,
% 2.05/2.29 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4783, 663])).
% 2.05/2.29 tff(4785,plain,
% 2.05/2.29 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4784])).
% 2.05/2.29 tff(4786,plain,
% 2.05/2.29 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[15, 4785])).
% 2.05/2.29 tff(4787,plain,
% 2.05/2.29 (r(elem!1, s(s(elem!1)))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[147, 4755, 4686])).
% 2.05/2.29 tff(4788,plain,
% 2.05/2.29 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3214, 163, 4787, 4732, 4731])).
% 2.05/2.29 tff(4789,plain,
% 2.05/2.29 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[703, 4788, 4786])).
% 2.05/2.29 tff(4790,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z))))))))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4791,plain,
% 2.05/2.29 (((~b(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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4792,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4791])).
% 2.05/2.29 tff(4793,plain,
% 2.05/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z))))))))))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4792, 4790])).
% 2.05/2.29 tff(4794,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.29 inference(quant_inst,[status(thm)],[])).
% 2.05/2.29 tff(4795,plain,
% 2.05/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(s(s(z)))))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4794, 4793])).
% 2.05/2.29 tff(4796,plain,
% 2.05/2.29 (~b(elem!1, s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4795, 198, 4789, 4782, 4781, 4702])).
% 2.05/2.29 tff(4797,plain,
% 2.05/2.29 (r(elem!1, s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1416, 4796, 4779])).
% 2.05/2.29 tff(4798,plain,
% 2.05/2.29 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4683])).
% 2.05/2.29 tff(4799,plain,
% 2.05/2.29 (r(s(elem!1), elem!1)),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4691, 4798])).
% 2.05/2.29 tff(4800,plain,
% 2.05/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4801,plain,
% 2.05/2.29 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4802,plain,
% 2.05/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4801])).
% 2.05/2.29 tff(4803,plain,
% 2.05/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(transitivity,[status(thm)],[4802, 4800])).
% 2.05/2.29 tff(4804,plain,
% 2.05/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(quant_inst,[status(thm)],[])).
% 2.05/2.29 tff(4805,plain,
% 2.05/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 2.05/2.29 tff(4806,plain,
% 2.05/2.29 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4805, 163, 4799, 4797, 4777])).
% 2.05/2.29 tff(4807,plain,
% 2.05/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 2.05/2.29 inference(rewrite,[status(thm)],[])).
% 2.05/2.29 tff(4808,plain,
% 2.05/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 2.05/2.29 inference(quant_inst,[status(thm)],[])).
% 2.05/2.29 tff(4809,plain,
% 2.05/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4808, 4807])).
% 2.05/2.29 tff(4810,plain,
% 2.05/2.29 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4809, 26])).
% 2.05/2.29 tff(4811,plain,
% 2.05/2.29 (b(elem!1, s(s(s(s(s(z))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[4810, 4806, 4744])).
% 2.05/2.29 tff(4812,plain,
% 2.05/2.29 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4741])).
% 2.05/2.29 tff(4813,plain,
% 2.05/2.29 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[366, 4812])).
% 2.05/2.29 tff(4814,plain,
% 2.05/2.29 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3114, 4777, 4787, 4799])).
% 2.05/2.29 tff(4815,plain,
% 2.05/2.29 (b(s(s(s(s(s(z))))), elem!1)),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[528, 4814, 4813])).
% 2.05/2.29 tff(4816,plain,
% 2.05/2.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1250, 4756])).
% 2.05/2.29 tff(4817,plain,
% 2.05/2.29 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4681])).
% 2.05/2.29 tff(4818,plain,
% 2.05/2.29 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 2.05/2.29 inference(symmetry,[status(thm)],[4817])).
% 2.05/2.29 tff(4819,plain,
% 2.05/2.29 ((~b(elem!1, s(elem!1))) <=> (~b(z, s(elem!1)))),
% 2.05/2.29 inference(monotonicity,[status(thm)],[4818])).
% 2.05/2.29 tff(4820,plain,
% 2.05/2.29 (~b(z, s(elem!1))),
% 2.05/2.29 inference(modus_ponens,[status(thm)],[4796, 4819])).
% 2.05/2.29 tff(4821,plain,
% 2.05/2.29 (r(z, s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1791, 4820])).
% 2.05/2.29 tff(4822,plain,
% 2.05/2.29 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[3214, 163, 405, 681, 680])).
% 2.05/2.29 tff(4823,plain,
% 2.05/2.29 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[703, 4822, 3002])).
% 2.05/2.29 tff(4824,plain,
% 2.05/2.29 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.05/2.29 inference(monotonicity,[status(thm)],[57])).
% 2.05/2.29 tff(4825,plain,
% 2.05/2.29 (~r(s(s(elem!1)), s(elem!1))),
% 2.05/2.29 inference(unit_resolution,[status(thm)],[1781, 790, 1474, 791])).
% 2.05/2.30 tff(4826,plain,
% 2.05/2.30 (b(s(s(elem!1)), s(elem!1))),
% 2.05/2.30 inference(unit_resolution,[status(thm)],[1143, 4825, 1701])).
% 2.05/2.30 tff(4827,plain,
% 2.05/2.30 (~r(s(s(s(elem!1))), z)),
% 2.05/2.30 inference(unit_resolution,[status(thm)],[1621, 4826, 790, 791, 1328, 1256])).
% 2.05/2.30 tff(4828,plain,
% 2.05/2.30 (b(s(s(s(elem!1))), z)),
% 2.05/2.30 inference(unit_resolution,[status(thm)],[1295, 4827])).
% 2.05/2.30 tff(4829,plain,
% 2.05/2.30 (b(s(s(s(elem!1))), elem!1)),
% 2.05/2.30 inference(modus_ponens,[status(thm)],[4828, 4824])).
% 2.05/2.30 tff(4830,plain,
% 2.05/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.30 inference(rewrite,[status(thm)],[])).
% 2.05/2.30 tff(4831,plain,
% 2.05/2.30 (((~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(z))))))))) | (~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(s(s(s(elem!1))), elem!1))) <=> ((~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(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.30 inference(rewrite,[status(thm)],[])).
% 2.05/2.30 tff(4832,plain,
% 2.05/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.05/2.30 inference(monotonicity,[status(thm)],[4831])).
% 2.05/2.30 tff(4833,plain,
% 2.05/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.05/2.30 inference(transitivity,[status(thm)],[4832, 4830])).
% 2.05/2.30 tff(4834,plain,
% 2.05/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.05/2.30 inference(quant_inst,[status(thm)],[])).
% 2.05/2.30 tff(4835,plain,
% 2.05/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4834, 4833])).
% 2.15/2.30 tff(4836,plain,
% 2.15/2.30 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4835, 198, 4829, 4823, 831])).
% 2.15/2.30 tff(4837,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.15/2.30 tff(4838,plain,
% 2.15/2.30 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4837])).
% 2.15/2.30 tff(4839,plain,
% 2.15/2.30 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(elem!1))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4838])).
% 2.15/2.30 tff(4840,plain,
% 2.15/2.30 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.15/2.30 inference(transitivity,[status(thm)],[276, 4839, 1246])).
% 2.15/2.30 tff(4841,plain,
% 2.15/2.30 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4840])).
% 2.15/2.30 tff(4842,plain,
% 2.15/2.30 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4841])).
% 2.15/2.30 tff(4843,plain,
% 2.15/2.30 (s(z) = s(s(s(s(s(z)))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[58, 135, 4842, 280])).
% 2.15/2.30 tff(4844,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3296, 4843])).
% 2.15/2.30 tff(4845,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4846,plain,
% 2.15/2.30 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4845, 57])).
% 2.15/2.30 tff(4847,plain,
% 2.15/2.30 (((~![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)))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4848,plain,
% 2.15/2.30 ((~![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)))))))))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4849,plain,
% 2.15/2.30 ((~![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))))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4848, 4847])).
% 2.15/2.30 tff(4850,plain,
% 2.15/2.30 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4849, 26, 4846, 4836])).
% 2.15/2.30 tff(4851,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4852,plain,
% 2.15/2.30 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(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))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4853,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(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))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4852])).
% 2.15/2.30 tff(4854,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(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))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4853, 4851])).
% 2.15/2.30 tff(4855,plain,
% 2.15/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(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))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4856,plain,
% 2.15/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 2.15/2.30 tff(4857,plain,
% 2.15/2.30 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4856, 163, 681, 680, 4850])).
% 2.15/2.30 tff(4858,plain,
% 2.15/2.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[1326, 4857, 1271])).
% 2.15/2.30 tff(4859,plain,
% 2.15/2.30 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3994, 163, 3066, 681, 680])).
% 2.15/2.30 tff(4860,plain,
% 2.15/2.30 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3400, 4859, 3385])).
% 2.15/2.30 tff(4861,plain,
% 2.15/2.30 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[58])).
% 2.15/2.30 tff(4862,plain,
% 2.15/2.30 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4861])).
% 2.15/2.30 tff(4863,plain,
% 2.15/2.30 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4862])).
% 2.15/2.30 tff(4864,plain,
% 2.15/2.30 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3983, 163, 3066, 681, 680])).
% 2.15/2.30 tff(4865,plain,
% 2.15/2.30 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[3385, 4750])).
% 2.15/2.30 tff(4866,plain,
% 2.15/2.30 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3086, 26, 4865, 4864])).
% 2.15/2.30 tff(4867,plain,
% 2.15/2.30 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4773, 198, 4826, 1328, 4866])).
% 2.15/2.30 tff(4868,plain,
% 2.15/2.30 (~b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4867, 4863])).
% 2.15/2.30 tff(4869,plain,
% 2.15/2.30 (r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[469, 4868])).
% 2.15/2.30 tff(4870,plain,
% 2.15/2.30 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3205, 4869, 57])).
% 2.15/2.30 tff(4871,plain,
% 2.15/2.30 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[3114, 4870, 405, 1474])).
% 2.15/2.30 tff(4872,plain,
% 2.15/2.30 (b(s(s(s(s(s(z))))), elem!1)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[528, 4871, 3037])).
% 2.15/2.30 tff(4873,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4874,plain,
% 2.15/2.30 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4875,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4874])).
% 2.15/2.30 tff(4876,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4875, 4873])).
% 2.15/2.30 tff(4877,plain,
% 2.15/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4878,plain,
% 2.15/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4877, 4876])).
% 2.15/2.30 tff(4879,plain,
% 2.15/2.30 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4878, 198, 4829, 4872, 4860])).
% 2.15/2.30 tff(4880,plain,
% 2.15/2.30 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4879, 4858])).
% 2.15/2.30 tff(4881,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4882,plain,
% 2.15/2.30 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4883,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4882])).
% 2.15/2.30 tff(4884,plain,
% 2.15/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4883, 4881])).
% 2.15/2.30 tff(4885,plain,
% 2.15/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4886,plain,
% 2.15/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 2.15/2.30 tff(4887,plain,
% 2.15/2.30 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4886, 163, 3066, 680, 4850])).
% 2.15/2.30 tff(4888,plain,
% 2.15/2.30 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2619, 1256])).
% 2.15/2.30 tff(4889,plain,
% 2.15/2.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[59])).
% 2.15/2.30 tff(4890,plain,
% 2.15/2.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4889])).
% 2.15/2.30 tff(4891,plain,
% 2.15/2.30 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4890])).
% 2.15/2.30 tff(4892,plain,
% 2.15/2.30 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4891])).
% 2.15/2.30 tff(4893,assumption,(s(s(s(elem!1))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.15/2.30 tff(4894,plain,
% 2.15/2.30 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4893])).
% 2.15/2.30 tff(4895,plain,
% 2.15/2.30 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4894])).
% 2.15/2.30 tff(4896,plain,
% 2.15/2.30 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 2.15/2.30 inference(symmetry,[status(thm)],[4895])).
% 2.15/2.30 tff(4897,plain,
% 2.15/2.30 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[1247, 4896, 288, 4892])).
% 2.15/2.30 tff(4898,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2624, 4897])).
% 2.15/2.30 tff(4899,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4900,plain,
% 2.15/2.30 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4899, 4888, 57])).
% 2.15/2.30 tff(4901,plain,
% 2.15/2.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), 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(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4902,plain,
% 2.15/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.15/2.30 inference(quant_inst,[status(thm)],[])).
% 2.15/2.30 tff(4903,plain,
% 2.15/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.15/2.30 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 2.15/2.30 tff(4904,plain,
% 2.15/2.30 ($false),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4903, 26, 4900, 4887, 4880])).
% 2.15/2.30 tff(4905,plain,((~r(s(s(elem!1)), z)) | (~r(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)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.30 tff(4906,plain,
% 2.15/2.30 (~r(s(s(elem!1)), z)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[4905, 4732, 4731, 4736, 4787, 4799, 4681, 4782, 4754, 4821, 4816, 4758])).
% 2.15/2.30 tff(4907,plain,
% 2.15/2.30 (b(s(s(elem!1)), z)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[801, 4906])).
% 2.15/2.30 tff(4908,plain,
% 2.15/2.30 (b(s(s(elem!1)), elem!1)),
% 2.15/2.30 inference(unit_resolution,[status(thm)],[2982, 4907, 4681])).
% 2.15/2.30 tff(4909,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4910,plain,
% 2.15/2.30 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(rewrite,[status(thm)],[])).
% 2.15/2.30 tff(4911,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.15/2.30 inference(monotonicity,[status(thm)],[4910])).
% 2.15/2.30 tff(4912,plain,
% 2.15/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.30 inference(transitivity,[status(thm)],[4911, 4909])).
% 2.15/2.30 tff(4913,plain,
% 2.15/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4914,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4913, 4912])).
% 2.15/2.31 tff(4915,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4914, 198, 4908, 4789, 4782, 4815, 4811, 4738])).
% 2.15/2.31 tff(4916,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(z), elem!1) | r(z, elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4917,plain,
% 2.15/2.31 (~r(s(z), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4916, 149, 2, 56, 42])).
% 2.15/2.31 tff(4918,plain,
% 2.15/2.31 (b(s(z), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[40, 4917])).
% 2.15/2.31 tff(4919,plain,
% 2.15/2.31 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.15/2.31 inference(symmetry,[status(thm)],[1206])).
% 2.15/2.31 tff(4920,plain,
% 2.15/2.31 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4919])).
% 2.15/2.31 tff(4921,plain,
% 2.15/2.31 (~b(s(z), z)),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[149, 4920])).
% 2.15/2.31 tff(4922,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1185, 4921])).
% 2.15/2.31 tff(4923,plain,((~(z = elem!1)) | (~b(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4924,plain,
% 2.15/2.31 (~(z = elem!1)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4923, 4918, 149])).
% 2.15/2.31 tff(4925,plain,
% 2.15/2.31 (b(z, elem!1)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[102, 4924, 56])).
% 2.15/2.31 tff(4926,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 2.15/2.31 tff(4927,plain,
% 2.15/2.31 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4926])).
% 2.15/2.31 tff(4928,plain,
% 2.15/2.31 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.15/2.31 inference(symmetry,[status(thm)],[4927])).
% 2.15/2.31 tff(4929,plain,
% 2.15/2.31 ((~b(z, s(s(z)))) <=> (~b(z, elem!1))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4928])).
% 2.15/2.31 tff(4930,plain,
% 2.15/2.31 (~b(z, elem!1)),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[42, 4929])).
% 2.15/2.31 tff(4931,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[95, 4930])).
% 2.15/2.31 tff(4932,plain,((~(elem!1 = s(s(z)))) | (~b(z, elem!1)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4933,plain,
% 2.15/2.31 (~(elem!1 = s(s(z)))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4932, 4925, 42])).
% 2.15/2.31 tff(4934,plain,
% 2.15/2.31 (r(s(s(z)), s(z))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[487, 482])).
% 2.15/2.31 tff(4935,plain,
% 2.15/2.31 (r(z, s(z))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[593, 4598])).
% 2.15/2.31 tff(4936,plain,
% 2.15/2.31 (~r(s(z), elem!1)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3636, 4935, 153, 4934])).
% 2.15/2.31 tff(4937,plain,
% 2.15/2.31 (s(z) = elem!1),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[217, 4936, 149])).
% 2.15/2.31 tff(4938,plain,
% 2.15/2.31 (~b(z, elem!1)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4600, 4937, 4598])).
% 2.15/2.31 tff(4939,plain,
% 2.15/2.31 (z = elem!1),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[102, 4938, 56])).
% 2.15/2.31 tff(4940,plain,
% 2.15/2.31 (elem!1 = s(z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[2914, 4937])).
% 2.15/2.31 tff(4941,plain,
% 2.15/2.31 (~b(s(elem!1), elem!1)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4570, 4940, 482])).
% 2.15/2.31 tff(4942,plain,
% 2.15/2.31 (~b(s(elem!1), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1770, 4941, 4939])).
% 2.15/2.31 tff(4943,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[1209, 4942, 4939, 1185])).
% 2.15/2.31 tff(4944,plain,(b(z, s(z)) | (~b(s(z), z)) | r(z, elem!1) | b(s(s(z)), s(z)) | b(s(z), elem!1) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4945,plain,
% 2.15/2.31 (b(z, s(z))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4944, 482, 56, 1185, 149, 153])).
% 2.15/2.31 tff(4946,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4947,plain,
% 2.15/2.31 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4948,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4947])).
% 2.15/2.31 tff(4949,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4948, 4946])).
% 2.15/2.31 tff(4950,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4951,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 2.15/2.31 tff(4952,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4951, 198, 1185, 595, 2, 330])).
% 2.15/2.31 tff(4953,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4954,plain,
% 2.15/2.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4953, 4945, 2, 1185])).
% 2.15/2.31 tff(4955,plain,
% 2.15/2.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[176, 4954])).
% 2.15/2.31 tff(4956,plain,
% 2.15/2.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4953, 595, 2, 1185])).
% 2.15/2.31 tff(4957,plain,
% 2.15/2.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[176, 4956])).
% 2.15/2.31 tff(4958,plain,
% 2.15/2.31 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4548, 3272, 153, 4957])).
% 2.15/2.31 tff(4959,plain,
% 2.15/2.31 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[31, 4958])).
% 2.15/2.31 tff(4960,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4961,plain,
% 2.15/2.31 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4962,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4961])).
% 2.15/2.31 tff(4963,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4962, 4960])).
% 2.15/2.31 tff(4964,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4965,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4964, 4963])).
% 2.15/2.31 tff(4966,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4965, 198, 1185, 595, 3615, 331, 2])).
% 2.15/2.31 tff(4967,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4968,plain,
% 2.15/2.31 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4967, 4959, 595, 1185, 2])).
% 2.15/2.31 tff(4969,plain,
% 2.15/2.31 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3613, 4968])).
% 2.15/2.31 tff(4970,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4971,plain,
% 2.15/2.31 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4972,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4971])).
% 2.15/2.31 tff(4973,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4972, 4970])).
% 2.15/2.31 tff(4974,plain,
% 2.15/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4975,plain,
% 2.15/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4974, 4973])).
% 2.15/2.31 tff(4976,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4975, 163, 3450, 4969, 3272, 4957])).
% 2.15/2.31 tff(4977,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4978,plain,
% 2.15/2.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4977, 4934, 4945, 1185, 2, 153])).
% 2.15/2.31 tff(4979,plain,
% 2.15/2.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[374, 4978])).
% 2.15/2.31 tff(4980,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4065, 163, 153, 3450, 423, 152])).
% 2.15/2.31 tff(4981,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(4982,plain,
% 2.15/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4981, 3450, 153, 152])).
% 2.15/2.31 tff(4983,plain,
% 2.15/2.31 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[420, 4982])).
% 2.15/2.31 tff(4984,plain,
% 2.15/2.31 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3882, 3828, 153, 152])).
% 2.15/2.31 tff(4985,plain,
% 2.15/2.31 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3098, 4984])).
% 2.15/2.31 tff(4986,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4987,plain,
% 2.15/2.31 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4988,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4987])).
% 2.15/2.31 tff(4989,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4988, 4986])).
% 2.15/2.31 tff(4990,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(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(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4991,plain,
% 2.15/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 2.15/2.31 tff(4992,plain,
% 2.15/2.31 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4991, 198, 4985, 348, 4983])).
% 2.15/2.31 tff(4993,plain,
% 2.15/2.31 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[511, 26, 508, 4992])).
% 2.15/2.31 tff(4994,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4995,plain,
% 2.15/2.31 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(4996,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[4995])).
% 2.15/2.31 tff(4997,plain,
% 2.15/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.31 inference(transitivity,[status(thm)],[4996, 4994])).
% 2.15/2.31 tff(4998,plain,
% 2.15/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.15/2.31 inference(quant_inst,[status(thm)],[])).
% 2.15/2.31 tff(4999,plain,
% 2.15/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.15/2.31 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 2.15/2.31 tff(5000,plain,
% 2.15/2.31 ($false),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[4999, 163, 153, 3450, 4993, 3828])).
% 2.15/2.31 tff(5001,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.31 tff(5002,plain,
% 2.15/2.31 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[5001, 4934, 153, 4979, 4955])).
% 2.15/2.31 tff(5003,plain,
% 2.15/2.31 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.31 inference(unit_resolution,[status(thm)],[3841, 5002])).
% 2.15/2.31 tff(5004,plain,
% 2.15/2.31 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.15/2.31 inference(rewrite,[status(thm)],[])).
% 2.15/2.31 tff(5005,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.15/2.31 inference(monotonicity,[status(thm)],[5004])).
% 2.15/2.31 tff(5006,plain,
% 2.15/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5005, 2657])).
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% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5008,plain,
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% 2.15/2.32 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 2.15/2.32 tff(5009,plain,
% 2.15/2.32 (~b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5008, 198, 1185, 4945, 5003])).
% 2.15/2.32 tff(5010,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[469, 5009])).
% 2.15/2.32 tff(5011,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 2.15/2.32 tff(5012,plain,
% 2.15/2.32 (~(z = elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4923, 1185, 149])).
% 2.15/2.32 tff(5013,plain,
% 2.15/2.32 (b(z, elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[102, 5012, 56])).
% 2.15/2.32 tff(5014,plain,
% 2.15/2.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4981, 4934, 153, 4955])).
% 2.15/2.32 tff(5015,plain,
% 2.15/2.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[420, 5014])).
% 2.15/2.32 tff(5016,plain,
% 2.15/2.32 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4967, 3615, 595, 1185, 2])).
% 2.15/2.32 tff(5017,plain,
% 2.15/2.32 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3468, 5016, 95])).
% 2.15/2.32 tff(5018,plain,
% 2.15/2.32 (~(elem!1 = z)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1079, 5012])).
% 2.15/2.32 tff(5019,plain,
% 2.15/2.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4977, 4934, 595, 1185, 2, 153])).
% 2.15/2.32 tff(5020,plain,
% 2.15/2.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[374, 5019])).
% 2.15/2.32 tff(5021,plain,
% 2.15/2.32 (s(s(s(z))) = s(s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[825])).
% 2.15/2.32 tff(5022,plain,
% 2.15/2.32 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5021])).
% 2.15/2.32 tff(5023,plain,
% 2.15/2.32 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5022])).
% 2.15/2.32 tff(5024,plain,
% 2.15/2.32 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5023])).
% 2.15/2.32 tff(5025,plain,
% 2.15/2.32 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[826, 5024])).
% 2.15/2.32 tff(5026,plain,
% 2.15/2.32 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5025, 496])).
% 2.15/2.32 tff(5027,plain,
% 2.15/2.32 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5026])).
% 2.15/2.32 tff(5028,plain,
% 2.15/2.32 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5027])).
% 2.15/2.32 tff(5029,plain,
% 2.15/2.32 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[508, 5028])).
% 2.15/2.32 tff(5030,plain,
% 2.15/2.32 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.15/2.32 inference(monotonicity,[status(thm)],[206])).
% 2.15/2.32 tff(5031,plain,
% 2.15/2.32 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5030])).
% 2.15/2.32 tff(5032,plain,
% 2.15/2.32 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[971, 5031])).
% 2.15/2.32 tff(5033,plain,
% 2.15/2.32 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[206])).
% 2.15/2.32 tff(5034,plain,
% 2.15/2.32 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[3615, 5033])).
% 2.15/2.32 tff(5035,plain,
% 2.15/2.32 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5023])).
% 2.15/2.32 tff(5036,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5035])).
% 2.15/2.32 tff(5037,plain,
% 2.15/2.32 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5036])).
% 2.15/2.32 tff(5038,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 2.15/2.32 tff(5039,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, 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))))))))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5040,plain,
% 2.15/2.32 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, 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))))))))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5041,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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)))))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5040])).
% 2.15/2.32 tff(5042,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, 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))))))))))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5041, 5039])).
% 2.15/2.32 tff(5043,plain,
% 2.15/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5044,plain,
% 2.15/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, 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)))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5043, 5042])).
% 2.15/2.32 tff(5045,plain,
% 2.15/2.32 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5044, 198, 95, 271, 5038, 707, 831])).
% 2.15/2.32 tff(5046,plain,
% 2.15/2.32 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5045, 5037])).
% 2.15/2.32 tff(5047,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3098, 5046])).
% 2.15/2.32 tff(5048,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.32 tff(5049,plain,
% 2.15/2.32 ((~b(s(s(s(s(elem!1)))), z)) <=> (~b(s(s(s(s(s(z))))), z))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5048])).
% 2.15/2.32 tff(5050,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5051,plain,
% 2.15/2.32 (((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5052,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5051])).
% 2.15/2.32 tff(5053,plain,
% 2.15/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5052, 5050])).
% 2.15/2.32 tff(5054,plain,
% 2.15/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5055,plain,
% 2.15/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 2.15/2.32 tff(5056,plain,
% 2.15/2.32 (~b(s(s(s(s(elem!1)))), z)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5055, 198, 95, 271, 5038])).
% 2.15/2.32 tff(5057,plain,
% 2.15/2.32 (~b(s(s(s(s(s(z))))), z)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5056, 5049])).
% 2.15/2.32 tff(5058,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), z)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3841, 5057])).
% 2.15/2.32 tff(5059,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3882, 5058, 5047, 153, 152])).
% 2.15/2.32 tff(5060,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(5061,plain,
% 2.15/2.32 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5060, 206, 4957, 153, 95, 1286, 5034, 2834])).
% 2.15/2.32 tff(5062,plain,
% 2.15/2.32 (((~![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))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5063,plain,
% 2.15/2.32 ((~![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))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5064,plain,
% 2.15/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 2.15/2.32 tff(5065,plain,
% 2.15/2.32 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5064, 26])).
% 2.15/2.32 tff(5066,plain,
% 2.15/2.32 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5065, 5061, 5032])).
% 2.15/2.32 tff(5067,plain,
% 2.15/2.32 (~b(s(z), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3679, 198, 3615, 5020, 3745, 2])).
% 2.15/2.32 tff(5068,plain,
% 2.15/2.32 (r(s(z), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[403, 5067])).
% 2.15/2.32 tff(5069,plain,
% 2.15/2.32 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[229])).
% 2.15/2.32 tff(5070,plain,
% 2.15/2.32 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5069])).
% 2.15/2.32 tff(5071,plain,
% 2.15/2.32 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[231])).
% 2.15/2.32 tff(5072,plain,
% 2.15/2.32 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5071, 5070])).
% 2.15/2.32 tff(5073,plain,
% 2.15/2.32 (r(elem!1, s(elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[328, 5072])).
% 2.15/2.32 tff(5074,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1411, 5073])).
% 2.15/2.32 tff(5075,plain,((~r(s(z), s(s(z)))) | r(elem!1, s(elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(5076,plain,
% 2.15/2.32 (r(elem!1, s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5075, 2915, 5068])).
% 2.15/2.32 tff(5077,plain,
% 2.15/2.32 (~(s(elem!1) = elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[778, 206, 3])).
% 2.15/2.32 tff(5078,plain,
% 2.15/2.32 (~b(s(elem!1), elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4570, 2915, 482])).
% 2.15/2.32 tff(5079,plain,
% 2.15/2.32 (r(s(elem!1), elem!1)),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[856, 5078, 5077])).
% 2.15/2.32 tff(5080,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5081,plain,
% 2.15/2.32 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5082,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5081])).
% 2.15/2.32 tff(5083,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5082, 5080])).
% 2.15/2.32 tff(5084,plain,
% 2.15/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5085,plain,
% 2.15/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5084, 5083])).
% 2.15/2.32 tff(5086,plain,
% 2.15/2.32 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5085, 163, 5079, 5076, 5066])).
% 2.15/2.32 tff(5087,plain,
% 2.15/2.32 (((~![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))))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5088,plain,
% 2.15/2.32 ((~![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))))))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5089,plain,
% 2.15/2.32 ((~![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)))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5088, 5087])).
% 2.15/2.32 tff(5090,plain,
% 2.15/2.32 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5089, 26, 5086])).
% 2.15/2.32 tff(5091,plain,
% 2.15/2.32 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5090, 5029])).
% 2.15/2.32 tff(5092,plain,
% 2.15/2.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1250, 978])).
% 2.15/2.32 tff(5093,plain,
% 2.15/2.32 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[2619, 5092])).
% 2.15/2.32 tff(5094,plain,
% 2.15/2.32 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[2626, 5093])).
% 2.15/2.32 tff(5095,plain,
% 2.15/2.32 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.32 tff(5096,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5095])).
% 2.15/2.32 tff(5097,plain,
% 2.15/2.32 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[825])).
% 2.15/2.32 tff(5098,plain,
% 2.15/2.32 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5097])).
% 2.15/2.32 tff(5099,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.32 tff(5100,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.32 inference(transitivity,[status(thm)],[5099, 5098])).
% 2.15/2.32 tff(5101,plain,
% 2.15/2.32 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024, 826])).
% 2.15/2.32 tff(5102,plain,
% 2.15/2.32 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5101])).
% 2.15/2.32 tff(5103,plain,
% 2.15/2.32 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5102])).
% 2.15/2.32 tff(5104,plain,
% 2.15/2.32 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[508, 5103])).
% 2.15/2.32 tff(5105,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5106,plain,
% 2.15/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5107,plain,
% 2.15/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5106, 5105])).
% 2.15/2.32 tff(5108,plain,
% 2.15/2.32 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5107, 163, 5079, 5076, 5066])).
% 2.15/2.32 tff(5109,plain,
% 2.15/2.32 (((~![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)))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5110,plain,
% 2.15/2.32 ((~![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)))),
% 2.15/2.32 inference(quant_inst,[status(thm)],[])).
% 2.15/2.32 tff(5111,plain,
% 2.15/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5110, 5109])).
% 2.15/2.32 tff(5112,plain,
% 2.15/2.32 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5111, 26, 5108])).
% 2.15/2.32 tff(5113,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5112, 5104])).
% 2.15/2.32 tff(5114,plain,
% 2.15/2.32 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5113, 5100])).
% 2.15/2.32 tff(5115,plain,
% 2.15/2.32 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4057, 5114, 5020, 3615, 2, 3745])).
% 2.15/2.32 tff(5116,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3098, 5115])).
% 2.15/2.32 tff(5117,plain,
% 2.15/2.32 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5116, 5096])).
% 2.15/2.32 tff(5118,plain,
% 2.15/2.32 (r(s(z), s(elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[328, 5071])).
% 2.15/2.32 tff(5119,plain,
% 2.15/2.32 ($false),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[1146, 5118])).
% 2.15/2.32 tff(5120,plain,((~r(s(z), s(s(z)))) | r(s(z), s(elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.32 tff(5121,plain,
% 2.15/2.32 (r(s(z), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5120, 2915, 5068])).
% 2.15/2.32 tff(5122,plain,
% 2.15/2.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[825])).
% 2.15/2.32 tff(5123,plain,
% 2.15/2.32 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[3745, 5122])).
% 2.15/2.32 tff(5124,plain,
% 2.15/2.32 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[825])).
% 2.15/2.32 tff(5125,plain,
% 2.15/2.32 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5020, 5124])).
% 2.15/2.32 tff(5126,plain,
% 2.15/2.32 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[31, 5016])).
% 2.15/2.32 tff(5127,plain,
% 2.15/2.32 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.32 tff(5128,plain,
% 2.15/2.32 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 2.15/2.32 inference(symmetry,[status(thm)],[5127])).
% 2.15/2.32 tff(5129,plain,
% 2.15/2.32 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.32 tff(5130,plain,
% 2.15/2.32 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5129])).
% 2.15/2.32 tff(5131,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 2.15/2.32 tff(5132,plain,
% 2.15/2.32 (~b(s(z), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3679, 198, 3615, 348, 3745, 2])).
% 2.15/2.32 tff(5133,plain,
% 2.15/2.32 (r(s(z), s(s(z)))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[403, 5132])).
% 2.15/2.32 tff(5134,plain,
% 2.15/2.32 (r(elem!1, s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5075, 2915, 5133])).
% 2.15/2.32 tff(5135,plain,
% 2.15/2.32 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5107, 163, 1474, 5134, 5131])).
% 2.15/2.32 tff(5136,plain,
% 2.15/2.32 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5111, 26, 5135])).
% 2.15/2.32 tff(5137,plain,
% 2.15/2.32 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[5136, 5104])).
% 2.15/2.32 tff(5138,plain,
% 2.15/2.32 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5137, 5100])).
% 2.15/2.32 tff(5139,plain,
% 2.15/2.32 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[4057, 5138, 348, 3615, 2, 3745])).
% 2.15/2.32 tff(5140,plain,
% 2.15/2.32 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(unit_resolution,[status(thm)],[3098, 5139])).
% 2.15/2.32 tff(5141,plain,
% 2.15/2.32 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.32 inference(modus_ponens,[status(thm)],[5140, 5096])).
% 2.15/2.32 tff(5142,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5143,plain,
% 2.15/2.32 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.32 inference(rewrite,[status(thm)],[])).
% 2.15/2.32 tff(5144,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.32 inference(monotonicity,[status(thm)],[5143])).
% 2.15/2.32 tff(5145,plain,
% 2.15/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5144, 5142])).
% 2.15/2.33 tff(5146,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5147,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5146, 5145])).
% 2.15/2.33 tff(5148,plain,
% 2.15/2.33 ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5147, 163, 33, 152])).
% 2.15/2.33 tff(5149,plain,
% 2.15/2.33 (~r(z, s(s(s(s(elem!1)))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5148, 5141])).
% 2.15/2.33 tff(5150,plain,
% 2.15/2.33 (~r(z, s(s(s(s(s(z))))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5149, 5130])).
% 2.15/2.33 tff(5151,plain,
% 2.15/2.33 (b(z, s(s(s(s(s(z))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[4110, 5150])).
% 2.15/2.33 tff(5152,plain,
% 2.15/2.33 (b(z, s(s(s(s(elem!1)))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5151, 5128])).
% 2.15/2.33 tff(5153,plain,
% 2.15/2.33 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5024])).
% 2.15/2.33 tff(5154,plain,
% 2.15/2.33 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.15/2.33 inference(symmetry,[status(thm)],[5153])).
% 2.15/2.33 tff(5155,plain,
% 2.15/2.33 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5154])).
% 2.15/2.33 tff(5156,plain,
% 2.15/2.33 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[3882, 5140, 153, 152])).
% 2.15/2.33 tff(5157,plain,
% 2.15/2.33 (~r(s(s(s(s(elem!1)))), z)),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5156, 5155])).
% 2.15/2.33 tff(5158,plain,
% 2.15/2.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5159,plain,
% 2.15/2.33 (~(s(s(s(s(elem!1)))) = z)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5158, 13])).
% 2.15/2.33 tff(5160,plain,
% 2.15/2.33 (((~![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))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5161,plain,
% 2.15/2.33 ((~![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))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5162,plain,
% 2.15/2.33 ((~![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)),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5161, 5160])).
% 2.15/2.33 tff(5163,plain,
% 2.15/2.33 (b(s(s(s(s(elem!1)))), z)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5162, 26, 5159, 5157])).
% 2.15/2.33 tff(5164,plain,
% 2.15/2.33 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5085, 163, 1474, 5134, 5131])).
% 2.15/2.33 tff(5165,plain,
% 2.15/2.33 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5089, 26, 5164])).
% 2.15/2.33 tff(5166,plain,
% 2.15/2.33 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5165, 5029])).
% 2.15/2.33 tff(5167,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5168,plain,
% 2.15/2.33 (((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5169,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5168])).
% 2.15/2.33 tff(5170,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5169, 5167])).
% 2.15/2.33 tff(5171,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, elem!1)) | (~b(s(elem!1), z)))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5172,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5171, 5170])).
% 2.15/2.33 tff(5173,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5172, 198, 95, 271, 1175, 5166, 5163, 5152])).
% 2.15/2.33 tff(5174,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~(s(z) = elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(5175,plain,
% 2.15/2.33 (~b(s(elem!1), z)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5174, 5066, 1286, 95, 206, 5126, 4957, 153, 5020, 3615, 2, 3745, 5079])).
% 2.15/2.33 tff(5176,plain,
% 2.15/2.33 (r(s(elem!1), z)),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1217, 5175])).
% 2.15/2.33 tff(5177,plain,
% 2.15/2.33 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[825])).
% 2.15/2.33 tff(5178,plain,
% 2.15/2.33 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5177, 803])).
% 2.15/2.33 tff(5179,plain,
% 2.15/2.33 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5178])).
% 2.15/2.33 tff(5180,plain,
% 2.15/2.33 (~(s(s(elem!1)) = s(elem!1))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[2106, 5179])).
% 2.15/2.33 tff(5181,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.15/2.33 tff(5182,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.15/2.33 tff(5183,plain,
% 2.15/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5184,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5185,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5184, 5183])).
% 2.15/2.33 tff(5186,plain,
% 2.15/2.33 (~r(s(s(elem!1)), s(z))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5185, 163, 1221, 1773, 1637])).
% 2.15/2.33 tff(5187,plain,
% 2.15/2.33 (b(s(s(elem!1)), s(z))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[624, 26, 620, 5186])).
% 2.15/2.33 tff(5188,plain,
% 2.15/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5189,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5190,plain,
% 2.15/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5189, 5188])).
% 2.15/2.33 tff(5191,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5190, 163, 1221, 1773, 682, 1637])).
% 2.15/2.33 tff(5192,plain,((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(5193,plain,
% 2.15/2.33 (~r(s(z), s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5192, 1637, 1773, 1221])).
% 2.15/2.33 tff(5194,plain,
% 2.15/2.33 (b(s(z), s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[642, 5193])).
% 2.15/2.33 tff(5195,plain,
% 2.15/2.33 (((~b(s(z), s(s(elem!1)))) | (~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(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5196,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5195])).
% 2.15/2.33 tff(5197,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5196, 644])).
% 2.15/2.33 tff(5198,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5199,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5198, 5197])).
% 2.15/2.33 tff(5200,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5199, 198, 5194, 5187, 595, 83])).
% 2.15/2.33 tff(5201,plain,((~r(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(5202,plain,
% 2.15/2.33 (~r(s(s(elem!1)), s(elem!1))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5201, 83, 1637, 595, 1221])).
% 2.15/2.33 tff(5203,plain,
% 2.15/2.33 (b(s(s(elem!1)), s(elem!1))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1143, 5202, 1701])).
% 2.15/2.33 tff(5204,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5205,plain,
% 2.15/2.33 (((~b(s(s(s(s(s(s(s(z))))))), 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(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(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(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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5206,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5205])).
% 2.15/2.33 tff(5207,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5206, 5204])).
% 2.15/2.33 tff(5208,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.15/2.33 inference(quant_inst,[status(thm)],[])).
% 2.15/2.33 tff(5209,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[5208, 5207])).
% 2.15/2.33 tff(5210,plain,
% 2.15/2.33 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5209, 198, 5203, 5182, 3317, 4703, 5181])).
% 2.15/2.33 tff(5211,plain,
% 2.15/2.33 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[934, 26, 696, 5210])).
% 2.15/2.33 tff(5212,plain,
% 2.15/2.33 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.15/2.33 inference(symmetry,[status(thm)],[5211])).
% 2.15/2.33 tff(5213,plain,
% 2.15/2.33 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(z, s(s(elem!1)))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5212])).
% 2.15/2.33 tff(5214,plain,
% 2.15/2.33 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.33 inference(symmetry,[status(thm)],[5213])).
% 2.15/2.33 tff(5215,plain,
% 2.15/2.33 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[83, 5214])).
% 2.15/2.33 tff(5216,plain,
% 2.15/2.33 ($false),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1, 5215])).
% 2.15/2.33 tff(5217,plain,((~b(z, s(s(elem!1)))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(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(s(s(elem!1)))), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(z), s(elem!1))) | (~b(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.33 tff(5218,plain,
% 2.15/2.33 (~b(z, s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5217, 696, 1, 5182, 3317, 4703, 5181, 5180, 1637, 595, 1221])).
% 2.15/2.33 tff(5219,plain,
% 2.15/2.33 (r(z, s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1096, 5218])).
% 2.15/2.33 tff(5220,plain,
% 2.15/2.33 (~b(s(s(elem!1)), s(z))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[2813, 1133, 820, 791, 1098, 1103, 595])).
% 2.15/2.33 tff(5221,plain,
% 2.15/2.33 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[2846, 5220, 831, 206])).
% 2.15/2.33 tff(5222,plain,
% 2.15/2.33 ((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))))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[934, 26, 696])).
% 2.15/2.33 tff(5223,plain,
% 2.15/2.33 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[5222, 5221])).
% 2.15/2.33 tff(5224,plain,
% 2.15/2.33 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5178, 804])).
% 2.15/2.33 tff(5225,plain,
% 2.15/2.33 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5224])).
% 2.15/2.33 tff(5226,plain,
% 2.15/2.33 (~(s(elem!1) = s(s(elem!1)))),
% 2.15/2.33 inference(modus_ponens,[status(thm)],[2106, 5225])).
% 2.15/2.33 tff(5227,plain,
% 2.15/2.33 (r(s(s(elem!1)), s(z))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[626, 5220])).
% 2.15/2.33 tff(5228,plain,
% 2.15/2.33 (~r(s(elem!1), s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1229, 5227, 1221, 1098])).
% 2.15/2.33 tff(5229,plain,
% 2.15/2.33 (b(s(elem!1), s(s(elem!1)))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[901, 5228, 5226])).
% 2.15/2.33 tff(5230,plain,
% 2.15/2.33 (b(s(s(elem!1)), s(elem!1))),
% 2.15/2.33 inference(unit_resolution,[status(thm)],[1143, 1133, 5180])).
% 2.15/2.33 tff(5231,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5232,plain,
% 2.15/2.33 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), 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(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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(rewrite,[status(thm)],[])).
% 2.15/2.33 tff(5233,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.33 inference(monotonicity,[status(thm)],[5232])).
% 2.15/2.33 tff(5234,plain,
% 2.15/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.33 inference(transitivity,[status(thm)],[5233, 5231])).
% 2.15/2.33 tff(5235,plain,
% 2.15/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5236,plain,
% 2.15/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5235, 5234])).
% 2.15/2.34 tff(5237,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5236, 198, 5230, 5229, 5223, 3317, 4703])).
% 2.15/2.34 tff(5238,plain,(r(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))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(5239,plain,
% 2.15/2.34 (r(s(s(elem!1)), s(elem!1))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5238, 696, 4703, 3317, 1221, 5219, 831, 206, 820, 791, 595])).
% 2.15/2.34 tff(5240,plain,
% 2.15/2.34 (~r(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2031, 5239, 5219, 1221])).
% 2.15/2.34 tff(5241,plain,
% 2.15/2.34 (b(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[801, 5240])).
% 2.15/2.34 tff(5242,plain,
% 2.15/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5243,plain,
% 2.15/2.34 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5244,plain,
% 2.15/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5243])).
% 2.15/2.34 tff(5245,plain,
% 2.15/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5244, 5242])).
% 2.15/2.34 tff(5246,plain,
% 2.15/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5247,plain,
% 2.15/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5246, 5245])).
% 2.15/2.34 tff(5248,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5247, 198, 95, 271, 723, 722, 1185, 595])).
% 2.15/2.34 tff(5249,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(5250,plain,
% 2.15/2.34 (~b(s(s(elem!1)), s(z))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5249, 5241, 1185, 95, 595, 1286])).
% 2.15/2.34 tff(5251,plain,
% 2.15/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1131, 5250, 206])).
% 2.15/2.34 tff(5252,plain,
% 2.15/2.34 (r(s(s(elem!1)), elem!1)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[602, 5251, 978])).
% 2.15/2.34 tff(5253,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2341, 163, 5252, 1474, 1473, 5239])).
% 2.15/2.34 tff(5254,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(z)) | (~r(z, s(elem!1))) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(5255,plain,
% 2.15/2.34 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5254, 5079, 5076, 206, 1185, 95, 595, 5176, 5125, 5123, 2834, 3618, 842, 5016, 5091, 5113, 5121])).
% 2.15/2.34 tff(5256,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5257,plain,
% 2.15/2.34 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5258,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5257])).
% 2.15/2.34 tff(5259,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5258, 5256])).
% 2.15/2.34 tff(5260,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5261,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5260, 5259])).
% 2.15/2.34 tff(5262,plain,
% 2.15/2.34 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5261, 163, 4957, 5255, 5117])).
% 2.15/2.34 tff(5263,plain,
% 2.15/2.34 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[2654, 5262, 5094])).
% 2.15/2.34 tff(5264,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5265,plain,
% 2.15/2.34 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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))))))))) | (~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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5266,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5265])).
% 2.15/2.34 tff(5267,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5266, 5264])).
% 2.15/2.34 tff(5268,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(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))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5269,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 2.15/2.34 tff(5270,plain,
% 2.15/2.34 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5269, 163, 4957, 5255, 5117])).
% 2.15/2.34 tff(5271,plain,
% 2.15/2.34 (((~![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))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5272,plain,
% 2.15/2.34 ((~![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))))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5273,plain,
% 2.15/2.34 ((~![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)))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5272, 5271])).
% 2.15/2.34 tff(5274,plain,
% 2.15/2.34 ((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)))))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5273, 26])).
% 2.15/2.34 tff(5275,plain,
% 2.15/2.34 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5274, 5270, 5093])).
% 2.15/2.34 tff(5276,plain,
% 2.15/2.34 (~(s(s(z)) = s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[822, 3618])).
% 2.15/2.34 tff(5277,plain,
% 2.15/2.34 (~(s(elem!1) = s(s(elem!1)))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5276, 5225])).
% 2.15/2.34 tff(5278,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5279,plain,
% 2.15/2.34 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5280,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5279])).
% 2.15/2.34 tff(5281,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5280, 5278])).
% 2.15/2.34 tff(5282,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5283,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5282, 5281])).
% 2.15/2.34 tff(5284,plain,
% 2.15/2.34 (~r(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5283, 163, 5126, 4957, 5255])).
% 2.15/2.34 tff(5285,plain,
% 2.15/2.34 (b(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[801, 5284])).
% 2.15/2.34 tff(5286,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5287,plain,
% 2.15/2.34 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5288,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5287])).
% 2.15/2.34 tff(5289,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5288, 5286])).
% 2.15/2.34 tff(5290,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(elem!1)))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5291,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 2.15/2.34 tff(5292,plain,
% 2.15/2.34 (~r(z, s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5291, 163, 5126, 4957, 5255])).
% 2.15/2.34 tff(5293,plain,
% 2.15/2.34 (b(z, s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1096, 5292])).
% 2.15/2.34 tff(5294,plain,
% 2.15/2.34 (~b(elem!1, s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1071, 5293, 1286, 5285])).
% 2.15/2.34 tff(5295,plain,
% 2.15/2.34 (r(elem!1, s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[147, 5294, 1103])).
% 2.15/2.34 tff(5296,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5297,plain,
% 2.15/2.34 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(s(elem!1)), z)))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5298,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5297])).
% 2.15/2.34 tff(5299,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5298, 5296])).
% 2.15/2.34 tff(5300,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5301,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5300, 5299])).
% 2.15/2.34 tff(5302,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5301, 163, 1473, 790, 1220, 405])).
% 2.15/2.34 tff(5303,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(5304,plain,
% 2.15/2.34 (~r(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5303, 1220, 405, 1473])).
% 2.15/2.34 tff(5305,plain,
% 2.15/2.34 (b(s(s(elem!1)), z)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[801, 5304])).
% 2.15/2.34 tff(5306,plain,
% 2.15/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[1491, 198, 95, 271, 5305])).
% 2.15/2.34 tff(5307,plain,
% 2.15/2.34 (r(s(s(elem!1)), elem!1)),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[602, 5306, 138])).
% 2.15/2.34 tff(5308,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5309,plain,
% 2.15/2.34 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 2.15/2.34 inference(rewrite,[status(thm)],[])).
% 2.15/2.34 tff(5310,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1)))))),
% 2.15/2.34 inference(monotonicity,[status(thm)],[5309])).
% 2.15/2.34 tff(5311,plain,
% 2.15/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))))),
% 2.15/2.34 inference(transitivity,[status(thm)],[5310, 5308])).
% 2.15/2.34 tff(5312,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 2.15/2.34 inference(quant_inst,[status(thm)],[])).
% 2.15/2.34 tff(5313,plain,
% 2.15/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1)))),
% 2.15/2.34 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 2.15/2.34 tff(5314,plain,
% 2.15/2.34 ($false),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5313, 163, 5307, 1473, 1220, 405])).
% 2.15/2.34 tff(5315,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.34 tff(5316,plain,
% 2.15/2.34 (~r(s(elem!1), s(s(elem!1)))),
% 2.15/2.34 inference(unit_resolution,[status(thm)],[5315, 5295, 95, 5076, 978, 1286])).
% 2.15/2.35 tff(5317,plain,
% 2.15/2.35 (b(s(elem!1), s(s(elem!1)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[901, 5316, 5277])).
% 2.15/2.35 tff(5318,plain,
% 2.15/2.35 (~(s(s(elem!1)) = s(elem!1))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5276, 5179])).
% 2.15/2.35 tff(5319,plain,
% 2.15/2.35 (~r(s(s(elem!1)), s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5201, 5293, 5121, 595, 5176])).
% 2.15/2.35 tff(5320,plain,
% 2.15/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1143, 5319, 5318])).
% 2.15/2.35 tff(5321,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5322,plain,
% 2.15/2.35 (((~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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5323,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5322])).
% 2.15/2.35 tff(5324,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5323, 5321])).
% 2.15/2.35 tff(5325,plain,
% 2.15/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5326,plain,
% 2.15/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5325, 5324])).
% 2.15/2.35 tff(5327,plain,
% 2.15/2.35 ($false),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5326, 198, 5320, 5317, 5275, 5263, 5091])).
% 2.15/2.35 tff(5328,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | b(s(s(z)), s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.35 tff(5329,plain,
% 2.15/2.35 (~(s(z) = elem!1)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5328, 3745, 595, 1185, 3615, 2, 95, 153, 482, 5012])).
% 2.15/2.35 tff(5330,plain,
% 2.15/2.35 (r(s(z), elem!1)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[217, 5329, 149])).
% 2.15/2.35 tff(5331,plain,
% 2.15/2.35 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4057, 3819, 348, 3615, 2, 3745])).
% 2.15/2.35 tff(5332,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[511, 26, 508, 5331])).
% 2.15/2.35 tff(5333,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5334,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5335,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5334, 5333])).
% 2.15/2.35 tff(5336,plain,
% 2.15/2.35 ($false),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5335, 163, 236, 3450, 3827, 5332])).
% 2.15/2.35 tff(5337,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.35 tff(5338,plain,
% 2.15/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5337, 5330, 4934, 3615, 2, 5020, 3745])).
% 2.15/2.35 tff(5339,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3098, 5338])).
% 2.15/2.35 tff(5340,plain,
% 2.15/2.35 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3882, 5339, 153, 4957])).
% 2.15/2.35 tff(5341,plain,
% 2.15/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3841, 5340])).
% 2.15/2.35 tff(5342,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5343,plain,
% 2.15/2.35 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5344,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5343])).
% 2.15/2.35 tff(5345,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5344, 5342])).
% 2.15/2.35 tff(5346,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5347,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 2.15/2.35 tff(5348,plain,
% 2.15/2.35 (~r(z, s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5347, 163, 5339, 5126, 4957])).
% 2.15/2.35 tff(5349,plain,
% 2.15/2.35 (b(z, s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4110, 5348])).
% 2.15/2.35 tff(5350,plain,
% 2.15/2.35 (~(s(s(z)) = s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[227, 5329])).
% 2.15/2.35 tff(5351,plain,
% 2.15/2.35 (~(elem!1 = s(z))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[234, 5350])).
% 2.15/2.35 tff(5352,plain,
% 2.15/2.35 (~b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5008, 198, 1185, 595, 5341])).
% 2.15/2.35 tff(5353,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[469, 5352])).
% 2.15/2.35 tff(5354,plain,
% 2.15/2.35 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5335, 163, 5330, 4934, 5353])).
% 2.15/2.35 tff(5355,plain,
% 2.15/2.35 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[511, 26, 508, 5354])).
% 2.15/2.35 tff(5356,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5357,plain,
% 2.15/2.35 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5358,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5357])).
% 2.15/2.35 tff(5359,plain,
% 2.15/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5358, 5356])).
% 2.15/2.35 tff(5360,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5361,plain,
% 2.15/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5360, 5359])).
% 2.15/2.35 tff(5362,plain,
% 2.15/2.35 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5361, 163, 5330, 4934, 5353])).
% 2.15/2.35 tff(5363,plain,
% 2.15/2.35 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[2715, 26, 507, 5362])).
% 2.15/2.35 tff(5364,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5365,plain,
% 2.15/2.35 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5366,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5365])).
% 2.15/2.35 tff(5367,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5366, 5364])).
% 2.15/2.35 tff(5368,plain,
% 2.15/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.15/2.35 inference(quant_inst,[status(thm)],[])).
% 2.15/2.35 tff(5369,plain,
% 2.15/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 2.15/2.35 tff(5370,plain,
% 2.15/2.35 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5369, 198, 3745, 5363, 5355])).
% 2.15/2.35 tff(5371,plain,
% 2.15/2.35 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3328, 26, 5370])).
% 2.15/2.35 tff(5372,plain,
% 2.15/2.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5371, 2935])).
% 2.15/2.35 tff(5373,plain,
% 2.15/2.35 (~b(s(s(z)), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4296, 198, 5349, 5341, 5363])).
% 2.15/2.35 tff(5374,plain,
% 2.15/2.35 (r(s(s(z)), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[345, 5373])).
% 2.15/2.35 tff(5375,plain,
% 2.15/2.35 (~(s(elem!1) = s(z))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[814, 5012])).
% 2.15/2.35 tff(5376,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.15/2.35 tff(5377,plain,
% 2.15/2.35 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5376])).
% 2.15/2.35 tff(5378,plain,
% 2.15/2.35 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.15/2.35 inference(symmetry,[status(thm)],[5377])).
% 2.15/2.35 tff(5379,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(elem!1), z)),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.35 tff(5380,plain,
% 2.15/2.35 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 2.15/2.35 inference(symmetry,[status(thm)],[5379])).
% 2.15/2.35 tff(5381,plain,
% 2.15/2.35 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5377])).
% 2.15/2.35 tff(5382,plain,
% 2.15/2.35 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5383,plain,
% 2.15/2.35 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(elem!1)), z)),
% 2.15/2.35 inference(symmetry,[status(thm)],[5382])).
% 2.15/2.35 tff(5384,plain,
% 2.15/2.35 (r(s(s(elem!1)), z)),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[4957, 5383])).
% 2.15/2.35 tff(5385,plain,
% 2.15/2.35 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5386,plain,
% 2.15/2.35 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(elem!1)))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5385])).
% 2.15/2.35 tff(5387,plain,
% 2.15/2.35 (r(z, s(s(elem!1)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[33, 5386])).
% 2.15/2.35 tff(5388,plain,
% 2.15/2.35 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5389,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5388])).
% 2.15/2.35 tff(5390,plain,
% 2.15/2.35 (b(s(s(elem!1)), s(z))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[2, 5389])).
% 2.15/2.35 tff(5391,plain,
% 2.15/2.35 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5376])).
% 2.15/2.35 tff(5392,plain,
% 2.15/2.35 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), elem!1)),
% 2.15/2.35 inference(symmetry,[status(thm)],[5391])).
% 2.15/2.35 tff(5393,plain,
% 2.15/2.35 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5394,plain,
% 2.15/2.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5393])).
% 2.15/2.35 tff(5395,plain,
% 2.15/2.35 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), elem!1)),
% 2.15/2.35 inference(transitivity,[status(thm)],[5394, 5392])).
% 2.15/2.35 tff(5396,plain,
% 2.15/2.35 (r(s(s(elem!1)), elem!1)),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[3368, 5395])).
% 2.15/2.35 tff(5397,plain,
% 2.15/2.35 (~r(z, s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[5347, 163, 3066, 33, 4957])).
% 2.15/2.35 tff(5398,plain,
% 2.15/2.35 (b(z, s(s(s(s(s(z))))))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[4110, 5397])).
% 2.15/2.35 tff(5399,plain,
% 2.15/2.35 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3882, 3066, 153, 4957])).
% 2.15/2.35 tff(5400,plain,
% 2.15/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[3841, 5399])).
% 2.15/2.35 tff(5401,plain,
% 2.15/2.35 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5376])).
% 2.15/2.35 tff(5402,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5401])).
% 2.15/2.35 tff(5403,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5404,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5403])).
% 2.15/2.35 tff(5405,plain,
% 2.15/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(elem!1)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5404, 5402])).
% 2.15/2.35 tff(5406,plain,
% 2.15/2.35 (r(elem!1, s(s(elem!1)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[3066, 5405])).
% 2.15/2.35 tff(5407,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.35 tff(5408,plain,
% 2.15/2.35 (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(s(s(z)))))))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5407])).
% 2.15/2.35 tff(5409,plain,
% 2.15/2.35 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5410,plain,
% 2.15/2.35 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5376])).
% 2.15/2.35 tff(5411,plain,
% 2.15/2.35 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 2.15/2.35 inference(symmetry,[status(thm)],[5410])).
% 2.15/2.35 tff(5412,plain,
% 2.15/2.35 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.35 tff(5413,plain,
% 2.15/2.35 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5412, 2932])).
% 2.15/2.35 tff(5414,plain,
% 2.15/2.35 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5413])).
% 2.15/2.35 tff(5415,plain,
% 2.15/2.35 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 2.15/2.35 inference(transitivity,[status(thm)],[5414, 5411])).
% 2.15/2.35 tff(5416,plain,
% 2.15/2.35 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5415])).
% 2.15/2.35 tff(5417,plain,
% 2.15/2.35 (~(s(s(elem!1)) = elem!1)),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[314, 5416])).
% 2.15/2.35 tff(5418,plain,
% 2.15/2.35 (~(s(elem!1) = s(s(elem!1)))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[140, 5417])).
% 2.15/2.35 tff(5419,plain,
% 2.15/2.35 (~(s(s(elem!1)) = s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1138, 5418])).
% 2.15/2.35 tff(5420,plain,
% 2.15/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1143, 1133, 5419])).
% 2.15/2.35 tff(5421,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5420, 5409])).
% 2.15/2.35 tff(5422,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[5421, 5408])).
% 2.15/2.35 tff(5423,plain,
% 2.15/2.35 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), s(elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.35 tff(5424,plain,
% 2.15/2.35 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5423])).
% 2.15/2.35 tff(5425,plain,
% 2.15/2.35 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.35 tff(5426,plain,
% 2.15/2.35 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5425])).
% 2.15/2.35 tff(5427,plain,
% 2.15/2.35 (r(s(elem!1), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5377])).
% 2.15/2.35 tff(5428,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.15/2.35 tff(5429,plain,
% 2.15/2.35 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(elem!1)))),
% 2.15/2.35 inference(transitivity,[status(thm)],[5414, 5411, 113])).
% 2.15/2.35 tff(5430,plain,
% 2.15/2.35 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5429])).
% 2.15/2.35 tff(5431,plain,
% 2.15/2.35 (~(elem!1 = s(s(elem!1)))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[314, 5430])).
% 2.15/2.35 tff(5432,plain,
% 2.15/2.35 (~r(z, s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[2813, 1133, 820, 722, 1098, 5431, 595])).
% 2.15/2.35 tff(5433,plain,
% 2.15/2.35 (b(z, s(elem!1))),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1791, 5432])).
% 2.15/2.35 tff(5434,plain,
% 2.15/2.35 (~(s(elem!1) = elem!1)),
% 2.15/2.35 inference(unit_resolution,[status(thm)],[1395, 5417])).
% 2.15/2.35 tff(5435,plain,
% 2.15/2.35 (s(s(s(s(s(z))))) = elem!1),
% 2.15/2.35 inference(symmetry,[status(thm)],[5376])).
% 2.15/2.35 tff(5436,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378, 5435])).
% 2.15/2.35 tff(5437,plain,
% 2.15/2.35 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5436])).
% 2.15/2.35 tff(5438,plain,
% 2.15/2.35 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(elem!1))),
% 2.15/2.35 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.35 tff(5439,plain,
% 2.15/2.35 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(symmetry,[status(thm)],[5438])).
% 2.15/2.35 tff(5440,plain,
% 2.15/2.35 (b(z, s(s(s(s(s(s(z)))))))),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[1801, 5439])).
% 2.15/2.35 tff(5441,plain,
% 2.15/2.35 (b(s(s(s(s(s(s(z)))))), z)),
% 2.15/2.35 inference(modus_ponens,[status(thm)],[1175, 5380])).
% 2.15/2.35 tff(5442,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5443,plain,
% 2.15/2.35 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.35 inference(rewrite,[status(thm)],[])).
% 2.15/2.35 tff(5444,plain,
% 2.15/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5443])).
% 2.15/2.36 tff(5445,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5444, 5442])).
% 2.15/2.36 tff(5446,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5447,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5446, 5445])).
% 2.15/2.36 tff(5448,plain,
% 2.15/2.36 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5447, 198, 5428, 4167])).
% 2.15/2.36 tff(5449,plain,
% 2.15/2.36 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5448, 5441, 5440])).
% 2.15/2.36 tff(5450,plain,
% 2.15/2.36 (~b(s(elem!1), elem!1)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5449, 5437])).
% 2.15/2.36 tff(5451,plain,
% 2.15/2.36 (r(s(elem!1), elem!1)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[856, 5450, 5434])).
% 2.15/2.36 tff(5452,plain,
% 2.15/2.36 (~b(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2244, 5451, 820, 236, 1115, 405])).
% 2.15/2.36 tff(5453,plain,
% 2.15/2.36 (~(elem!1 = s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1400, 5434])).
% 2.15/2.36 tff(5454,plain,
% 2.15/2.36 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5376])).
% 2.15/2.36 tff(5455,plain,
% 2.15/2.36 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.15/2.36 inference(symmetry,[status(thm)],[5454])).
% 2.15/2.36 tff(5456,plain,
% 2.15/2.36 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.36 tff(5457,plain,
% 2.15/2.36 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(elem!1))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5456, 5455])).
% 2.15/2.36 tff(5458,plain,
% 2.15/2.36 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~b(elem!1, s(elem!1)))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5457])).
% 2.15/2.36 tff(5459,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5460,plain,
% 2.15/2.36 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5461,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5460])).
% 2.15/2.36 tff(5462,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5461, 5459])).
% 2.15/2.36 tff(5463,plain,
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% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5464,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 2.15/2.36 tff(5465,plain,
% 2.15/2.36 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5464, 198, 4167])).
% 2.15/2.36 tff(5466,plain,
% 2.15/2.36 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5465, 5441, 5440])).
% 2.15/2.36 tff(5467,plain,
% 2.15/2.36 (~b(elem!1, s(elem!1))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5466, 5458])).
% 2.15/2.36 tff(5468,plain,
% 2.15/2.36 (r(elem!1, s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1416, 5467, 5453])).
% 2.15/2.36 tff(5469,plain,
% 2.15/2.36 (~r(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[3583, 5451, 1115, 5468])).
% 2.15/2.36 tff(5470,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[901, 5469, 5452, 5418])).
% 2.15/2.36 tff(5471,plain,((~b(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5472,plain,
% 2.15/2.36 (~b(s(elem!1), z)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5471, 5433, 820, 236, 405, 5376, 4167, 5428, 1115])).
% 2.15/2.36 tff(5473,plain,
% 2.15/2.36 (r(s(elem!1), z)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1217, 5472])).
% 2.15/2.36 tff(5474,plain,
% 2.15/2.36 (r(s(s(s(s(s(s(z)))))), z)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5473, 5427])).
% 2.15/2.36 tff(5475,plain,
% 2.15/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5476,plain,
% 2.15/2.36 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5477,plain,
% 2.15/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5476])).
% 2.15/2.36 tff(5478,plain,
% 2.15/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5477, 5475])).
% 2.15/2.36 tff(5479,plain,
% 2.15/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5480,plain,
% 2.15/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5479, 5478])).
% 2.15/2.36 tff(5481,plain,
% 2.15/2.36 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5480, 163, 153, 332, 5474])).
% 2.15/2.36 tff(5482,plain,
% 2.15/2.36 (~r(s(s(z)), s(elem!1))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5481, 5426])).
% 2.15/2.36 tff(5483,plain,
% 2.15/2.36 (b(s(s(z)), s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2378, 5482, 232])).
% 2.15/2.36 tff(5484,plain,
% 2.15/2.36 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5483, 5424])).
% 2.15/2.36 tff(5485,plain,
% 2.15/2.36 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.36 tff(5486,plain,
% 2.15/2.36 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(symmetry,[status(thm)],[5485])).
% 2.15/2.36 tff(5487,plain,
% 2.15/2.36 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.36 tff(5488,plain,
% 2.15/2.36 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5381])).
% 2.15/2.36 tff(5489,plain,
% 2.15/2.36 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(symmetry,[status(thm)],[5488])).
% 2.15/2.36 tff(5490,plain,
% 2.15/2.36 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5378])).
% 2.15/2.36 tff(5491,plain,
% 2.15/2.36 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5490, 5489])).
% 2.15/2.36 tff(5492,plain,
% 2.15/2.36 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5491])).
% 2.15/2.36 tff(5493,plain,
% 2.15/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5494,plain,
% 2.15/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5495,plain,
% 2.15/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 2.15/2.36 tff(5496,plain,
% 2.15/2.36 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5495, 163, 153, 152, 5474])).
% 2.15/2.36 tff(5497,plain,
% 2.15/2.36 (~r(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5496, 5492])).
% 2.15/2.36 tff(5498,plain,
% 2.15/2.36 (b(s(elem!1), s(s(elem!1)))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[901, 5497, 5418])).
% 2.15/2.36 tff(5499,plain,
% 2.15/2.36 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5498, 5487])).
% 2.15/2.36 tff(5500,plain,
% 2.15/2.36 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5499, 5486])).
% 2.15/2.36 tff(5501,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5502,plain,
% 2.15/2.36 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5503,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5502])).
% 2.15/2.36 tff(5504,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5503, 5501])).
% 2.15/2.36 tff(5505,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5506,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5505, 5504])).
% 2.15/2.36 tff(5507,plain,
% 2.15/2.36 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5506, 198, 348, 5500, 5484])).
% 2.15/2.36 tff(5508,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5507, 5422])).
% 2.15/2.36 tff(5509,plain,(r(s(s(elem!1)), s(elem!1)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5510,plain,
% 2.15/2.36 (r(s(s(elem!1)), s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5509, 5376, 348, 232, 153, 332, 4957, 820, 236, 5406, 5400, 5398, 5396, 5390, 5387, 595])).
% 2.15/2.36 tff(5511,plain,
% 2.15/2.36 (~r(s(elem!1), z)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[2031, 5510, 5387, 5384])).
% 2.15/2.36 tff(5512,plain,
% 2.15/2.36 (b(s(elem!1), z)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1217, 5511])).
% 2.15/2.36 tff(5513,plain,
% 2.15/2.36 (b(s(s(s(s(s(s(z)))))), z)),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5512, 5380])).
% 2.15/2.36 tff(5514,plain,
% 2.15/2.36 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.15/2.36 inference(symmetry,[status(thm)],[5436])).
% 2.15/2.36 tff(5515,plain,
% 2.15/2.36 (~b(z, s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5471, 5512, 820, 236, 5406, 5376, 5400, 5398, 5396])).
% 2.15/2.36 tff(5516,plain,
% 2.15/2.36 (r(z, s(elem!1))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1791, 5515])).
% 2.15/2.36 tff(5517,plain,
% 2.15/2.36 (~r(s(elem!1), elem!1)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[1781, 5516, 5384, 5510])).
% 2.15/2.36 tff(5518,plain,
% 2.15/2.36 (b(s(elem!1), elem!1)),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[856, 5517, 5434])).
% 2.15/2.36 tff(5519,plain,
% 2.15/2.36 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5518, 5514])).
% 2.15/2.36 tff(5520,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5521,plain,
% 2.15/2.36 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(rewrite,[status(thm)],[])).
% 2.15/2.36 tff(5522,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.15/2.36 inference(monotonicity,[status(thm)],[5521])).
% 2.15/2.36 tff(5523,plain,
% 2.15/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(transitivity,[status(thm)],[5522, 5520])).
% 2.15/2.36 tff(5524,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.15/2.36 inference(quant_inst,[status(thm)],[])).
% 2.15/2.36 tff(5525,plain,
% 2.15/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.15/2.36 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 2.15/2.36 tff(5526,plain,
% 2.15/2.36 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5525, 198, 1185, 595, 5398, 5400])).
% 2.15/2.36 tff(5527,plain,
% 2.15/2.36 ($false),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5526, 5519, 5513])).
% 2.15/2.36 tff(5528,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~r(z, s(s(z)))) | (~r(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(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.36 tff(5529,plain,
% 2.15/2.36 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.15/2.36 inference(unit_resolution,[status(thm)],[5528, 5330, 595, 5375, 1185, 5020, 5350, 153, 5374, 5339, 5372, 2, 5126])).
% 2.15/2.36 tff(5530,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 2.15/2.36 tff(5531,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5532,plain,
% 2.15/2.37 (((~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5533,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5532])).
% 2.15/2.37 tff(5534,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5533, 5531])).
% 2.15/2.37 tff(5535,plain,
% 2.15/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5536,plain,
% 2.15/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5535, 5534])).
% 2.15/2.37 tff(5537,plain,
% 2.15/2.37 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5536, 198, 95, 271, 5428, 4167])).
% 2.15/2.37 tff(5538,plain,
% 2.15/2.37 (r(elem!1, s(s(s(s(s(z))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[4810, 5537, 5530])).
% 2.15/2.37 tff(5539,plain,
% 2.15/2.37 (~b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5008, 198, 1185, 595, 4167])).
% 2.15/2.37 tff(5540,plain,
% 2.15/2.37 (r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[469, 5539])).
% 2.15/2.37 tff(5541,plain,
% 2.15/2.37 (~b(elem!1, s(z))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[1694, 198, 95, 271, 1185, 595])).
% 2.15/2.37 tff(5542,plain,
% 2.15/2.37 (r(elem!1, s(z))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[242, 5541, 237])).
% 2.15/2.37 tff(5543,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5544,plain,
% 2.15/2.37 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5545,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5544])).
% 2.15/2.37 tff(5546,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5545, 5543])).
% 2.15/2.37 tff(5547,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5548,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5547, 5546])).
% 2.15/2.37 tff(5549,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5548, 163, 236, 5542, 5540, 5538])).
% 2.15/2.37 tff(5550,plain,((~b(elem!1, z)) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5551,plain,
% 2.15/2.37 (~b(elem!1, z)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5550, 5330, 5529, 5351, 95, 5349, 5341, 1185, 595])).
% 2.15/2.37 tff(5552,plain,
% 2.15/2.37 (r(elem!1, z)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[187, 5551, 5018])).
% 2.15/2.37 tff(5553,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5554,plain,
% 2.15/2.37 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5555,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5554])).
% 2.15/2.37 tff(5556,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5555, 5553])).
% 2.15/2.37 tff(5557,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5558,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5557, 5556])).
% 2.15/2.37 tff(5559,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5558, 163, 833, 153, 258, 152])).
% 2.15/2.37 tff(5560,plain,((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5561,plain,
% 2.15/2.37 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5560, 5552, 153, 4957])).
% 2.15/2.37 tff(5562,plain,
% 2.15/2.37 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[3792, 5017])).
% 2.15/2.37 tff(5563,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5564,plain,
% 2.15/2.37 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5565,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5564])).
% 2.15/2.37 tff(5566,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5565, 5563])).
% 2.15/2.37 tff(5567,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5568,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5567, 5566])).
% 2.15/2.37 tff(5569,plain,
% 2.15/2.37 (~r(elem!1, s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5568, 163, 833, 153, 332])).
% 2.15/2.37 tff(5570,plain,
% 2.15/2.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5571,plain,
% 2.15/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5572,plain,
% 2.15/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5571, 5570])).
% 2.15/2.37 tff(5573,plain,
% 2.15/2.37 (b(elem!1, s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 5569])).
% 2.15/2.37 tff(5574,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5575,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5576,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5575, 5574])).
% 2.15/2.37 tff(5577,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5576, 163, 153, 332, 423, 152])).
% 2.15/2.37 tff(5578,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5579,plain,
% 2.15/2.37 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5578, 332, 153, 152])).
% 2.15/2.37 tff(5580,plain,
% 2.15/2.37 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[420, 5579])).
% 2.15/2.37 tff(5581,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5582,plain,
% 2.15/2.37 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5583,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5582])).
% 2.15/2.37 tff(5584,plain,
% 2.15/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5583, 5581])).
% 2.15/2.37 tff(5585,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5586,plain,
% 2.15/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5585, 5584])).
% 2.15/2.37 tff(5587,plain,
% 2.15/2.37 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5586, 163, 833, 153, 152])).
% 2.15/2.37 tff(5588,plain,
% 2.15/2.37 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[703, 5587, 673])).
% 2.15/2.37 tff(5589,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5590,plain,
% 2.15/2.37 (((~b(s(s(z)), 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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, 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)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5591,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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)))))))))))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5590])).
% 2.15/2.37 tff(5592,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), 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))))))))))),
% 2.15/2.37 inference(transitivity,[status(thm)],[5591, 5589])).
% 2.15/2.37 tff(5593,plain,
% 2.15/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(elem!1, 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))))))))))),
% 2.15/2.37 inference(quant_inst,[status(thm)],[])).
% 2.15/2.37 tff(5594,plain,
% 2.15/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 2.15/2.37 tff(5595,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5594, 198, 5588, 348, 831, 5580, 5573])).
% 2.15/2.37 tff(5596,plain,((~r(elem!1, z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5597,plain,
% 2.15/2.37 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5596, 5552, 5011, 5562, 5020, 153, 4957, 5374])).
% 2.15/2.37 tff(5598,plain,
% 2.15/2.37 ($false),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[256, 5597, 5561, 5017])).
% 2.15/2.37 tff(5599,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (elem!1 = s(s(z))) | (~r(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.37 tff(5600,plain,
% 2.15/2.37 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5599, 5015, 153, 5013, 1185, 4945, 2, 5011, 149, 482])).
% 2.15/2.37 tff(5601,plain,
% 2.15/2.37 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[3613, 5600])).
% 2.15/2.37 tff(5602,plain,
% 2.15/2.37 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.15/2.37 inference(symmetry,[status(thm)],[5048])).
% 2.15/2.37 tff(5603,plain,
% 2.15/2.37 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[348, 5124])).
% 2.15/2.37 tff(5604,plain,
% 2.15/2.37 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[4981, 4934, 153, 152])).
% 2.15/2.37 tff(5605,plain,
% 2.15/2.37 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[420, 5604])).
% 2.15/2.37 tff(5606,plain,
% 2.15/2.37 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5605, 5122])).
% 2.15/2.37 tff(5607,plain,
% 2.15/2.37 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 2.15/2.37 inference(monotonicity,[status(thm)],[5602])).
% 2.15/2.37 tff(5608,plain,
% 2.15/2.37 (~b(s(s(s(s(elem!1)))), z)),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[3839, 5607])).
% 2.15/2.37 tff(5609,plain,
% 2.15/2.37 (r(s(s(s(s(elem!1)))), z)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[5162, 26, 5159, 5608])).
% 2.15/2.37 tff(5610,plain,
% 2.15/2.37 (r(s(s(s(s(s(z))))), z)),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[3841, 3839])).
% 2.15/2.37 tff(5611,plain,
% 2.15/2.37 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[3882, 5610, 153, 152])).
% 2.15/2.37 tff(5612,plain,
% 2.15/2.37 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(unit_resolution,[status(thm)],[3098, 5611])).
% 2.15/2.37 tff(5613,plain,
% 2.15/2.37 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.37 inference(modus_ponens,[status(thm)],[5612, 5035])).
% 2.15/2.37 tff(5614,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5615,plain,
% 2.15/2.37 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.37 inference(rewrite,[status(thm)],[])).
% 2.15/2.37 tff(5616,plain,
% 2.15/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5615])).
% 2.15/2.38 tff(5617,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5616, 5614])).
% 2.15/2.38 tff(5618,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5619,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 2.15/2.38 tff(5620,plain,
% 2.15/2.38 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5619, 198, 3317, 4703, 5613])).
% 2.15/2.38 tff(5621,plain,
% 2.15/2.38 ((s(s(s(s(elem!1)))) = s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5111, 26, 5620])).
% 2.15/2.38 tff(5622,plain,
% 2.15/2.38 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5621, 5104])).
% 2.15/2.38 tff(5623,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5624,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5625,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5624, 5623])).
% 2.15/2.38 tff(5626,plain,
% 2.15/2.38 ($false),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5625, 163, 1474, 842, 5622, 5609])).
% 2.15/2.38 tff(5627,plain,(b(s(s(s(s(s(z))))), z) | (~r(s(elem!1), elem!1)) | (~(s(z) = 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))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.38 tff(5628,plain,
% 2.15/2.38 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5627, 5079, 206, 5606, 5603, 153, 152])).
% 2.15/2.38 tff(5629,plain,
% 2.15/2.38 (b(s(s(s(s(elem!1)))), z)),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5628, 5602])).
% 2.15/2.38 tff(5630,plain,
% 2.15/2.38 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5631,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5630])).
% 2.15/2.38 tff(5632,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5631, 5050])).
% 2.15/2.38 tff(5633,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5634,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 2.15/2.38 tff(5635,plain,
% 2.15/2.38 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5634, 198, 95, 1286])).
% 2.15/2.38 tff(5636,plain,
% 2.15/2.38 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5635, 5629])).
% 2.15/2.38 tff(5637,plain,
% 2.15/2.38 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5065, 5636, 5032])).
% 2.15/2.38 tff(5638,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5639,plain,
% 2.15/2.38 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5640,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5639])).
% 2.15/2.38 tff(5641,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5640, 5638])).
% 2.15/2.38 tff(5642,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5643,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5642, 5641])).
% 2.15/2.38 tff(5644,plain,
% 2.15/2.38 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5643, 163, 5079, 5637, 2836])).
% 2.15/2.38 tff(5645,plain,
% 2.15/2.38 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5111, 26, 5644])).
% 2.15/2.38 tff(5646,plain,
% 2.15/2.38 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5645, 5104])).
% 2.15/2.38 tff(5647,plain,
% 2.15/2.38 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5648,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5647])).
% 2.15/2.38 tff(5649,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5648, 5614])).
% 2.15/2.38 tff(5650,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5651,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5650, 5649])).
% 2.15/2.38 tff(5652,plain,
% 2.15/2.38 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5651, 198, 5606, 5603, 5646])).
% 2.15/2.38 tff(5653,plain,
% 2.15/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5652, 5037])).
% 2.15/2.38 tff(5654,plain,
% 2.15/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[3098, 5653])).
% 2.15/2.38 tff(5655,plain,
% 2.15/2.38 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5654, 5096])).
% 2.15/2.38 tff(5656,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5657,plain,
% 2.15/2.38 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5658,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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)))))))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5657])).
% 2.15/2.38 tff(5659,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5658, 5656])).
% 2.15/2.38 tff(5660,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5661,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5660, 5659])).
% 2.15/2.38 tff(5662,plain,
% 2.15/2.38 ($false),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5661, 163, 5637, 2836, 152, 5655])).
% 2.15/2.38 tff(5663,plain,((~(s(z) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | b(s(s(z)), s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.38 tff(5664,plain,
% 2.15/2.38 (~(s(z) = elem!1)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5663, 4955, 5013, 153, 4979, 5601, 1185, 482, 5012])).
% 2.15/2.38 tff(5665,plain,
% 2.15/2.38 (r(s(z), elem!1)),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[217, 5664, 149])).
% 2.15/2.38 tff(5666,plain,
% 2.15/2.38 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5335, 163, 5665, 4934, 5010])).
% 2.15/2.38 tff(5667,plain,
% 2.15/2.38 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[511, 26, 508, 5666])).
% 2.15/2.38 tff(5668,plain,
% 2.15/2.38 (((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5669,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5668])).
% 2.15/2.38 tff(5670,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5669, 4986])).
% 2.15/2.38 tff(5671,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5672,plain,
% 2.15/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5671, 5670])).
% 2.15/2.38 tff(5673,plain,
% 2.15/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5672, 198, 4979, 5015, 5667])).
% 2.15/2.38 tff(5674,plain,
% 2.15/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[3098, 5673])).
% 2.15/2.38 tff(5675,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5676,plain,
% 2.15/2.38 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(rewrite,[status(thm)],[])).
% 2.15/2.38 tff(5677,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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)))))))))))),
% 2.15/2.38 inference(monotonicity,[status(thm)],[5676])).
% 2.15/2.38 tff(5678,plain,
% 2.15/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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))))))))))),
% 2.15/2.38 inference(transitivity,[status(thm)],[5677, 5675])).
% 2.15/2.38 tff(5679,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.15/2.38 inference(quant_inst,[status(thm)],[])).
% 2.15/2.38 tff(5680,plain,
% 2.15/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.38 inference(modus_ponens,[status(thm)],[5679, 5678])).
% 2.15/2.38 tff(5681,plain,
% 2.15/2.38 ($false),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5680, 163, 5674, 5601, 4955, 5010])).
% 2.15/2.38 tff(5682,plain,(b(s(s(z)), s(z)) | (~b(s(z), z)) | (~r(z, s(s(z)))) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.15/2.38 tff(5683,plain,
% 2.15/2.38 (b(s(s(z)), s(z))),
% 2.15/2.38 inference(unit_resolution,[status(thm)],[5682, 4918, 55, 149, 2, 4933, 56])).
% 2.15/2.38 tff(5684,plain,
% 2.15/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5685,plain,
% 2.15/2.39 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5686,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5685])).
% 2.15/2.39 tff(5687,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5686, 5684])).
% 2.15/2.39 tff(5688,plain,
% 2.15/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5689,plain,
% 2.15/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 2.15/2.39 tff(5690,plain,
% 2.15/2.39 ($false),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5689, 198, 1185, 560, 348, 347, 2])).
% 2.15/2.39 tff(5691,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.39 tff(5692,plain,
% 2.15/2.39 (~b(s(s(z)), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5691, 348, 560, 1185, 2])).
% 2.15/2.39 tff(5693,plain,
% 2.15/2.39 (r(s(s(z)), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[345, 5692])).
% 2.15/2.39 tff(5694,plain,
% 2.15/2.39 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5578, 5693, 153, 152])).
% 2.15/2.39 tff(5695,plain,
% 2.15/2.39 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[420, 5694])).
% 2.15/2.39 tff(5696,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5697,plain,
% 2.15/2.39 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5698,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5697])).
% 2.15/2.39 tff(5699,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5698, 5696])).
% 2.15/2.39 tff(5700,plain,
% 2.15/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5701,plain,
% 2.15/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5700, 5699])).
% 2.15/2.39 tff(5702,plain,
% 2.15/2.39 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5701, 198, 560, 3819, 348, 2])).
% 2.15/2.39 tff(5703,plain,
% 2.15/2.39 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[2715, 26, 507, 5702])).
% 2.15/2.39 tff(5704,plain,
% 2.15/2.39 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[4991, 198, 3819, 348, 3745])).
% 2.15/2.39 tff(5705,plain,
% 2.15/2.39 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[511, 26, 508, 5704])).
% 2.15/2.39 tff(5706,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5707,plain,
% 2.15/2.39 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5708,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5707])).
% 2.15/2.39 tff(5709,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5708, 5706])).
% 2.15/2.39 tff(5710,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5711,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5710, 5709])).
% 2.15/2.39 tff(5712,plain,
% 2.15/2.39 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5711, 163, 153, 5705, 5703])).
% 2.15/2.39 tff(5713,plain,
% 2.15/2.39 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3841, 5712])).
% 2.15/2.39 tff(5714,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5715,plain,
% 2.15/2.39 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5716,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5715])).
% 2.15/2.39 tff(5717,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5716, 5714])).
% 2.15/2.39 tff(5718,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5719,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5718, 5717])).
% 2.15/2.39 tff(5720,plain,
% 2.15/2.39 (~r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5719, 163, 328, 5705, 5703])).
% 2.15/2.39 tff(5721,plain,
% 2.15/2.39 (b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[469, 5720])).
% 2.15/2.39 tff(5722,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5723,plain,
% 2.15/2.39 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5724,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5723])).
% 2.15/2.39 tff(5725,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5724, 5722])).
% 2.15/2.39 tff(5726,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5727,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5726, 5725])).
% 2.15/2.39 tff(5728,plain,
% 2.15/2.39 (~r(z, s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5727, 163, 328, 153, 5693])).
% 2.15/2.39 tff(5729,plain,
% 2.15/2.39 (b(z, s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[593, 5728])).
% 2.15/2.39 tff(5730,plain,
% 2.15/2.39 ($false),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[2662, 198, 1185, 5729, 5721, 5713])).
% 2.15/2.39 tff(5731,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.39 tff(5732,plain,
% 2.15/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5731, 348, 153, 328, 1185, 5695, 560, 2])).
% 2.15/2.39 tff(5733,plain,
% 2.15/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3098, 5732])).
% 2.15/2.39 tff(5734,plain,
% 2.15/2.39 (~r(s(s(s(s(s(z))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3882, 5733, 153, 152])).
% 2.15/2.39 tff(5735,plain,
% 2.15/2.39 (b(s(s(s(s(s(z))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3841, 5734])).
% 2.15/2.39 tff(5736,plain,
% 2.15/2.39 (~r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5680, 163, 5733, 151, 152])).
% 2.15/2.39 tff(5737,plain,
% 2.15/2.39 (b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[469, 5736])).
% 2.15/2.39 tff(5738,plain,
% 2.15/2.39 ($false),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[2662, 198, 1185, 5729, 5737, 5735])).
% 2.15/2.39 tff(5739,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.39 tff(5740,plain,
% 2.15/2.39 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5739, 328, 151, 152, 153, 1185, 560, 2])).
% 2.15/2.39 tff(5741,plain,
% 2.15/2.39 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[374, 5740])).
% 2.15/2.39 tff(5742,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5743,plain,
% 2.15/2.39 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5744,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5743])).
% 2.15/2.39 tff(5745,plain,
% 2.15/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.39 inference(transitivity,[status(thm)],[5744, 5742])).
% 2.15/2.39 tff(5746,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 2.15/2.39 inference(quant_inst,[status(thm)],[])).
% 2.15/2.39 tff(5747,plain,
% 2.15/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.15/2.39 inference(modus_ponens,[status(thm)],[5746, 5745])).
% 2.15/2.39 tff(5748,plain,
% 2.15/2.39 ($false),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5747, 163, 328, 151, 5741, 152])).
% 2.15/2.39 tff(5749,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.39 tff(5750,plain,
% 2.15/2.39 (~r(s(z), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5749, 152, 151, 153, 1185, 560, 2])).
% 2.15/2.39 tff(5751,plain,
% 2.15/2.39 (b(s(z), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[403, 5750])).
% 2.15/2.39 tff(5752,plain,
% 2.15/2.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3753, 5751, 560, 2])).
% 2.15/2.39 tff(5753,plain,
% 2.15/2.39 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[420, 5752])).
% 2.15/2.39 tff(5754,plain,
% 2.15/2.39 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[3763, 5753, 152, 153])).
% 2.15/2.39 tff(5755,plain,
% 2.15/2.39 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[374, 5754])).
% 2.15/2.39 tff(5756,plain,
% 2.15/2.39 (~r(s(s(z)), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5578, 5753, 153, 152])).
% 2.15/2.39 tff(5757,plain,
% 2.15/2.39 (b(s(s(z)), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[345, 5756])).
% 2.15/2.39 tff(5758,plain,
% 2.15/2.39 ($false),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5691, 5757, 5755, 560, 1185, 2])).
% 2.15/2.39 tff(5759,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.39 tff(5760,plain,
% 2.15/2.39 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[5759, 560, 4918, 2, 55, 151])).
% 2.15/2.39 tff(5761,plain,
% 2.15/2.39 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.39 inference(unit_resolution,[status(thm)],[176, 5760])).
% 2.15/2.39 tff(5762,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5763,plain,
% 2.15/2.39 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.39 inference(rewrite,[status(thm)],[])).
% 2.15/2.39 tff(5764,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.15/2.39 inference(monotonicity,[status(thm)],[5763])).
% 2.15/2.39 tff(5765,plain,
% 2.15/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.15/2.40 inference(transitivity,[status(thm)],[5764, 5762])).
% 2.15/2.40 tff(5766,plain,
% 2.15/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.15/2.40 inference(quant_inst,[status(thm)],[])).
% 2.15/2.40 tff(5767,plain,
% 2.15/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.15/2.40 inference(modus_ponens,[status(thm)],[5766, 5765])).
% 2.15/2.40 tff(5768,plain,
% 2.15/2.40 ($false),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[5767, 198, 1185, 560, 3745, 2, 330])).
% 2.15/2.40 tff(5769,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.15/2.40 tff(5770,plain,
% 2.15/2.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[5769, 5761, 4918, 2, 560])).
% 2.15/2.40 tff(5771,plain,
% 2.15/2.40 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[420, 5770])).
% 2.15/2.40 tff(5772,plain,
% 2.15/2.40 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[5759, 560, 1185, 2, 153, 151])).
% 2.15/2.40 tff(5773,plain,
% 2.15/2.40 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[176, 5772])).
% 2.15/2.40 tff(5774,plain,
% 2.15/2.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[5769, 5773, 1185, 2, 560])).
% 2.15/2.40 tff(5775,plain,
% 2.15/2.40 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[420, 5774])).
% 2.15/2.40 tff(5776,plain,
% 2.15/2.40 (~b(z, s(z))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[4953, 5773, 2, 1185])).
% 2.15/2.40 tff(5777,plain,
% 2.15/2.40 (r(z, s(z))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[593, 5776])).
% 2.15/2.40 tff(5778,plain,
% 2.15/2.40 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 2.15/2.40 inference(modus_ponens,[status(thm)],[424, 2934])).
% 2.15/2.40 tff(5779,plain,
% 2.15/2.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[5769, 330, 560, 2, 1185])).
% 2.15/2.40 tff(5780,plain,
% 2.15/2.40 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[419, 5779, 368])).
% 2.15/2.40 tff(5781,plain,
% 2.15/2.40 (~r(s(s(s(s(s(z))))), s(z))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[455, 424, 5780, 151, 331, 330, 406])).
% 2.15/2.40 tff(5782,plain,
% 2.15/2.40 (b(s(s(s(s(s(z))))), s(z))),
% 2.15/2.40 inference(unit_resolution,[status(thm)],[469, 5781])).
% 2.15/2.40 tff(5783,plain,
% 2.15/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.40 inference(rewrite,[status(thm)],[])).
% 2.15/2.40 tff(5784,plain,
% 2.15/2.40 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.15/2.40 inference(rewrite,[status(thm)],[])).
% 2.15/2.40 tff(5785,plain,
% 2.15/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5784])).
% 2.25/2.40 tff(5786,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5785, 5783])).
% 2.25/2.40 tff(5787,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5788,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5787, 5786])).
% 2.25/2.40 tff(5789,plain,
% 2.25/2.40 (~r(s(z), s(s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5788, 163, 151, 3272, 5780])).
% 2.25/2.40 tff(5790,plain,
% 2.25/2.40 (b(s(z), s(s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[403, 5789])).
% 2.25/2.40 tff(5791,plain,
% 2.25/2.40 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[494, 198, 560, 5790, 5782])).
% 2.25/2.40 tff(5792,plain,
% 2.25/2.40 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[511, 26, 508, 5791])).
% 2.25/2.40 tff(5793,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5794,plain,
% 2.25/2.40 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5795,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5794])).
% 2.25/2.40 tff(5796,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5795, 5793])).
% 2.25/2.40 tff(5797,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5798,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5797, 5796])).
% 2.25/2.40 tff(5799,plain,
% 2.25/2.40 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5798, 163, 3272, 5780, 5792])).
% 2.25/2.40 tff(5800,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5801,plain,
% 2.25/2.40 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5802,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5801])).
% 2.25/2.40 tff(5803,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5802, 5800])).
% 2.25/2.40 tff(5804,plain,
% 2.25/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5805,plain,
% 2.25/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5804, 5803])).
% 2.25/2.40 tff(5806,plain,
% 2.25/2.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5805, 198, 1185, 2, 330, 5782])).
% 2.25/2.40 tff(5807,plain,
% 2.25/2.40 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[3328, 26, 5806])).
% 2.25/2.40 tff(5808,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5807, 5799, 5778])).
% 2.25/2.40 tff(5809,plain,((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5810,plain,
% 2.25/2.40 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5809, 314])).
% 2.25/2.40 tff(5811,plain,
% 2.25/2.40 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5810, 3272, 2, 1185, 560, 151, 5773, 5777])).
% 2.25/2.40 tff(5812,plain,
% 2.25/2.40 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[31, 5811])).
% 2.25/2.40 tff(5813,plain,
% 2.25/2.40 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5814,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5813])).
% 2.25/2.40 tff(5815,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5814, 4660])).
% 2.25/2.40 tff(5816,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5817,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5816, 5815])).
% 2.25/2.40 tff(5818,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5817, 163, 153, 3272, 5812, 5775])).
% 2.25/2.40 tff(5819,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5820,plain,
% 2.25/2.40 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5819, 560, 2, 4918, 55, 151])).
% 2.25/2.40 tff(5821,plain,
% 2.25/2.40 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[374, 5820])).
% 2.25/2.40 tff(5822,plain,
% 2.25/2.40 (~b(s(s(z)), z)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5691, 5821, 560, 4918, 2])).
% 2.25/2.40 tff(5823,plain,
% 2.25/2.40 (r(s(s(z)), z)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[345, 5822])).
% 2.25/2.40 tff(5824,plain,
% 2.25/2.40 (r(z, s(s(elem!1)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1096, 88])).
% 2.25/2.40 tff(5825,plain,
% 2.25/2.40 (~r(s(z), elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[3427, 5824, 151, 2, 330, 57, 111, 42])).
% 2.25/2.40 tff(5826,plain,
% 2.25/2.40 (s(z) = elem!1),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[217, 5825, 149])).
% 2.25/2.40 tff(5827,plain,
% 2.25/2.40 (elem!1 = z),
% 2.25/2.40 inference(symmetry,[status(thm)],[57])).
% 2.25/2.40 tff(5828,plain,
% 2.25/2.40 (s(elem!1) = s(z)),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5827])).
% 2.25/2.40 tff(5829,plain,
% 2.25/2.40 (s(elem!1) = elem!1),
% 2.25/2.40 inference(transitivity,[status(thm)],[5828, 5826])).
% 2.25/2.40 tff(5830,plain,
% 2.25/2.40 (~(s(elem!1) = elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[1395, 119])).
% 2.25/2.40 tff(5831,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5830, 5829])).
% 2.25/2.40 tff(5832,plain,((~(z = elem!1)) | b(s(z), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(z, s(s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5833,plain,
% 2.25/2.40 (~(z = elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5832, 5761, 151, 2, 149, 42, 56])).
% 2.25/2.40 tff(5834,plain,
% 2.25/2.40 (b(z, elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[102, 5833, 56])).
% 2.25/2.40 tff(5835,plain,
% 2.25/2.40 (~(elem!1 = s(s(z)))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4932, 5834, 42])).
% 2.25/2.40 tff(5836,plain,
% 2.25/2.40 (~b(z, s(z))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4953, 5761, 2, 4918])).
% 2.25/2.40 tff(5837,plain,
% 2.25/2.40 (~(s(z) = elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[4600, 5834, 5836])).
% 2.25/2.40 tff(5838,plain,
% 2.25/2.40 (~(s(s(z)) = s(elem!1))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[227, 5837])).
% 2.25/2.40 tff(5839,plain,
% 2.25/2.40 (~(elem!1 = s(z))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[234, 5838])).
% 2.25/2.40 tff(5840,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5841,plain,
% 2.25/2.40 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5842,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5841])).
% 2.25/2.40 tff(5843,plain,
% 2.25/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5842, 5840])).
% 2.25/2.40 tff(5844,plain,
% 2.25/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5845,plain,
% 2.25/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.25/2.40 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 2.25/2.40 tff(5846,plain,
% 2.25/2.40 ($false),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5845, 198, 95, 1185, 831, 2, 330])).
% 2.25/2.40 tff(5847,plain,((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.40 tff(5848,plain,
% 2.25/2.40 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[5847, 5834, 4918, 2, 5761])).
% 2.25/2.40 tff(5849,plain,
% 2.25/2.40 (r(s(z), elem!1)),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[217, 5837, 149])).
% 2.25/2.40 tff(5850,plain,
% 2.25/2.40 (b(elem!1, s(z))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[269, 5849, 151, 5848, 5839, 2])).
% 2.25/2.40 tff(5851,plain,
% 2.25/2.40 (r(z, s(z))),
% 2.25/2.40 inference(unit_resolution,[status(thm)],[593, 5836])).
% 2.25/2.40 tff(5852,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5853,plain,
% 2.25/2.40 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(rewrite,[status(thm)],[])).
% 2.25/2.40 tff(5854,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.40 inference(monotonicity,[status(thm)],[5853])).
% 2.25/2.40 tff(5855,plain,
% 2.25/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(transitivity,[status(thm)],[5854, 5852])).
% 2.25/2.40 tff(5856,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.40 inference(quant_inst,[status(thm)],[])).
% 2.25/2.40 tff(5857,plain,
% 2.25/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5856, 5855])).
% 2.25/2.41 tff(5858,plain,
% 2.25/2.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5857, 163, 55, 5823, 5771])).
% 2.25/2.41 tff(5859,plain,
% 2.25/2.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[31, 5858])).
% 2.25/2.41 tff(5860,plain,
% 2.25/2.41 (~r(s(s(s(s(s(z))))), s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[456, 5859, 151, 5761, 5851, 5771])).
% 2.25/2.41 tff(5861,plain,
% 2.25/2.41 (b(s(s(s(s(s(z))))), s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[469, 5860])).
% 2.25/2.41 tff(5862,plain,
% 2.25/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5805, 198, 4918, 2, 5761, 5861])).
% 2.25/2.41 tff(5863,plain,
% 2.25/2.41 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3328, 26, 5862])).
% 2.25/2.41 tff(5864,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5863, 2935])).
% 2.25/2.41 tff(5865,plain,
% 2.25/2.41 (~b(elem!1, s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[552, 198, 320, 560, 407])).
% 2.25/2.41 tff(5866,plain,
% 2.25/2.41 (r(elem!1, s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 5865])).
% 2.25/2.41 tff(5867,plain,
% 2.25/2.41 (s(s(s(s(s(z))))) = elem!1),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[580, 5866, 95, 559, 332, 320, 153, 560, 407])).
% 2.25/2.41 tff(5868,plain,
% 2.25/2.41 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5867])).
% 2.25/2.41 tff(5869,plain,
% 2.25/2.41 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5868])).
% 2.25/2.41 tff(5870,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5869])).
% 2.25/2.41 tff(5871,plain,
% 2.25/2.41 (r(s(s(elem!1)), s(s(z)))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[423, 5870])).
% 2.25/2.41 tff(5872,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5869])).
% 2.25/2.41 tff(5873,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5867])).
% 2.25/2.41 tff(5874,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[3368, 5873])).
% 2.25/2.41 tff(5875,plain,
% 2.25/2.41 (r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5874, 5872])).
% 2.25/2.41 tff(5876,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5877,plain,
% 2.25/2.41 (((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5878,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5877])).
% 2.25/2.41 tff(5879,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5878, 5876])).
% 2.25/2.41 tff(5880,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5881,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5880, 5879])).
% 2.25/2.41 tff(5882,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5881, 163, 5875, 332, 5871, 5866])).
% 2.25/2.41 tff(5883,plain,((~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5884,plain,
% 2.25/2.41 (~b(s(z), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5883, 5823, 5771, 5864, 5834, 5861, 5850, 55, 560, 5835])).
% 2.25/2.41 tff(5885,plain,
% 2.25/2.41 (r(s(z), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[403, 5884])).
% 2.25/2.41 tff(5886,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5887,plain,
% 2.25/2.41 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5888,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5887])).
% 2.25/2.41 tff(5889,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5888, 5886])).
% 2.25/2.41 tff(5890,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5891,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 2.25/2.41 tff(5892,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5891, 163, 5885, 151, 5823, 5771])).
% 2.25/2.41 tff(5893,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(z), elem!1) | b(z, s(s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5894,plain,
% 2.25/2.41 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5893, 5683, 2, 149, 42, 56])).
% 2.25/2.41 tff(5895,plain,
% 2.25/2.41 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3613, 5894])).
% 2.25/2.41 tff(5896,plain,
% 2.25/2.41 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3626, 5895, 2, 5683])).
% 2.25/2.41 tff(5897,plain,
% 2.25/2.41 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[374, 5896])).
% 2.25/2.41 tff(5898,plain,
% 2.25/2.41 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5847, 330, 1185, 2, 95])).
% 2.25/2.41 tff(5899,plain,
% 2.25/2.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3701, 5898, 153, 3272, 95])).
% 2.25/2.41 tff(5900,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5901,plain,
% 2.25/2.41 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5902,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5901])).
% 2.25/2.41 tff(5903,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5902, 5900])).
% 2.25/2.41 tff(5904,plain,
% 2.25/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5905,plain,
% 2.25/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 2.25/2.41 tff(5906,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5905, 198, 1185, 3615, 5899, 2, 330])).
% 2.25/2.41 tff(5907,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5908,plain,
% 2.25/2.41 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5907, 4918, 5895, 2, 55, 5897, 4925])).
% 2.25/2.41 tff(5909,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[176, 5908])).
% 2.25/2.41 tff(5910,plain,
% 2.25/2.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3763, 5909, 5897, 55])).
% 2.25/2.41 tff(5911,plain,
% 2.25/2.41 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[420, 5910])).
% 2.25/2.41 tff(5912,plain,
% 2.25/2.41 (~b(s(z), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3753, 5911, 5683, 2])).
% 2.25/2.41 tff(5913,plain,
% 2.25/2.41 (r(s(z), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[403, 5912])).
% 2.25/2.41 tff(5914,plain,
% 2.25/2.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[4548, 5909, 55, 5897])).
% 2.25/2.41 tff(5915,plain,
% 2.25/2.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[31, 5914])).
% 2.25/2.41 tff(5916,plain,
% 2.25/2.41 (~b(z, s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[4967, 5915, 5895, 4918, 2])).
% 2.25/2.41 tff(5917,plain,
% 2.25/2.41 (r(z, s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[593, 5916])).
% 2.25/2.41 tff(5918,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5919,plain,
% 2.25/2.41 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5920,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5919])).
% 2.25/2.41 tff(5921,plain,
% 2.25/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5920, 5918])).
% 2.25/2.41 tff(5922,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5923,plain,
% 2.25/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5922, 5921])).
% 2.25/2.41 tff(5924,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5923, 163, 5917, 5913, 55, 5897])).
% 2.25/2.41 tff(5925,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, s(s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5926,plain,
% 2.25/2.41 (b(s(z), elem!1)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5925, 56, 42, 2])).
% 2.25/2.41 tff(5927,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 2.25/2.41 tff(5928,plain,
% 2.25/2.41 (b(s(z), z)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5927, 4919])).
% 2.25/2.41 tff(5929,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[34, 5928])).
% 2.25/2.41 tff(5930,plain,((~(z = elem!1)) | b(s(z), z) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5931,plain,
% 2.25/2.41 (b(s(z), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5930, 57, 5926])).
% 2.25/2.41 tff(5932,plain,
% 2.25/2.41 (~(s(s(elem!1)) = s(elem!1))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1138, 141])).
% 2.25/2.41 tff(5933,plain,
% 2.25/2.41 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[58])).
% 2.25/2.41 tff(5934,plain,
% 2.25/2.41 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.25/2.41 inference(symmetry,[status(thm)],[5933])).
% 2.25/2.41 tff(5935,plain,
% 2.25/2.41 (b(s(s(z)), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[59])).
% 2.25/2.41 tff(5936,plain,
% 2.25/2.41 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 2.25/2.41 inference(symmetry,[status(thm)],[5935])).
% 2.25/2.41 tff(5937,plain,
% 2.25/2.41 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5936, 5934])).
% 2.25/2.41 tff(5938,plain,
% 2.25/2.41 (b(s(s(z)), s(z))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[1145, 5937])).
% 2.25/2.41 tff(5939,plain,
% 2.25/2.41 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5819, 151, 2, 1185, 153, 5938])).
% 2.25/2.41 tff(5940,plain,
% 2.25/2.41 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[374, 5939])).
% 2.25/2.41 tff(5941,plain,
% 2.25/2.41 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5940, 3402])).
% 2.25/2.41 tff(5942,plain,
% 2.25/2.41 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(monotonicity,[status(thm)],[59])).
% 2.25/2.41 tff(5943,plain,
% 2.25/2.41 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(transitivity,[status(thm)],[61, 5942])).
% 2.25/2.41 tff(5944,plain,
% 2.25/2.41 (~b(s(s(z)), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5691, 5940, 1185, 5938, 2])).
% 2.25/2.41 tff(5945,plain,
% 2.25/2.41 (r(s(s(z)), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[345, 5944])).
% 2.25/2.41 tff(5946,plain,
% 2.25/2.41 (r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5945, 5943])).
% 2.25/2.41 tff(5947,plain,
% 2.25/2.41 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5759, 151, 1185, 2, 153, 5938])).
% 2.25/2.41 tff(5948,plain,
% 2.25/2.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[176, 5947])).
% 2.25/2.41 tff(5949,plain,
% 2.25/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5769, 5948, 1185, 2, 5938])).
% 2.25/2.41 tff(5950,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[420, 5949])).
% 2.25/2.41 tff(5951,plain,
% 2.25/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5950, 2959])).
% 2.25/2.41 tff(5952,plain,
% 2.25/2.41 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[2942, 151, 57])).
% 2.25/2.41 tff(5953,plain,
% 2.25/2.41 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5759, 4957, 1185, 2, 153, 560])).
% 2.25/2.41 tff(5954,plain,
% 2.25/2.41 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3613, 5953])).
% 2.25/2.41 tff(5955,plain,
% 2.25/2.41 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3626, 5954, 2, 560])).
% 2.25/2.41 tff(5956,plain,
% 2.25/2.41 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[374, 5955])).
% 2.25/2.41 tff(5957,plain,
% 2.25/2.41 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[4967, 5954, 595, 1185, 2])).
% 2.25/2.41 tff(5958,plain,
% 2.25/2.41 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[31, 5957])).
% 2.25/2.41 tff(5959,plain,
% 2.25/2.41 ($false),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[4548, 5958, 5956, 153, 4957])).
% 2.25/2.41 tff(5960,plain,((~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.41 tff(5961,plain,
% 2.25/2.41 (~b(z, s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[5960, 5938, 1185, 2, 153])).
% 2.25/2.41 tff(5962,plain,
% 2.25/2.41 (r(z, s(z))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[593, 5961])).
% 2.25/2.41 tff(5963,plain,
% 2.25/2.41 (r(z, s(elem!1))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3155, 5962, 79])).
% 2.25/2.41 tff(5964,plain,
% 2.25/2.41 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.25/2.41 inference(monotonicity,[status(thm)],[57])).
% 2.25/2.41 tff(5965,plain,
% 2.25/2.41 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.25/2.41 inference(symmetry,[status(thm)],[5964])).
% 2.25/2.41 tff(5966,plain,
% 2.25/2.41 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.25/2.41 inference(transitivity,[status(thm)],[61, 5942, 5965])).
% 2.25/2.41 tff(5967,plain,
% 2.25/2.41 (r(s(s(elem!1)), z)),
% 2.25/2.41 inference(modus_ponens,[status(thm)],[5945, 5966])).
% 2.25/2.41 tff(5968,plain,
% 2.25/2.41 (~r(s(elem!1), s(s(elem!1)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[1530, 5967, 5963, 1098])).
% 2.25/2.41 tff(5969,plain,
% 2.25/2.41 (b(s(elem!1), s(s(elem!1)))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[901, 5968, 890])).
% 2.25/2.41 tff(5970,plain,
% 2.25/2.41 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3096, 5969, 57, 1145, 5952, 5951, 5946])).
% 2.25/2.41 tff(5971,plain,
% 2.25/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(unit_resolution,[status(thm)],[3098, 5970])).
% 2.25/2.41 tff(5972,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5973,plain,
% 2.25/2.41 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(rewrite,[status(thm)],[])).
% 2.25/2.41 tff(5974,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.25/2.41 inference(monotonicity,[status(thm)],[5973])).
% 2.25/2.41 tff(5975,plain,
% 2.25/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(transitivity,[status(thm)],[5974, 5972])).
% 2.25/2.41 tff(5976,plain,
% 2.25/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.41 inference(quant_inst,[status(thm)],[])).
% 2.25/2.41 tff(5977,plain,
% 2.25/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[5976, 5975])).
% 2.25/2.42 tff(5978,plain,
% 2.25/2.42 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5977, 198, 1145, 5971, 5941, 4705])).
% 2.25/2.42 tff(5979,plain,
% 2.25/2.42 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3400, 5978, 3385])).
% 2.25/2.42 tff(5980,plain,
% 2.25/2.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1032, 5948, 79])).
% 2.25/2.42 tff(5981,plain,
% 2.25/2.42 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3062, 163, 5946, 405, 5951])).
% 2.25/2.42 tff(5982,plain,
% 2.25/2.42 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[703, 5981, 3002])).
% 2.25/2.42 tff(5983,plain,
% 2.25/2.42 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3105, 198, 5971, 5982, 5980])).
% 2.25/2.42 tff(5984,plain,
% 2.25/2.42 (r(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[528, 5983, 3037])).
% 2.25/2.42 tff(5985,plain,
% 2.25/2.42 (r(elem!1, s(elem!1))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3231, 5963, 79])).
% 2.25/2.42 tff(5986,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(5987,plain,
% 2.25/2.42 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(5988,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[5987])).
% 2.25/2.42 tff(5989,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(transitivity,[status(thm)],[5988, 5986])).
% 2.25/2.42 tff(5990,plain,
% 2.25/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(5991,plain,
% 2.25/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 2.25/2.42 tff(5992,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5991, 163, 5946, 5985, 5984, 5979])).
% 2.25/2.42 tff(5993,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(5994,plain,
% 2.25/2.42 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5993, 1145, 57, 890, 1098, 405, 1185, 2, 153])).
% 2.25/2.42 tff(5995,plain,
% 2.25/2.42 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3613, 5994])).
% 2.25/2.42 tff(5996,plain,
% 2.25/2.42 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4701, 5995, 57])).
% 2.25/2.42 tff(5997,plain,
% 2.25/2.42 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3626, 5995, 2, 5938])).
% 2.25/2.42 tff(5998,plain,
% 2.25/2.42 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[374, 5997])).
% 2.25/2.42 tff(5999,plain,
% 2.25/2.42 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[58, 59])).
% 2.25/2.42 tff(6000,plain,
% 2.25/2.42 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.25/2.42 inference(symmetry,[status(thm)],[5999])).
% 2.25/2.42 tff(6001,plain,
% 2.25/2.42 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3275, 5998, 57])).
% 2.25/2.42 tff(6002,plain,
% 2.25/2.42 (~r(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3361, 6001, 405, 5985])).
% 2.25/2.42 tff(6003,plain,
% 2.25/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[901, 6002, 890])).
% 2.25/2.42 tff(6004,plain,
% 2.25/2.42 (b(s(z), s(s(z)))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6003, 6000])).
% 2.25/2.42 tff(6005,plain,
% 2.25/2.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3753, 6004, 5938, 2])).
% 2.25/2.42 tff(6006,plain,
% 2.25/2.42 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[420, 6005])).
% 2.25/2.42 tff(6007,plain,
% 2.25/2.42 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3763, 6006, 5998, 153])).
% 2.25/2.42 tff(6008,plain,
% 2.25/2.42 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[176, 6007])).
% 2.25/2.42 tff(6009,plain,
% 2.25/2.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1032, 6008, 79])).
% 2.25/2.42 tff(6010,plain,
% 2.25/2.42 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[59])).
% 2.25/2.42 tff(6011,plain,
% 2.25/2.42 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6010, 2838])).
% 2.25/2.42 tff(6012,plain,
% 2.25/2.42 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6011])).
% 2.25/2.42 tff(6013,plain,
% 2.25/2.42 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[369, 6012])).
% 2.25/2.42 tff(6014,plain,
% 2.25/2.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3051, 198, 1145, 6003, 4705])).
% 2.25/2.42 tff(6015,plain,
% 2.25/2.42 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4221, 6014, 6013])).
% 2.25/2.42 tff(6016,plain,
% 2.25/2.42 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3973, 6015, 5998, 153])).
% 2.25/2.42 tff(6017,plain,
% 2.25/2.42 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[31, 6016])).
% 2.25/2.42 tff(6018,plain,
% 2.25/2.42 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6017, 2997])).
% 2.25/2.42 tff(6019,plain,
% 2.25/2.42 (b(s(elem!1), z)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1209, 1185, 57])).
% 2.25/2.42 tff(6020,plain,
% 2.25/2.42 (b(s(elem!1), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1770, 6019, 57])).
% 2.25/2.42 tff(6021,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(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))))))))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6022,plain,
% 2.25/2.42 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(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))))))))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6023,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(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)))))))))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6022])).
% 2.25/2.42 tff(6024,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(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))))))))))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6023, 6021])).
% 2.25/2.42 tff(6025,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), elem!1)))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(6026,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6025, 6024])).
% 2.25/2.42 tff(6027,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6026, 198, 6020, 6018, 6009, 5996])).
% 2.25/2.42 tff(6028,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(6029,plain,
% 2.25/2.42 (~b(s(s(elem!1)), s(elem!1))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6028, 57, 55, 2, 141, 148, 5824, 5931])).
% 2.25/2.42 tff(6030,plain,
% 2.25/2.42 (r(s(s(elem!1)), s(elem!1))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[1143, 6029, 5932])).
% 2.25/2.42 tff(6031,plain,
% 2.25/2.42 (r(s(s(z)), s(z))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4766, 6030, 57])).
% 2.25/2.42 tff(6032,plain,
% 2.25/2.42 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[59])).
% 2.25/2.42 tff(6033,plain,
% 2.25/2.42 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[58])).
% 2.25/2.42 tff(6034,plain,
% 2.25/2.42 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6033, 6032])).
% 2.25/2.42 tff(6035,plain,
% 2.25/2.42 (b(s(s(z)), z)),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[2682, 2946])).
% 2.25/2.42 tff(6036,plain,
% 2.25/2.42 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.25/2.42 inference(transitivity,[status(thm)],[4759, 4761])).
% 2.25/2.42 tff(6037,plain,
% 2.25/2.42 (r(s(s(elem!1)), s(elem!1))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[3450, 6036])).
% 2.25/2.42 tff(6038,plain,
% 2.25/2.42 (b(s(s(elem!1)), elem!1)),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[2682, 2947])).
% 2.25/2.42 tff(6039,plain,
% 2.25/2.42 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4981, 4957, 153, 3450])).
% 2.25/2.42 tff(6040,plain,
% 2.25/2.42 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[420, 6039])).
% 2.25/2.42 tff(6041,plain,
% 2.25/2.42 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6040, 60])).
% 2.25/2.42 tff(6042,plain,
% 2.25/2.42 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4977, 595, 1185, 3450, 2, 153])).
% 2.25/2.42 tff(6043,plain,
% 2.25/2.42 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[374, 6042])).
% 2.25/2.42 tff(6044,plain,
% 2.25/2.42 (~r(s(s(s(s(s(z))))), z)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[5001, 4957, 3450, 6043, 153])).
% 2.25/2.42 tff(6045,plain,
% 2.25/2.42 (b(s(s(s(s(s(z))))), z)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3841, 6044])).
% 2.25/2.42 tff(6046,plain,
% 2.25/2.42 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.42 inference(monotonicity,[status(thm)],[57])).
% 2.25/2.42 tff(6047,plain,
% 2.25/2.42 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 2.25/2.42 inference(symmetry,[status(thm)],[6046])).
% 2.25/2.42 tff(6048,plain,
% 2.25/2.42 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(s(z))))), z))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6047])).
% 2.25/2.42 tff(6049,assumption,(~b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.25/2.42 tff(6050,plain,
% 2.25/2.42 (~b(s(s(s(s(s(z))))), z)),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 2.25/2.42 tff(6051,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4167, 6050])).
% 2.25/2.42 tff(6052,plain,(b(s(s(s(s(s(z))))), elem!1) | (~b(s(s(s(s(s(z))))), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(6053,plain,
% 2.25/2.42 (b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6052, 6045, 57])).
% 2.25/2.42 tff(6054,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.25/2.42 tff(6055,plain,
% 2.25/2.42 (b(elem!1, s(elem!1))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[595, 4711])).
% 2.25/2.42 tff(6056,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6057,plain,
% 2.25/2.42 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6058,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6057])).
% 2.25/2.42 tff(6059,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6058, 6056])).
% 2.25/2.42 tff(6060,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(6061,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 2.25/2.42 tff(6062,plain,
% 2.25/2.42 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6061, 198, 6020, 6055, 6054])).
% 2.25/2.42 tff(6063,plain,
% 2.25/2.42 (~b(s(s(s(s(s(z))))), s(z))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6062, 4863])).
% 2.25/2.42 tff(6064,plain,
% 2.25/2.42 (r(s(s(s(s(s(z))))), s(z))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[469, 6063])).
% 2.25/2.42 tff(6065,plain,
% 2.25/2.42 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3205, 6064, 57])).
% 2.25/2.42 tff(6066,plain,
% 2.25/2.42 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.42 inference(monotonicity,[status(thm)],[57])).
% 2.25/2.42 tff(6067,plain,
% 2.25/2.42 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[4957, 6066])).
% 2.25/2.42 tff(6068,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6069,plain,
% 2.25/2.42 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6070,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6069])).
% 2.25/2.42 tff(6071,plain,
% 2.25/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6070, 6068])).
% 2.25/2.42 tff(6072,plain,
% 2.25/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(6073,plain,
% 2.25/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6072, 6071])).
% 2.25/2.42 tff(6074,plain,
% 2.25/2.42 ($false),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6073, 163, 3066, 258, 3108, 3065])).
% 2.25/2.42 tff(6075,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.42 tff(6076,plain,
% 2.25/2.42 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6075, 3066, 6067, 6065])).
% 2.25/2.42 tff(6077,plain,
% 2.25/2.42 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[2942, 6076, 57])).
% 2.25/2.42 tff(6078,plain,
% 2.25/2.42 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[3613, 6077])).
% 2.25/2.42 tff(6079,plain,
% 2.25/2.42 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[4701, 6078, 57])).
% 2.25/2.42 tff(6080,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 2.25/2.42 tff(6081,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6082,plain,
% 2.25/2.42 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6083,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1))))))),
% 2.25/2.42 inference(monotonicity,[status(thm)],[6082])).
% 2.25/2.42 tff(6084,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1)))))),
% 2.25/2.42 inference(transitivity,[status(thm)],[6083, 6081])).
% 2.25/2.42 tff(6085,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.42 inference(quant_inst,[status(thm)],[])).
% 2.25/2.42 tff(6086,plain,
% 2.25/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))))), s(s(elem!1))))),
% 2.25/2.42 inference(modus_ponens,[status(thm)],[6085, 6084])).
% 2.25/2.42 tff(6087,plain,
% 2.25/2.42 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6086, 198, 1128, 6020, 6080])).
% 2.25/2.42 tff(6088,plain,
% 2.25/2.42 (~b(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[6087, 6079])).
% 2.25/2.42 tff(6089,plain,
% 2.25/2.42 (r(s(elem!1), s(s(elem!1)))),
% 2.25/2.42 inference(unit_resolution,[status(thm)],[901, 6088, 890])).
% 2.25/2.42 tff(6090,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6091,plain,
% 2.25/2.42 (((~b(s(elem!1), elem!1)) | (~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(elem!1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.25/2.42 inference(rewrite,[status(thm)],[])).
% 2.25/2.42 tff(6092,plain,
% 2.25/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6091])).
% 2.25/2.43 tff(6093,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6092, 6090])).
% 2.25/2.43 tff(6094,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6095,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6094, 6093])).
% 2.25/2.43 tff(6096,plain,
% 2.25/2.43 (~b(s(s(elem!1)), s(elem!1))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6095, 198, 1128, 6020, 6055])).
% 2.25/2.43 tff(6097,plain,
% 2.25/2.43 (r(s(s(elem!1)), s(elem!1))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[1143, 6096, 2968])).
% 2.25/2.43 tff(6098,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6099,plain,
% 2.25/2.43 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6100,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6099])).
% 2.25/2.43 tff(6101,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6100, 6098])).
% 2.25/2.43 tff(6102,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6103,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6102, 6101])).
% 2.25/2.43 tff(6104,plain,
% 2.25/2.43 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6103, 163, 6097, 6089, 6065])).
% 2.25/2.43 tff(6105,plain,
% 2.25/2.43 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[3400, 6104, 3385])).
% 2.25/2.43 tff(6106,plain,
% 2.25/2.43 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[3035, 4740])).
% 2.25/2.43 tff(6107,plain,
% 2.25/2.43 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6106])).
% 2.25/2.43 tff(6108,plain,
% 2.25/2.43 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[366, 6107])).
% 2.25/2.43 tff(6109,plain,
% 2.25/2.43 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[4967, 6078, 595, 1185, 2])).
% 2.25/2.43 tff(6110,plain,
% 2.25/2.43 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[31, 6109])).
% 2.25/2.43 tff(6111,plain,
% 2.25/2.43 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6110, 2944])).
% 2.25/2.43 tff(6112,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6113,plain,
% 2.25/2.43 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6114,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6113])).
% 2.25/2.43 tff(6115,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6114, 6112])).
% 2.25/2.43 tff(6116,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6117,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6116, 6115])).
% 2.25/2.43 tff(6118,plain,
% 2.25/2.43 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6117, 163, 3066, 6111, 6067])).
% 2.25/2.43 tff(6119,plain,
% 2.25/2.43 (b(elem!1, s(s(s(s(s(z))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[4810, 6118, 6108])).
% 2.25/2.43 tff(6120,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6121,plain,
% 2.25/2.43 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6122,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6121])).
% 2.25/2.43 tff(6123,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6122, 6120])).
% 2.25/2.43 tff(6124,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6125,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6124, 6123])).
% 2.25/2.43 tff(6126,plain,
% 2.25/2.43 ($false),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6125, 198, 1128, 6020, 6055, 6054, 6119, 6105])).
% 2.25/2.43 tff(6127,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(z = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.43 tff(6128,plain,
% 2.25/2.43 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6127, 6053, 1128, 57, 890, 6041, 595, 1185, 2])).
% 2.25/2.43 tff(6129,plain,
% 2.25/2.43 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[3098, 6128])).
% 2.25/2.43 tff(6130,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6131,plain,
% 2.25/2.43 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6132,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6131])).
% 2.25/2.43 tff(6133,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6132, 6130])).
% 2.25/2.43 tff(6134,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6135,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6134, 6133])).
% 2.25/2.43 tff(6136,plain,
% 2.25/2.43 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6135, 198, 1128, 6053, 6041])).
% 2.25/2.43 tff(6137,plain,
% 2.25/2.43 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6136, 6129])).
% 2.25/2.43 tff(6138,plain,
% 2.25/2.43 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6043, 3402])).
% 2.25/2.43 tff(6139,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6140,plain,
% 2.25/2.43 (((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6141,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6140])).
% 2.25/2.43 tff(6142,plain,
% 2.25/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6141, 6139])).
% 2.25/2.43 tff(6143,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6144,plain,
% 2.25/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.25/2.43 inference(modus_ponens,[status(thm)],[6143, 6142])).
% 2.25/2.43 tff(6145,plain,
% 2.25/2.43 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[6144, 198, 3819, 721, 6080])).
% 2.25/2.43 tff(6146,plain,
% 2.25/2.43 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.43 inference(unit_resolution,[status(thm)],[3086, 26, 4865, 6145])).
% 2.25/2.43 tff(6147,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6148,plain,
% 2.25/2.43 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(rewrite,[status(thm)],[])).
% 2.25/2.43 tff(6149,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.25/2.43 inference(monotonicity,[status(thm)],[6148])).
% 2.25/2.43 tff(6150,plain,
% 2.25/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(transitivity,[status(thm)],[6149, 6147])).
% 2.25/2.43 tff(6151,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.25/2.43 inference(quant_inst,[status(thm)],[])).
% 2.25/2.43 tff(6152,plain,
% 2.25/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 2.25/2.44 tff(6153,plain,
% 2.25/2.44 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6152, 163, 1773, 1220, 6146])).
% 2.25/2.44 tff(6154,plain,
% 2.25/2.44 (~r(s(s(s(s(s(z))))), s(z))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3205, 6153, 57])).
% 2.25/2.44 tff(6155,plain,
% 2.25/2.44 (b(s(s(s(s(s(z))))), s(z))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[469, 6154])).
% 2.25/2.44 tff(6156,plain,
% 2.25/2.44 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6155, 4861])).
% 2.25/2.44 tff(6157,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6158,plain,
% 2.25/2.44 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6159,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6158])).
% 2.25/2.44 tff(6160,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6159, 6157])).
% 2.25/2.44 tff(6161,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6162,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6161, 6160])).
% 2.25/2.44 tff(6163,plain,
% 2.25/2.44 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6162, 163, 1773, 405, 6146])).
% 2.25/2.44 tff(6164,plain,
% 2.25/2.44 (b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[528, 6163, 3037])).
% 2.25/2.44 tff(6165,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6166,plain,
% 2.25/2.44 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6167,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6166])).
% 2.25/2.44 tff(6168,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6167, 6165])).
% 2.25/2.44 tff(6169,plain,
% 2.25/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6170,plain,
% 2.25/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6169, 6168])).
% 2.25/2.44 tff(6171,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6170, 198, 1128, 1200, 3819, 6164, 6080, 6156, 3317])).
% 2.25/2.44 tff(6172,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(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(elem!1))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6173,plain,
% 2.25/2.44 (~r(s(elem!1), s(s(elem!1)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6172, 6129, 6020, 6041, 4705, 57, 6097, 405, 1128, 6138])).
% 2.25/2.44 tff(6174,plain,
% 2.25/2.44 (b(s(elem!1), s(s(elem!1)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[901, 6173, 890])).
% 2.25/2.44 tff(6175,plain,
% 2.25/2.44 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6086, 198, 1128, 6020, 6041])).
% 2.25/2.44 tff(6176,plain,
% 2.25/2.44 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6175, 6174])).
% 2.25/2.44 tff(6177,plain,
% 2.25/2.44 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[4701, 6176, 57])).
% 2.25/2.44 tff(6178,plain,
% 2.25/2.44 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3613, 6177])).
% 2.25/2.44 tff(6179,plain,
% 2.25/2.44 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[2942, 6178, 57])).
% 2.25/2.44 tff(6180,plain,
% 2.25/2.44 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6061, 198, 6020, 6055, 6053])).
% 2.25/2.44 tff(6181,plain,
% 2.25/2.44 (~b(s(s(s(s(s(z))))), s(z))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6180, 4863])).
% 2.25/2.44 tff(6182,plain,
% 2.25/2.44 (r(s(s(s(s(s(z))))), s(z))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[469, 6181])).
% 2.25/2.44 tff(6183,plain,
% 2.25/2.44 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3205, 6182, 57])).
% 2.25/2.44 tff(6184,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6185,plain,
% 2.25/2.44 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6186,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6185])).
% 2.25/2.44 tff(6187,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6186, 6184])).
% 2.25/2.44 tff(6188,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6189,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6188, 6187])).
% 2.25/2.44 tff(6190,plain,
% 2.25/2.44 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6189, 163, 6097, 6183, 6179])).
% 2.25/2.44 tff(6191,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3086, 26, 4865, 6190, 6137])).
% 2.25/2.44 tff(6192,plain,((~b(z, s(z))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6193,plain,
% 2.25/2.44 (~b(z, s(z))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6192, 6038, 57, 890, 405, 1185, 2, 153, 3450])).
% 2.25/2.44 tff(6194,plain,
% 2.25/2.44 (r(z, s(z))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[593, 6193])).
% 2.25/2.44 tff(6195,plain,
% 2.25/2.44 (r(z, s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3155, 6194, 79])).
% 2.25/2.44 tff(6196,plain,
% 2.25/2.44 (r(elem!1, s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3231, 6195, 79])).
% 2.25/2.44 tff(6197,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6198,plain,
% 2.25/2.44 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6199,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6198])).
% 2.25/2.44 tff(6200,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6199, 6197])).
% 2.25/2.44 tff(6201,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6202,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 2.25/2.44 tff(6203,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6202, 163, 1473, 1773, 405, 3065])).
% 2.25/2.44 tff(6204,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6205,plain,
% 2.25/2.44 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6204, 6196, 6037, 405])).
% 2.25/2.44 tff(6206,plain,
% 2.25/2.44 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[2942, 6205, 57])).
% 2.25/2.44 tff(6207,plain,
% 2.25/2.44 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3613, 6206])).
% 2.25/2.44 tff(6208,plain,
% 2.25/2.44 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[4701, 6207, 57])).
% 2.25/2.44 tff(6209,plain,
% 2.25/2.44 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[4981, 423, 153, 3450])).
% 2.25/2.44 tff(6210,plain,
% 2.25/2.44 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[176, 6209])).
% 2.25/2.44 tff(6211,plain,
% 2.25/2.44 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[1032, 6210, 79])).
% 2.25/2.44 tff(6212,plain,
% 2.25/2.44 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[423, 2959])).
% 2.25/2.44 tff(6213,plain,
% 2.25/2.44 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3008, 163, 6037, 405, 6212])).
% 2.25/2.44 tff(6214,plain,
% 2.25/2.44 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[703, 6213, 3002])).
% 2.25/2.44 tff(6215,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6026, 198, 1200, 6214, 6211, 4703])).
% 2.25/2.44 tff(6216,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6217,plain,
% 2.25/2.44 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6216, 6208, 6020, 405, 57, 153, 3450])).
% 2.25/2.44 tff(6218,plain,
% 2.25/2.44 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[420, 6217])).
% 2.25/2.44 tff(6219,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6220,plain,
% 2.25/2.44 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6221,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6220])).
% 2.25/2.44 tff(6222,plain,
% 2.25/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6221, 6219])).
% 2.25/2.44 tff(6223,plain,
% 2.25/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6224,plain,
% 2.25/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6223, 6222])).
% 2.25/2.44 tff(6225,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6224, 198, 1185, 407, 3615, 347, 3745])).
% 2.25/2.44 tff(6226,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6227,plain,
% 2.25/2.44 (~b(s(z), s(s(z)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6226, 6218, 1185, 6207, 6035])).
% 2.25/2.44 tff(6228,plain,
% 2.25/2.44 (r(s(z), s(s(z)))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[403, 6227])).
% 2.25/2.44 tff(6229,plain,
% 2.25/2.44 (r(s(elem!1), s(s(elem!1)))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6228, 6034])).
% 2.25/2.44 tff(6230,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6231,plain,
% 2.25/2.44 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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(s(elem!1)), s(elem!1))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6232,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6231])).
% 2.25/2.44 tff(6233,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6232, 6230])).
% 2.25/2.44 tff(6234,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6235,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6234, 6233])).
% 2.25/2.44 tff(6236,plain,
% 2.25/2.44 ($false),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6235, 163, 6196, 6037, 6229, 405])).
% 2.25/2.44 tff(6237,plain,((~b(s(s(z)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.44 tff(6238,plain,
% 2.25/2.44 (~b(s(s(z)), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[6237, 6031, 57, 5931, 55, 148, 141, 2])).
% 2.25/2.44 tff(6239,plain,
% 2.25/2.44 (r(s(s(z)), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[2139, 6238, 65])).
% 2.25/2.44 tff(6240,plain,
% 2.25/2.44 (r(s(s(z)), z)),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6239, 62])).
% 2.25/2.44 tff(6241,plain,
% 2.25/2.44 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.25/2.44 inference(transitivity,[status(thm)],[5942, 5965])).
% 2.25/2.44 tff(6242,plain,
% 2.25/2.44 (r(s(s(elem!1)), z)),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6239, 6241])).
% 2.25/2.44 tff(6243,plain,
% 2.25/2.44 (b(s(elem!1), z)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[1209, 5931, 57])).
% 2.25/2.44 tff(6244,plain,
% 2.25/2.44 (b(s(elem!1), elem!1)),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[1770, 6243, 57])).
% 2.25/2.44 tff(6245,plain,
% 2.25/2.44 (r(s(s(elem!1)), elem!1)),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6239, 5942])).
% 2.25/2.44 tff(6246,plain,
% 2.25/2.44 (r(z, s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3155, 406, 79])).
% 2.25/2.44 tff(6247,plain,
% 2.25/2.44 (r(elem!1, s(elem!1))),
% 2.25/2.44 inference(unit_resolution,[status(thm)],[3231, 6246, 79])).
% 2.25/2.44 tff(6248,plain,
% 2.25/2.44 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.25/2.44 inference(symmetry,[status(thm)],[3284])).
% 2.25/2.44 tff(6249,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.25/2.44 tff(6250,plain,
% 2.25/2.44 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6249, 6248])).
% 2.25/2.44 tff(6251,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6252,plain,
% 2.25/2.44 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(rewrite,[status(thm)],[])).
% 2.25/2.44 tff(6253,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.25/2.44 inference(monotonicity,[status(thm)],[6252])).
% 2.25/2.44 tff(6254,plain,
% 2.25/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.44 inference(transitivity,[status(thm)],[6253, 6251])).
% 2.25/2.44 tff(6255,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.25/2.44 inference(quant_inst,[status(thm)],[])).
% 2.25/2.44 tff(6256,plain,
% 2.25/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.25/2.44 inference(modus_ponens,[status(thm)],[6255, 6254])).
% 2.25/2.44 tff(6257,plain,
% 2.25/2.44 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6256, 163, 1115, 1473, 1773])).
% 2.25/2.45 tff(6258,plain,
% 2.25/2.45 ($false),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6257, 6250])).
% 2.25/2.45 tff(6259,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.45 tff(6260,plain,
% 2.25/2.45 (~r(s(z), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6259, 6247, 1115, 57, 6037])).
% 2.25/2.45 tff(6261,plain,
% 2.25/2.45 (b(s(z), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3301, 6260])).
% 2.25/2.45 tff(6262,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.25/2.45 tff(6263,plain,
% 2.25/2.45 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6262, 3283])).
% 2.25/2.45 tff(6264,assumption,(~b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.25/2.45 tff(6265,plain,
% 2.25/2.45 ($false),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6264, 6263])).
% 2.25/2.45 tff(6266,plain,(b(s(elem!1), s(s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.45 tff(6267,plain,
% 2.25/2.45 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6266, 6261, 57])).
% 2.25/2.45 tff(6268,plain,
% 2.25/2.45 (~r(s(elem!1), s(s(elem!1)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[1530, 6246, 790, 1098])).
% 2.25/2.45 tff(6269,plain,
% 2.25/2.45 (b(s(elem!1), s(s(elem!1)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[901, 6268, 890])).
% 2.25/2.45 tff(6270,plain,
% 2.25/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6271,plain,
% 2.25/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.45 inference(quant_inst,[status(thm)],[])).
% 2.25/2.45 tff(6272,plain,
% 2.25/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 2.25/2.45 tff(6273,plain,
% 2.25/2.45 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6272, 163, 1115, 1473, 3109])).
% 2.25/2.45 tff(6274,plain,
% 2.25/2.45 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[3396, 4750])).
% 2.25/2.45 tff(6275,plain,
% 2.25/2.45 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3086, 26, 6274, 6273])).
% 2.25/2.45 tff(6276,assumption,(b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.25/2.45 tff(6277,plain,
% 2.25/2.45 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[5991, 163, 1115, 1473, 3109])).
% 2.25/2.45 tff(6278,plain,
% 2.25/2.45 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3400, 6277, 3396])).
% 2.25/2.45 tff(6279,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6280,plain,
% 2.25/2.45 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6281,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6280])).
% 2.25/2.45 tff(6282,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[6281, 6279])).
% 2.25/2.45 tff(6283,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.25/2.45 inference(quant_inst,[status(thm)],[])).
% 2.25/2.45 tff(6284,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6283, 6282])).
% 2.25/2.45 tff(6285,plain,
% 2.25/2.45 ($false),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6284, 198, 1328, 6278, 6276, 6275])).
% 2.25/2.45 tff(6286,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.45 tff(6287,plain,
% 2.25/2.45 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6286, 6269, 6267, 3385, 1115, 6247])).
% 2.25/2.45 tff(6288,plain,
% 2.25/2.45 (b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[528, 6287, 3037])).
% 2.25/2.45 tff(6289,plain,
% 2.25/2.45 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(symmetry,[status(thm)],[3402])).
% 2.25/2.45 tff(6290,plain,
% 2.25/2.45 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6289])).
% 2.25/2.45 tff(6291,plain,
% 2.25/2.45 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6204, 6247, 6037, 405])).
% 2.25/2.45 tff(6292,plain,
% 2.25/2.45 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[2942, 6291, 57])).
% 2.25/2.45 tff(6293,plain,
% 2.25/2.45 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3613, 6292])).
% 2.25/2.45 tff(6294,plain,
% 2.25/2.45 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[4701, 6293, 57])).
% 2.25/2.45 tff(6295,plain,
% 2.25/2.45 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6216, 6294, 1200, 405, 57, 153, 3450])).
% 2.25/2.45 tff(6296,plain,
% 2.25/2.45 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[420, 6295])).
% 2.25/2.45 tff(6297,plain,
% 2.25/2.45 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6296, 60])).
% 2.25/2.45 tff(6298,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6299,plain,
% 2.25/2.45 (((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6300,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6299])).
% 2.25/2.45 tff(6301,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[6300, 6298])).
% 2.25/2.45 tff(6302,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.25/2.45 inference(quant_inst,[status(thm)],[])).
% 2.25/2.45 tff(6303,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6302, 6301])).
% 2.25/2.45 tff(6304,plain,
% 2.25/2.45 ($false),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6303, 198, 1328, 721, 6080, 4703])).
% 2.25/2.45 tff(6305,plain,((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.45 tff(6306,plain,
% 2.25/2.45 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6305, 6269, 6297, 6294])).
% 2.25/2.45 tff(6307,plain,
% 2.25/2.45 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6306, 6290])).
% 2.25/2.45 tff(6308,plain,
% 2.25/2.45 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[374, 6307])).
% 2.25/2.45 tff(6309,plain,
% 2.25/2.45 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[4031, 6308, 332, 406])).
% 2.25/2.45 tff(6310,plain,
% 2.25/2.45 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[176, 6309])).
% 2.25/2.45 tff(6311,plain,
% 2.25/2.45 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[1032, 6310, 79])).
% 2.25/2.45 tff(6312,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6313,plain,
% 2.25/2.45 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6314,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6313])).
% 2.25/2.45 tff(6315,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.45 inference(transitivity,[status(thm)],[6314, 6312])).
% 2.25/2.45 tff(6316,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.25/2.45 inference(quant_inst,[status(thm)],[])).
% 2.25/2.45 tff(6317,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 2.25/2.45 tff(6318,plain,
% 2.25/2.45 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6317, 198, 6311, 6288, 3317, 6267])).
% 2.25/2.45 tff(6319,plain,
% 2.25/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3328, 26, 6318])).
% 2.25/2.45 tff(6320,plain,
% 2.25/2.45 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6319, 2935])).
% 2.25/2.45 tff(6321,plain,
% 2.25/2.45 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6010])).
% 2.25/2.45 tff(6322,plain,
% 2.25/2.45 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[369, 6321])).
% 2.25/2.45 tff(6323,plain,
% 2.25/2.45 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[934, 26, 6306, 6322])).
% 2.25/2.45 tff(6324,plain,
% 2.25/2.45 (b(s(z), s(s(z)))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6269, 6000])).
% 2.25/2.45 tff(6325,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6326,plain,
% 2.25/2.45 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6327,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.45 inference(monotonicity,[status(thm)],[6326])).
% 2.25/2.45 tff(6328,plain,
% 2.25/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.45 inference(transitivity,[status(thm)],[6327, 6325])).
% 2.25/2.45 tff(6329,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(quant_inst,[status(thm)],[])).
% 2.25/2.45 tff(6330,plain,
% 2.25/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.45 inference(modus_ponens,[status(thm)],[6329, 6328])).
% 2.25/2.45 tff(6331,plain,
% 2.25/2.45 ($false),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6330, 198, 407, 3819, 6262, 3615, 3745])).
% 2.25/2.45 tff(6332,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.45 tff(6333,plain,
% 2.25/2.45 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[6332, 6261, 6296, 6293, 6324])).
% 2.25/2.45 tff(6334,plain,
% 2.25/2.45 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(unit_resolution,[status(thm)],[3098, 6333])).
% 2.25/2.45 tff(6335,plain,
% 2.25/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6336,plain,
% 2.25/2.45 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.25/2.45 inference(rewrite,[status(thm)],[])).
% 2.25/2.45 tff(6337,plain,
% 2.25/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6336])).
% 2.25/2.46 tff(6338,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6337, 6335])).
% 2.25/2.46 tff(6339,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6340,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6339, 6338])).
% 2.25/2.46 tff(6341,plain,
% 2.25/2.46 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6340, 163, 6334, 6323, 6320])).
% 2.25/2.46 tff(6342,plain,
% 2.25/2.46 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[3400, 6341, 3385])).
% 2.25/2.46 tff(6343,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6344,plain,
% 2.25/2.46 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6345,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6344])).
% 2.25/2.46 tff(6346,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6345, 6343])).
% 2.25/2.46 tff(6347,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6348,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 2.25/2.46 tff(6349,plain,
% 2.25/2.46 ($false),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6348, 198, 6269, 1200, 6288, 6342, 6267])).
% 2.25/2.46 tff(6350,plain,((~r(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.46 tff(6351,plain,
% 2.25/2.46 (~r(z, s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6350, 6245, 4705, 6244, 57, 6031, 148, 55, 6240, 141, 6242, 5824])).
% 2.25/2.46 tff(6352,plain,
% 2.25/2.46 (b(z, s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[593, 6351])).
% 2.25/2.46 tff(6353,plain,
% 2.25/2.46 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[4953, 6352, 2, 5931])).
% 2.25/2.46 tff(6354,plain,
% 2.25/2.46 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[176, 6353])).
% 2.25/2.46 tff(6355,plain,
% 2.25/2.46 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[5578, 6354, 55, 6240])).
% 2.25/2.46 tff(6356,plain,
% 2.25/2.46 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[420, 6355])).
% 2.25/2.46 tff(6357,plain,
% 2.25/2.46 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6356, 60])).
% 2.25/2.46 tff(6358,plain,
% 2.25/2.46 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[4977, 6352, 5931, 6031, 2, 55])).
% 2.25/2.46 tff(6359,plain,
% 2.25/2.46 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[374, 6358])).
% 2.25/2.46 tff(6360,plain,
% 2.25/2.46 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6359, 3402])).
% 2.25/2.46 tff(6361,plain,
% 2.25/2.46 (~r(s(s(s(s(s(z))))), z)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[5001, 6359, 6031, 6354, 55])).
% 2.25/2.46 tff(6362,plain,
% 2.25/2.46 (b(s(s(s(s(s(z))))), z)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[3841, 6361])).
% 2.25/2.46 tff(6363,plain,
% 2.25/2.46 (b(s(s(s(s(s(z))))), elem!1)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6052, 6362, 57])).
% 2.25/2.46 tff(6364,plain,
% 2.25/2.46 (b(elem!1, s(elem!1))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6352, 4711])).
% 2.25/2.46 tff(6365,plain,
% 2.25/2.46 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6061, 198, 6244, 6364, 6363])).
% 2.25/2.46 tff(6366,plain,
% 2.25/2.46 (~b(s(s(s(s(s(z))))), s(z))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6365, 4863])).
% 2.25/2.46 tff(6367,plain,
% 2.25/2.46 (r(s(s(s(s(s(z))))), s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[469, 6366])).
% 2.25/2.46 tff(6368,plain,
% 2.25/2.46 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[3205, 6367, 57])).
% 2.25/2.46 tff(6369,plain,
% 2.25/2.46 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6354, 6066])).
% 2.25/2.46 tff(6370,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[58])).
% 2.25/2.46 tff(6371,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(symmetry,[status(thm)],[6370])).
% 2.25/2.46 tff(6372,plain,
% 2.25/2.46 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6371])).
% 2.25/2.46 tff(6373,plain,
% 2.25/2.46 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.25/2.46 inference(monotonicity,[status(thm)],[57])).
% 2.25/2.46 tff(6374,plain,
% 2.25/2.46 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6373])).
% 2.25/2.46 tff(6375,plain,
% 2.25/2.46 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[5159, 6374])).
% 2.25/2.46 tff(6376,plain,
% 2.25/2.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[1250, 119])).
% 2.25/2.46 tff(6377,plain,
% 2.25/2.46 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[2619, 6376])).
% 2.25/2.46 tff(6378,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.25/2.46 tff(6379,plain,
% 2.25/2.46 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 2.25/2.46 inference(symmetry,[status(thm)],[6378])).
% 2.25/2.46 tff(6380,plain,
% 2.25/2.46 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6379])).
% 2.25/2.46 tff(6381,plain,
% 2.25/2.46 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(symmetry,[status(thm)],[6380])).
% 2.25/2.46 tff(6382,plain,
% 2.25/2.46 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[965, 6381, 275])).
% 2.25/2.46 tff(6383,plain,
% 2.25/2.46 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6382])).
% 2.25/2.46 tff(6384,plain,
% 2.25/2.46 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[1247, 6383, 280])).
% 2.25/2.46 tff(6385,plain,
% 2.25/2.46 ($false),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[3396, 6384])).
% 2.25/2.46 tff(6386,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.46 tff(6387,plain,
% 2.25/2.46 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6386, 3385])).
% 2.25/2.46 tff(6388,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6389,plain,
% 2.25/2.46 (((~r(elem!1, s(s(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(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, 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(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6390,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6389])).
% 2.25/2.46 tff(6391,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6390, 6388])).
% 2.25/2.46 tff(6392,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6393,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 2.25/2.46 tff(6394,plain,
% 2.25/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6393, 163, 5131, 405, 258])).
% 2.25/2.46 tff(6395,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.25/2.46 tff(6396,plain,
% 2.25/2.46 (((~![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)))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6397,plain,
% 2.25/2.46 ((~![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)))))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6398,plain,
% 2.25/2.46 ((~![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))))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 2.25/2.46 tff(6399,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6398, 26, 6395, 6394])).
% 2.25/2.46 tff(6400,plain,
% 2.25/2.46 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[2626, 2624])).
% 2.25/2.46 tff(6401,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6402,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6403,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6402, 6401])).
% 2.25/2.46 tff(6404,plain,
% 2.25/2.46 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6403, 163, 1115, 5131, 405])).
% 2.25/2.46 tff(6405,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[2654, 6404, 6400])).
% 2.25/2.46 tff(6406,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6407,plain,
% 2.25/2.46 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(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(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6408,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6407])).
% 2.25/2.46 tff(6409,plain,
% 2.25/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6408, 6406])).
% 2.25/2.46 tff(6410,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6411,plain,
% 2.25/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6410, 6409])).
% 2.25/2.46 tff(6412,plain,
% 2.25/2.46 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6411, 163, 1115, 5131, 405])).
% 2.25/2.46 tff(6413,plain,
% 2.25/2.46 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[5274, 6412, 2624])).
% 2.25/2.46 tff(6414,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(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))))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6415,plain,
% 2.25/2.46 (((~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(elem!1)))) | (~b(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))))))))) | (~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(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6416,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))) | (~b(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(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)))))))))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6415])).
% 2.25/2.46 tff(6417,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))) | (~b(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(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))))))))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6416, 6414])).
% 2.25/2.46 tff(6418,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))) | (~b(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))))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6419,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 2.25/2.46 tff(6420,plain,
% 2.25/2.46 ($false),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6419, 198, 6413, 6405, 721, 6080, 6399])).
% 2.25/2.46 tff(6421,plain,((~r(s(s(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))))))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.46 tff(6422,plain,
% 2.25/2.46 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6421, 6360, 6357, 6387, 6377, 6245, 148, 6369])).
% 2.25/2.46 tff(6423,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[5065, 6422, 6375])).
% 2.25/2.46 tff(6424,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6425,plain,
% 2.25/2.46 (((~b(s(elem!1), elem!1)) | (~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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6426,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[6425])).
% 2.25/2.46 tff(6427,plain,
% 2.25/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.25/2.46 inference(transitivity,[status(thm)],[6426, 6424])).
% 2.25/2.46 tff(6428,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6429,plain,
% 2.25/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6428, 6427])).
% 2.25/2.46 tff(6430,plain,
% 2.25/2.46 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6429, 198, 6244, 6423, 6364])).
% 2.25/2.46 tff(6431,plain,
% 2.25/2.46 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6430, 6372])).
% 2.25/2.46 tff(6432,plain,
% 2.25/2.46 (((~![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)))),
% 2.25/2.46 inference(rewrite,[status(thm)],[])).
% 2.25/2.46 tff(6433,plain,
% 2.25/2.46 ((~![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)))),
% 2.25/2.46 inference(quant_inst,[status(thm)],[])).
% 2.25/2.46 tff(6434,plain,
% 2.25/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(modus_ponens,[status(thm)],[6433, 6432])).
% 2.25/2.46 tff(6435,plain,
% 2.25/2.46 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6434, 26])).
% 2.25/2.46 tff(6436,plain,
% 2.25/2.46 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6435, 971])).
% 2.25/2.46 tff(6437,plain,
% 2.25/2.46 (r(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(unit_resolution,[status(thm)],[6436, 6431])).
% 2.25/2.46 tff(6438,plain,
% 2.25/2.46 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.25/2.46 inference(monotonicity,[status(thm)],[2936])).
% 2.25/2.47 tff(6439,plain,
% 2.25/2.47 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.25/2.47 inference(symmetry,[status(thm)],[6438])).
% 2.25/2.47 tff(6440,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 2.25/2.47 tff(6441,plain,
% 2.25/2.47 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6440, 6439])).
% 2.25/2.47 tff(6442,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.25/2.47 tff(6443,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6442, 6441])).
% 2.25/2.47 tff(6444,plain,((~r(s(s(s(s(elem!1)))), s(z))) | r(s(s(s(s(elem!1)))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6445,plain,
% 2.25/2.47 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6444, 6437, 57])).
% 2.25/2.47 tff(6446,plain,
% 2.25/2.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[1263, 6376])).
% 2.25/2.47 tff(6447,plain,
% 2.25/2.47 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[2736, 6446])).
% 2.25/2.47 tff(6448,plain,
% 2.25/2.47 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[4889])).
% 2.25/2.47 tff(6449,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.25/2.47 tff(6450,plain,
% 2.25/2.47 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(z))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6449])).
% 2.25/2.47 tff(6451,plain,
% 2.25/2.47 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[965, 6450, 288, 6448])).
% 2.25/2.47 tff(6452,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.25/2.47 tff(6453,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6452, 6451])).
% 2.25/2.47 tff(6454,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6455,plain,
% 2.25/2.47 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6454, 6447, 57])).
% 2.25/2.47 tff(6456,assumption,(s(s(s(s(s(z))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.25/2.47 tff(6457,plain,
% 2.25/2.47 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.25/2.47 inference(symmetry,[status(thm)],[6456])).
% 2.25/2.47 tff(6458,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 2.25/2.47 tff(6459,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6458, 6457])).
% 2.25/2.47 tff(6460,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6461,plain,
% 2.25/2.47 (~(s(s(s(s(s(z))))) = s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6460, 6455])).
% 2.25/2.47 tff(6462,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6463,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6464,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 2.25/2.47 tff(6465,plain,
% 2.25/2.47 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6464, 163, 1773, 1220, 3108])).
% 2.25/2.47 tff(6466,plain,
% 2.25/2.47 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3086, 26, 3860, 6465])).
% 2.25/2.47 tff(6467,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.25/2.47 tff(6468,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6469,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6470,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 2.25/2.47 tff(6471,plain,
% 2.25/2.47 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6470, 163, 1220, 6467, 3108])).
% 2.25/2.47 tff(6472,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.25/2.47 tff(6473,plain,
% 2.25/2.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | r(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(z))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6474,plain,
% 2.25/2.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6475,plain,
% 2.25/2.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6474, 6473])).
% 2.25/2.47 tff(6476,plain,
% 2.25/2.47 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6475, 26, 6472, 6471])).
% 2.25/2.47 tff(6477,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6478,plain,
% 2.25/2.47 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6479,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6478])).
% 2.25/2.47 tff(6480,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[6479, 6477])).
% 2.25/2.47 tff(6481,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6482,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 2.25/2.47 tff(6483,plain,
% 2.25/2.47 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6482, 163, 1773, 1220, 6467])).
% 2.25/2.47 tff(6484,plain,
% 2.25/2.47 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[5274, 6483, 2624])).
% 2.25/2.47 tff(6485,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6486,plain,
% 2.25/2.47 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(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(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6487,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(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(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6486])).
% 2.25/2.47 tff(6488,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(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(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[6487, 6485])).
% 2.25/2.47 tff(6489,plain,
% 2.25/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(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(s(z))))), s(s(elem!1)))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6490,plain,
% 2.25/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6489, 6488])).
% 2.25/2.47 tff(6491,plain,
% 2.25/2.47 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6490, 198, 5038, 6484, 6054])).
% 2.25/2.47 tff(6492,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6491, 6476, 6466])).
% 2.25/2.47 tff(6493,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6494,plain,
% 2.25/2.47 (~r(s(elem!1), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6493, 6423, 6363, 6461, 4865, 6377, 6445, 6368, 6030])).
% 2.25/2.47 tff(6495,plain,
% 2.25/2.47 (b(s(elem!1), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[901, 6494, 141])).
% 2.25/2.47 tff(6496,plain,
% 2.25/2.47 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6305, 6495, 6360, 6357])).
% 2.25/2.47 tff(6497,plain,
% 2.25/2.47 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[4701, 6496, 57])).
% 2.25/2.47 tff(6498,plain,
% 2.25/2.47 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3613, 6497])).
% 2.25/2.47 tff(6499,plain,
% 2.25/2.47 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[2942, 6498, 57])).
% 2.25/2.47 tff(6500,plain,
% 2.25/2.47 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6075, 6499, 6369, 6368])).
% 2.25/2.47 tff(6501,plain,
% 2.25/2.47 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3098, 6500])).
% 2.25/2.47 tff(6502,plain,
% 2.25/2.47 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6144, 198, 6501, 6360, 6357])).
% 2.25/2.47 tff(6503,plain,
% 2.25/2.47 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6189, 163, 6030, 6368, 6499])).
% 2.25/2.47 tff(6504,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3086, 26, 4865, 6503, 6502])).
% 2.25/2.47 tff(6505,plain,((~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6506,plain,
% 2.25/2.47 (~(z = elem!1)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6505, 56, 2, 42])).
% 2.25/2.47 tff(6507,plain,
% 2.25/2.47 (~(elem!1 = z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[1079, 6506])).
% 2.25/2.47 tff(6508,plain,
% 2.25/2.47 (b(z, elem!1)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[102, 6506, 56])).
% 2.25/2.47 tff(6509,plain,
% 2.25/2.47 (~(elem!1 = s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[4932, 6508, 42])).
% 2.25/2.47 tff(6510,plain,
% 2.25/2.47 (~(s(elem!1) = s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[814, 6506])).
% 2.25/2.47 tff(6511,plain,
% 2.25/2.47 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3763, 423, 152, 153])).
% 2.25/2.47 tff(6512,plain,
% 2.25/2.47 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[374, 6511])).
% 2.25/2.47 tff(6513,plain,
% 2.25/2.47 (~r(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[4981, 423, 153, 152])).
% 2.25/2.47 tff(6514,plain,
% 2.25/2.47 (b(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[487, 6513])).
% 2.25/2.47 tff(6515,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3626, 6514, 6512, 2, 3615])).
% 2.25/2.47 tff(6516,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6517,plain,
% 2.25/2.47 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6516, 152, 3615, 153, 2])).
% 2.25/2.47 tff(6518,plain,
% 2.25/2.47 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[420, 6517])).
% 2.25/2.47 tff(6519,plain,
% 2.25/2.47 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[4548, 3272, 153, 152])).
% 2.25/2.47 tff(6520,plain,
% 2.25/2.47 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[31, 6519])).
% 2.25/2.47 tff(6521,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6522,plain,
% 2.25/2.47 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6523,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6522])).
% 2.25/2.47 tff(6524,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[6523, 6521])).
% 2.25/2.47 tff(6525,plain,
% 2.25/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6526,plain,
% 2.25/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6525, 6524])).
% 2.25/2.47 tff(6527,plain,
% 2.25/2.47 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6526, 198, 95, 5927, 2])).
% 2.25/2.47 tff(6528,plain,
% 2.25/2.47 (~b(z, s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6527, 6520])).
% 2.25/2.47 tff(6529,plain,
% 2.25/2.47 (r(z, s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[593, 6528])).
% 2.25/2.47 tff(6530,plain,
% 2.25/2.47 (~r(s(s(z)), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[4031, 6529, 152, 3272])).
% 2.25/2.47 tff(6531,plain,
% 2.25/2.47 (b(s(s(z)), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[345, 6530])).
% 2.25/2.47 tff(6532,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6533,plain,
% 2.25/2.47 (((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6534,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6533])).
% 2.25/2.47 tff(6535,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[6534, 6532])).
% 2.25/2.47 tff(6536,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6537,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6536, 6535])).
% 2.25/2.47 tff(6538,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6537, 163, 150, 406, 153, 3450])).
% 2.25/2.47 tff(6539,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6540,plain,
% 2.25/2.47 (~r(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6539, 150, 406, 153])).
% 2.25/2.47 tff(6541,plain,
% 2.25/2.47 (b(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[487, 6540])).
% 2.25/2.47 tff(6542,plain,
% 2.25/2.47 (~r(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3712, 150, 153, 3272])).
% 2.25/2.47 tff(6543,plain,
% 2.25/2.47 (b(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[403, 6542])).
% 2.25/2.47 tff(6544,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3753, 6543, 6541, 3745, 2])).
% 2.25/2.47 tff(6545,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6546,plain,
% 2.25/2.47 (~r(s(z), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6545, 3272, 2, 153, 3745, 6529])).
% 2.25/2.47 tff(6547,plain,
% 2.25/2.47 (b(s(z), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[40, 6546])).
% 2.25/2.47 tff(6548,plain,
% 2.25/2.47 (~b(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6226, 6547, 3615, 3745, 6531])).
% 2.25/2.47 tff(6549,plain,
% 2.25/2.47 (r(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[403, 6548])).
% 2.25/2.47 tff(6550,plain,
% 2.25/2.47 ($false),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[5923, 163, 6529, 6549, 153, 3272])).
% 2.25/2.47 tff(6551,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.47 tff(6552,plain,
% 2.25/2.47 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6551, 6518, 3615, 153, 2, 152, 95, 5927])).
% 2.25/2.47 tff(6553,plain,
% 2.25/2.47 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[374, 6552])).
% 2.25/2.47 tff(6554,plain,
% 2.25/2.47 (~b(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3626, 6553, 2, 3615])).
% 2.25/2.47 tff(6555,plain,
% 2.25/2.47 (r(s(s(z)), s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[487, 6554])).
% 2.25/2.47 tff(6556,plain,
% 2.25/2.47 (~b(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3679, 198, 3615, 6553, 6518, 2])).
% 2.25/2.47 tff(6557,plain,
% 2.25/2.47 (r(s(z), s(s(z)))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[403, 6556])).
% 2.25/2.47 tff(6558,plain,
% 2.25/2.47 (~r(s(z), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[3687, 163, 6557, 153, 6555])).
% 2.25/2.47 tff(6559,plain,
% 2.25/2.47 (b(s(z), z)),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[40, 6558])).
% 2.25/2.47 tff(6560,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6561,plain,
% 2.25/2.47 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6562,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.25/2.47 inference(monotonicity,[status(thm)],[6561])).
% 2.25/2.47 tff(6563,plain,
% 2.25/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.25/2.47 inference(transitivity,[status(thm)],[6562, 6560])).
% 2.25/2.47 tff(6564,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 2.25/2.47 inference(quant_inst,[status(thm)],[])).
% 2.25/2.47 tff(6565,plain,
% 2.25/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.25/2.47 inference(modus_ponens,[status(thm)],[6564, 6563])).
% 2.25/2.47 tff(6566,plain,
% 2.25/2.47 (~r(z, s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[6565, 163, 6557, 153, 6555])).
% 2.25/2.47 tff(6567,plain,
% 2.25/2.47 (b(z, s(z))),
% 2.25/2.47 inference(unit_resolution,[status(thm)],[593, 6566])).
% 2.25/2.47 tff(6568,plain,
% 2.25/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.47 inference(rewrite,[status(thm)],[])).
% 2.25/2.47 tff(6569,plain,
% 2.25/2.48 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6570,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6569])).
% 2.25/2.48 tff(6571,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6570, 6568])).
% 2.25/2.48 tff(6572,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6573,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6572, 6571])).
% 2.25/2.48 tff(6574,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6573, 198, 95, 5927, 320, 595])).
% 2.25/2.48 tff(6575,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6576,plain,
% 2.25/2.48 (~b(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6575, 6567, 5927, 95])).
% 2.25/2.48 tff(6577,plain,
% 2.25/2.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[251, 6576, 2])).
% 2.25/2.48 tff(6578,plain,
% 2.25/2.48 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[229])).
% 2.25/2.48 tff(6579,plain,
% 2.25/2.48 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 2.25/2.48 inference(symmetry,[status(thm)],[6578])).
% 2.25/2.48 tff(6580,plain,
% 2.25/2.48 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6579])).
% 2.25/2.48 tff(6581,plain,
% 2.25/2.48 (b(elem!1, elem!1) <=> b(s(z), s(z))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[229, 229])).
% 2.25/2.48 tff(6582,plain,
% 2.25/2.48 ((~b(elem!1, elem!1)) <=> (~b(s(z), s(z)))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6581])).
% 2.25/2.48 tff(6583,plain,
% 2.25/2.48 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 2.25/2.48 inference(bind,[status(th)],[])).
% 2.25/2.48 tff(6584,plain,
% 2.25/2.48 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 2.25/2.48 inference(quant_intro,[status(thm)],[6583])).
% 2.25/2.48 tff(6585,plain,
% 2.25/2.48 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6586,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 2.25/2.48 tff(6587,plain,
% 2.25/2.48 (![X: $i] : (~b(X, X))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6586, 6585])).
% 2.25/2.48 tff(6588,plain,(
% 2.25/2.48 ![X: $i] : (~b(X, X))),
% 2.25/2.48 inference(skolemize,[status(sab)],[6587])).
% 2.25/2.48 tff(6589,plain,
% 2.25/2.48 (![X: $i] : (~b(X, X))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6588, 6584])).
% 2.25/2.48 tff(6590,plain,
% 2.25/2.48 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6591,plain,
% 2.25/2.48 (~b(elem!1, elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6590, 6589])).
% 2.25/2.48 tff(6592,plain,
% 2.25/2.48 (~b(s(z), s(z))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6591, 6582])).
% 2.25/2.48 tff(6593,plain,
% 2.25/2.48 (~b(s(z), elem!1)),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6592, 6580])).
% 2.25/2.48 tff(6594,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[5927, 6593])).
% 2.25/2.48 tff(6595,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6596,plain,
% 2.25/2.48 (~(elem!1 = s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6595, 5927])).
% 2.25/2.48 tff(6597,plain,
% 2.25/2.48 (r(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[242, 6576, 6596])).
% 2.25/2.48 tff(6598,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6599,plain,
% 2.25/2.48 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6600,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6599])).
% 2.25/2.48 tff(6601,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6600, 6598])).
% 2.25/2.48 tff(6602,plain,
% 2.25/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6603,plain,
% 2.25/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6602, 6601])).
% 2.25/2.48 tff(6604,plain,
% 2.25/2.48 (~r(elem!1, s(s(z)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6603, 163, 6597, 6557, 6555])).
% 2.25/2.48 tff(6605,plain,
% 2.25/2.48 (b(elem!1, s(s(z)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 6604])).
% 2.25/2.48 tff(6606,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, 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(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6607,plain,
% 2.25/2.48 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6608,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, 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(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6607])).
% 2.25/2.48 tff(6609,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6608, 6606])).
% 2.25/2.48 tff(6610,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6611,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6610, 6609])).
% 2.25/2.48 tff(6612,plain,
% 2.25/2.48 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6611, 198, 5927, 6518, 2, 6605])).
% 2.25/2.48 tff(6613,plain,
% 2.25/2.48 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[256, 6612, 6577])).
% 2.25/2.48 tff(6614,plain,
% 2.25/2.48 (~r(elem!1, z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[5560, 6613, 153, 152])).
% 2.25/2.48 tff(6615,plain,
% 2.25/2.48 (b(elem!1, z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[187, 6614, 76])).
% 2.25/2.48 tff(6616,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[2275, 198, 95, 6615, 5927, 6559])).
% 2.25/2.48 tff(6617,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6618,plain,
% 2.25/2.48 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6617, 3615, 5927, 76, 153, 2, 5011, 95])).
% 2.25/2.48 tff(6619,plain,
% 2.25/2.48 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[176, 6618])).
% 2.25/2.48 tff(6620,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6621,plain,
% 2.25/2.48 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6622,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6621])).
% 2.25/2.48 tff(6623,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6622, 6620])).
% 2.25/2.48 tff(6624,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6625,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6624, 6623])).
% 2.25/2.48 tff(6626,plain,
% 2.25/2.48 (~b(s(z), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6625, 198, 95, 5927, 3615, 6619])).
% 2.25/2.48 tff(6627,plain,
% 2.25/2.48 (r(s(z), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[40, 6626])).
% 2.25/2.48 tff(6628,plain,
% 2.25/2.48 (~r(s(s(z)), s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6539, 4935, 150, 153])).
% 2.25/2.48 tff(6629,plain,
% 2.25/2.48 (b(s(s(z)), s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[487, 6628])).
% 2.25/2.48 tff(6630,plain,
% 2.25/2.48 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.25/2.48 inference(commutativity,[status(thm)],[])).
% 2.25/2.48 tff(6631,plain,
% 2.25/2.48 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.25/2.48 inference(symmetry,[status(thm)],[6630])).
% 2.25/2.48 tff(6632,plain,
% 2.25/2.48 (elem!1 = s(s(z))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[2082, 6631])).
% 2.25/2.48 tff(6633,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[5011, 6632])).
% 2.25/2.48 tff(6634,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6635,plain,
% 2.25/2.48 (~(s(s(z)) = elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6634, 5011])).
% 2.25/2.48 tff(6636,plain,
% 2.25/2.48 (~(s(z) = elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[4600, 4598, 95])).
% 2.25/2.48 tff(6637,plain,
% 2.25/2.48 (~(s(s(z)) = s(elem!1))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[227, 6636])).
% 2.25/2.48 tff(6638,plain,
% 2.25/2.48 (~r(s(s(z)), s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6539, 406, 150, 153])).
% 2.25/2.48 tff(6639,plain,
% 2.25/2.48 (b(s(s(z)), s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[487, 6638])).
% 2.25/2.48 tff(6640,plain,
% 2.25/2.48 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[3753, 4201, 6639, 2])).
% 2.25/2.48 tff(6641,plain,
% 2.25/2.48 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[420, 6640])).
% 2.25/2.48 tff(6642,plain,
% 2.25/2.48 (~(elem!1 = s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[234, 232])).
% 2.25/2.48 tff(6643,assumption,(~b(elem!1, z)), introduced(assumption)).
% 2.25/2.48 tff(6644,plain,
% 2.25/2.48 (r(elem!1, z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[187, 6643, 76])).
% 2.25/2.48 tff(6645,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6646,plain,
% 2.25/2.48 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6647,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6646])).
% 2.25/2.48 tff(6648,plain,
% 2.25/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6647, 6645])).
% 2.25/2.48 tff(6649,plain,
% 2.25/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6650,plain,
% 2.25/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6649, 6648])).
% 2.25/2.48 tff(6651,plain,
% 2.25/2.48 ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6650, 163])).
% 2.25/2.48 tff(6652,plain,
% 2.25/2.48 (~r(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6651, 6644, 150, 406])).
% 2.25/2.48 tff(6653,plain,
% 2.25/2.48 (b(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[242, 6652, 6642])).
% 2.25/2.48 tff(6654,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6655,plain,
% 2.25/2.48 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6656,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6655])).
% 2.25/2.48 tff(6657,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.25/2.48 inference(transitivity,[status(thm)],[6656, 6654])).
% 2.25/2.48 tff(6658,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 2.25/2.48 inference(quant_inst,[status(thm)],[])).
% 2.25/2.48 tff(6659,plain,
% 2.25/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6658, 6657])).
% 2.25/2.48 tff(6660,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6659, 198, 5927, 320, 2682, 560])).
% 2.25/2.48 tff(6661,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6662,plain,
% 2.25/2.48 (~b(s(s(z)), elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6661, 6653, 5927, 6639])).
% 2.25/2.48 tff(6663,plain,
% 2.25/2.48 (r(s(s(z)), elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[2139, 6662, 6635])).
% 2.25/2.48 tff(6664,plain,
% 2.25/2.48 (~r(s(s(elem!1)), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[3739, 407, 150, 153, 2106, 406, 6639])).
% 2.25/2.48 tff(6665,plain,
% 2.25/2.48 (b(s(s(elem!1)), z)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[801, 6664])).
% 2.25/2.48 tff(6666,plain,
% 2.25/2.48 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.25/2.48 inference(monotonicity,[status(thm)],[114])).
% 2.25/2.48 tff(6667,plain,
% 2.25/2.48 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.25/2.48 inference(symmetry,[status(thm)],[6666])).
% 2.25/2.48 tff(6668,plain,
% 2.25/2.48 ((~b(elem!1, z)) <=> (~b(s(s(elem!1)), z))),
% 2.25/2.48 inference(monotonicity,[status(thm)],[6667])).
% 2.25/2.48 tff(6669,plain,
% 2.25/2.48 (~b(s(s(elem!1)), z)),
% 2.25/2.48 inference(modus_ponens,[status(thm)],[6643, 6668])).
% 2.25/2.48 tff(6670,plain,
% 2.25/2.48 ($false),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[723, 6669])).
% 2.25/2.48 tff(6671,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(elem!1)), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.48 tff(6672,plain,
% 2.25/2.48 (~(s(s(elem!1)) = elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6671, 6643, 6665])).
% 2.25/2.48 tff(6673,plain,
% 2.25/2.48 (~r(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[6651, 833, 150, 406])).
% 2.25/2.48 tff(6674,plain,
% 2.25/2.48 (b(elem!1, s(z))),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[242, 6673, 237])).
% 2.25/2.48 tff(6675,plain,
% 2.25/2.48 (b(s(elem!1), elem!1)),
% 2.25/2.48 inference(unit_resolution,[status(thm)],[856, 851, 1651])).
% 2.25/2.48 tff(6676,plain,
% 2.25/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.48 tff(6677,plain,
% 2.25/2.48 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.48 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6678,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6677])).
% 2.25/2.49 tff(6679,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6678, 6676])).
% 2.25/2.49 tff(6680,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6681,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6680, 6679])).
% 2.25/2.49 tff(6682,plain,
% 2.25/2.49 ($false),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6681, 198, 5927, 1200, 320, 2107])).
% 2.25/2.49 tff(6683,plain,((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.49 tff(6684,plain,
% 2.25/2.49 (~b(s(elem!1), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6683, 6675, 5927, 6674])).
% 2.25/2.49 tff(6685,plain,
% 2.25/2.49 (r(s(elem!1), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1150, 26, 820, 6684])).
% 2.25/2.49 tff(6686,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6687,plain,
% 2.25/2.49 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6688,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6687])).
% 2.25/2.49 tff(6689,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6688, 6686])).
% 2.25/2.49 tff(6690,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6691,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 2.25/2.49 tff(6692,plain,
% 2.25/2.49 (~r(s(elem!1), z)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6691, 163, 150, 406, 6685])).
% 2.25/2.49 tff(6693,plain,
% 2.25/2.49 (b(s(elem!1), z)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1217, 6692])).
% 2.25/2.49 tff(6694,plain,
% 2.25/2.49 (~r(elem!1, s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6651, 150, 833, 406])).
% 2.25/2.49 tff(6695,plain,
% 2.25/2.49 (b(elem!1, s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[242, 6694, 237])).
% 2.25/2.49 tff(6696,plain,
% 2.25/2.49 (~b(s(elem!1), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6683, 6695, 1200, 5927])).
% 2.25/2.49 tff(6697,plain,
% 2.25/2.49 (r(s(elem!1), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1150, 26, 820, 6696])).
% 2.25/2.49 tff(6698,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6699,plain,
% 2.25/2.49 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6700,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6699])).
% 2.25/2.49 tff(6701,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6700, 6698])).
% 2.25/2.49 tff(6702,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6703,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6702, 6701])).
% 2.25/2.49 tff(6704,plain,
% 2.25/2.49 ($false),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6703, 163, 791, 150, 406, 6697])).
% 2.25/2.49 tff(6705,plain,((~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.49 tff(6706,plain,
% 2.25/2.49 (~r(z, s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6705, 6675, 5927, 150, 820, 406, 237, 833])).
% 2.25/2.49 tff(6707,plain,
% 2.25/2.49 (b(z, s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1791, 6706])).
% 2.25/2.49 tff(6708,plain,
% 2.25/2.49 (~(s(elem!1) = s(s(elem!1)))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[140, 138])).
% 2.25/2.49 tff(6709,plain,
% 2.25/2.49 (~(s(s(elem!1)) = s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1138, 6708])).
% 2.25/2.49 tff(6710,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6711,plain,
% 2.25/2.49 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6712,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6711])).
% 2.25/2.49 tff(6713,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6712, 6710])).
% 2.25/2.49 tff(6714,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6715,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 2.25/2.49 tff(6716,plain,
% 2.25/2.49 ($false),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6715, 198, 95, 1175, 723, 1328, 1200])).
% 2.25/2.49 tff(6717,plain,((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.49 tff(6718,plain,
% 2.25/2.49 (~b(s(elem!1), s(s(elem!1)))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6717, 6693, 95, 723, 6675])).
% 2.25/2.49 tff(6719,plain,
% 2.25/2.49 (r(s(elem!1), s(s(elem!1)))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[901, 6718, 6708])).
% 2.25/2.49 tff(6720,plain,
% 2.25/2.49 (~r(s(s(elem!1)), elem!1)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[3574, 6719, 723, 95, 6709, 851, 6707, 1651, 6693])).
% 2.25/2.49 tff(6721,plain,
% 2.25/2.49 (b(s(s(elem!1)), elem!1)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[602, 6720, 138])).
% 2.25/2.49 tff(6722,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6723,plain,
% 2.25/2.49 (((~b(s(z), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6724,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6723])).
% 2.25/2.49 tff(6725,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6724, 6722])).
% 2.25/2.49 tff(6726,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6727,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6726, 6725])).
% 2.25/2.49 tff(6728,plain,
% 2.25/2.49 (~b(s(s(elem!1)), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6727, 198, 6721, 5927, 6674])).
% 2.25/2.49 tff(6729,plain,
% 2.25/2.49 (r(s(s(elem!1)), s(z))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[626, 6728])).
% 2.25/2.49 tff(6730,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6731,plain,
% 2.25/2.49 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(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)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6732,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6731])).
% 2.25/2.49 tff(6733,plain,
% 2.25/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6732, 6730])).
% 2.25/2.49 tff(6734,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6735,plain,
% 2.25/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6734, 6733])).
% 2.25/2.49 tff(6736,plain,
% 2.25/2.49 (~b(s(s(elem!1)), s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6735, 198, 95, 6721, 6693, 723])).
% 2.25/2.49 tff(6737,plain,
% 2.25/2.49 (r(s(s(elem!1)), s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1143, 6736, 6709])).
% 2.25/2.49 tff(6738,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6739,plain,
% 2.25/2.49 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6740,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6739])).
% 2.25/2.49 tff(6741,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6740, 6738])).
% 2.25/2.49 tff(6742,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6743,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6742, 6741])).
% 2.25/2.49 tff(6744,plain,
% 2.25/2.49 ($false),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6743, 163, 6737, 150, 6729, 6685])).
% 2.25/2.49 tff(6745,plain,(r(s(elem!1), elem!1) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = elem!1) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.49 tff(6746,plain,
% 2.25/2.49 (r(s(elem!1), elem!1)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6745, 6672, 5927, 95, 6665, 150, 406, 820, 6642, 6644])).
% 2.25/2.49 tff(6747,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6748,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6749,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6748, 6747])).
% 2.25/2.49 tff(6750,plain,
% 2.25/2.49 (~r(s(s(z)), s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[6749, 163, 6644, 6746, 6663])).
% 2.25/2.49 tff(6751,plain,
% 2.25/2.49 (b(s(s(z)), s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[2378, 6750, 232])).
% 2.25/2.49 tff(6752,plain,
% 2.25/2.49 (~(s(elem!1) = elem!1)),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1395, 6672])).
% 2.25/2.49 tff(6753,plain,
% 2.25/2.49 (~(elem!1 = s(elem!1))),
% 2.25/2.49 inference(unit_resolution,[status(thm)],[1400, 6752])).
% 2.25/2.49 tff(6754,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6755,plain,
% 2.25/2.49 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.25/2.49 inference(rewrite,[status(thm)],[])).
% 2.25/2.49 tff(6756,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 2.25/2.49 inference(monotonicity,[status(thm)],[6755])).
% 2.25/2.49 tff(6757,plain,
% 2.25/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.25/2.49 inference(transitivity,[status(thm)],[6756, 6754])).
% 2.25/2.49 tff(6758,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.25/2.49 inference(quant_inst,[status(thm)],[])).
% 2.25/2.49 tff(6759,plain,
% 2.25/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.25/2.49 inference(modus_ponens,[status(thm)],[6758, 6757])).
% 2.25/2.50 tff(6760,plain,
% 2.25/2.50 ($false),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[6759, 163, 833, 406, 2113, 332])).
% 2.25/2.50 tff(6761,plain,((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.50 tff(6762,plain,
% 2.25/2.50 (~r(s(s(z)), z)),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[6761, 6644, 406, 6663])).
% 2.25/2.50 tff(6763,plain,
% 2.25/2.50 (b(s(s(z)), z)),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[345, 6762])).
% 2.25/2.50 tff(6764,plain,
% 2.25/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))))),
% 2.25/2.50 inference(rewrite,[status(thm)],[])).
% 2.25/2.50 tff(6765,plain,
% 2.25/2.50 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))))),
% 2.25/2.50 inference(rewrite,[status(thm)],[])).
% 2.25/2.50 tff(6766,plain,
% 2.25/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z)))))),
% 2.25/2.50 inference(monotonicity,[status(thm)],[6765])).
% 2.25/2.50 tff(6767,plain,
% 2.25/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z))))),
% 2.25/2.50 inference(transitivity,[status(thm)],[6766, 6764])).
% 2.25/2.50 tff(6768,plain,
% 2.25/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 2.25/2.50 inference(quant_inst,[status(thm)],[])).
% 2.25/2.50 tff(6769,plain,
% 2.25/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(z, s(z)))),
% 2.25/2.50 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 2.25/2.50 tff(6770,plain,
% 2.25/2.50 ($false),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[6769, 163, 833, 1474, 1221, 406])).
% 2.25/2.50 tff(6771,plain,((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.50 tff(6772,plain,
% 2.25/2.50 (~r(s(elem!1), z)),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[6771, 6644, 6746, 406])).
% 2.25/2.50 tff(6773,plain,
% 2.25/2.50 (b(s(elem!1), z)),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[1217, 6772])).
% 2.25/2.50 tff(6774,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 2.25/2.50 tff(6775,plain,
% 2.25/2.50 ($false),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[3939, 198, 1175, 1801, 347, 6774])).
% 2.25/2.50 tff(6776,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.25/2.50 tff(6777,plain,
% 2.25/2.50 (~b(z, s(elem!1))),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[6776, 6773, 6763, 6751])).
% 2.25/2.50 tff(6778,plain,
% 2.25/2.50 (r(z, s(elem!1))),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[1791, 6777])).
% 2.25/2.50 tff(6779,plain,
% 2.25/2.50 (~r(elem!1, s(elem!1))),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[2523, 6778, 6644, 6746])).
% 2.25/2.50 tff(6780,plain,
% 2.25/2.50 (b(elem!1, s(elem!1))),
% 2.25/2.50 inference(unit_resolution,[status(thm)],[1416, 6779, 6753])).
% 2.25/2.50 tff(6781,plain,
% 2.25/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6782,plain,
% 2.35/2.50 (((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6783,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6782])).
% 2.35/2.50 tff(6784,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6783, 6781])).
% 2.35/2.50 tff(6785,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6786,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6785, 6784])).
% 2.35/2.50 tff(6787,plain,
% 2.35/2.50 (~b(elem!1, s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6786, 198, 5927, 6780, 6653, 407, 6751])).
% 2.35/2.50 tff(6788,plain,
% 2.35/2.50 (r(elem!1, s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 6787])).
% 2.35/2.50 tff(6789,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6790,plain,
% 2.35/2.50 (((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6791,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6790])).
% 2.35/2.50 tff(6792,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6791, 6789])).
% 2.35/2.50 tff(6793,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6794,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6793, 6792])).
% 2.35/2.50 tff(6795,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6794, 163, 6644, 6663, 153, 6788])).
% 2.35/2.50 tff(6796,plain,(b(elem!1, z) | (~r(z, s(s(z)))) | (elem!1 = s(s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (s(s(z)) = s(elem!1)) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(6797,plain,
% 2.35/2.50 (b(elem!1, z)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6796, 4201, 5011, 5927, 153, 406, 232, 95, 150, 820, 76])).
% 2.35/2.50 tff(6798,plain,
% 2.35/2.50 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[204, 198, 95, 6797, 330])).
% 2.35/2.50 tff(6799,plain,
% 2.35/2.50 (~r(s(s(elem!1)), z)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3739, 4201, 150, 153, 2106, 406, 6639])).
% 2.35/2.50 tff(6800,plain,
% 2.35/2.50 (b(s(s(elem!1)), z)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[801, 6799])).
% 2.35/2.50 tff(6801,plain,
% 2.35/2.50 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[4665, 163, 153, 3272, 6641])).
% 2.35/2.50 tff(6802,plain,
% 2.35/2.50 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[31, 6801])).
% 2.35/2.50 tff(6803,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6804,plain,
% 2.35/2.50 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6805,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6804])).
% 2.35/2.50 tff(6806,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6805, 6803])).
% 2.35/2.50 tff(6807,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6808,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6807, 6806])).
% 2.35/2.50 tff(6809,plain,
% 2.35/2.50 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6808, 198, 95, 6797, 6802, 330])).
% 2.35/2.50 tff(6810,plain,
% 2.35/2.50 (~b(s(s(elem!1)), elem!1)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[1491, 198, 95, 6797, 6800])).
% 2.35/2.50 tff(6811,plain,
% 2.35/2.50 (~r(s(s(s(s(s(z))))), s(z))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3836, 3828, 153, 150])).
% 2.35/2.50 tff(6812,plain,
% 2.35/2.50 (b(s(s(s(s(s(z))))), s(z))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[469, 6811])).
% 2.35/2.50 tff(6813,plain,
% 2.35/2.50 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[494, 198, 560, 4201, 6812])).
% 2.35/2.50 tff(6814,plain,
% 2.35/2.50 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[511, 26, 508, 6813])).
% 2.35/2.50 tff(6815,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6816,plain,
% 2.35/2.50 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6817,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6816])).
% 2.35/2.50 tff(6818,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6817, 6815])).
% 2.35/2.50 tff(6819,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6820,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6819, 6818])).
% 2.35/2.50 tff(6821,plain,
% 2.35/2.50 ($false),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6820, 163, 153, 3272, 6814, 3828])).
% 2.35/2.50 tff(6822,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.50 tff(6823,plain,
% 2.35/2.50 (~r(s(s(s(s(s(z))))), z)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6822, 3272, 153, 6639, 150])).
% 2.35/2.50 tff(6824,plain,
% 2.35/2.50 (b(s(s(s(s(s(z))))), z)),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3841, 6823])).
% 2.35/2.50 tff(6825,plain,
% 2.35/2.50 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[4174, 6802, 330, 6824])).
% 2.35/2.50 tff(6826,plain,
% 2.35/2.50 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3098, 6825])).
% 2.35/2.50 tff(6827,plain,
% 2.35/2.50 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[4502, 163, 6826, 3272, 6641])).
% 2.35/2.50 tff(6828,plain,
% 2.35/2.50 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[511, 26, 508, 6827])).
% 2.35/2.50 tff(6829,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6830,plain,
% 2.35/2.50 (((~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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6831,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z)), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6830])).
% 2.35/2.50 tff(6832,plain,
% 2.35/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z)), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6831, 6829])).
% 2.35/2.50 tff(6833,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6834,plain,
% 2.35/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6833, 6832])).
% 2.35/2.50 tff(6835,plain,
% 2.35/2.50 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6834, 163, 6826, 3272, 6641])).
% 2.35/2.50 tff(6836,plain,
% 2.35/2.50 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[2715, 26, 507, 6835])).
% 2.35/2.50 tff(6837,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6838,plain,
% 2.35/2.50 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(rewrite,[status(thm)],[])).
% 2.35/2.50 tff(6839,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.35/2.50 inference(monotonicity,[status(thm)],[6838])).
% 2.35/2.50 tff(6840,plain,
% 2.35/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.35/2.50 inference(transitivity,[status(thm)],[6839, 6837])).
% 2.35/2.50 tff(6841,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.35/2.50 inference(quant_inst,[status(thm)],[])).
% 2.35/2.50 tff(6842,plain,
% 2.35/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.35/2.50 inference(modus_ponens,[status(thm)],[6841, 6840])).
% 2.35/2.50 tff(6843,plain,
% 2.35/2.50 (~b(s(z), s(s(s(s(s(z))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[6842, 198, 4201, 6836, 6828])).
% 2.35/2.50 tff(6844,plain,
% 2.35/2.50 (r(s(z), s(s(s(s(s(z))))))),
% 2.35/2.50 inference(unit_resolution,[status(thm)],[3301, 6843])).
% 2.35/2.50 tff(6845,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6846,plain,
% 2.35/2.51 (((~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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6847,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6846])).
% 2.35/2.51 tff(6848,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6847, 6845])).
% 2.35/2.51 tff(6849,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6850,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6849, 6848])).
% 2.35/2.51 tff(6851,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6850, 163, 3066, 6249, 151, 423])).
% 2.35/2.51 tff(6852,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(6853,plain,
% 2.35/2.51 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6852, 6826, 6844, 6641])).
% 2.35/2.51 tff(6854,plain,
% 2.35/2.51 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3613, 6853])).
% 2.35/2.51 tff(6855,plain,
% 2.35/2.51 (~(s(elem!1) = s(s(elem!1)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4186, 244, 150, 2, 3615, 153, 271, 95])).
% 2.35/2.51 tff(6856,plain,
% 2.35/2.51 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3753, 4201, 560, 2])).
% 2.35/2.51 tff(6857,plain,
% 2.35/2.51 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[420, 6856])).
% 2.35/2.51 tff(6858,plain,
% 2.35/2.51 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4665, 163, 153, 3272, 6857])).
% 2.35/2.51 tff(6859,plain,
% 2.35/2.51 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[31, 6858])).
% 2.35/2.51 tff(6860,plain,
% 2.35/2.51 (r(elem!1, s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[242, 238, 6642])).
% 2.35/2.51 tff(6861,assumption,(~b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.35/2.51 tff(6862,plain,
% 2.35/2.51 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[3792, 252])).
% 2.35/2.51 tff(6863,plain,
% 2.35/2.51 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[703, 6862, 6861])).
% 2.35/2.51 tff(6864,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6865,plain,
% 2.35/2.51 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6866,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6865])).
% 2.35/2.51 tff(6867,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6866, 6864])).
% 2.35/2.51 tff(6868,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6869,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6868, 6867])).
% 2.35/2.51 tff(6870,plain,
% 2.35/2.51 (~r(s(s(z)), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6869, 163, 6863, 3272, 257])).
% 2.35/2.51 tff(6871,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6872,plain,
% 2.35/2.51 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(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(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6873,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6872])).
% 2.35/2.51 tff(6874,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6873, 6871])).
% 2.35/2.51 tff(6875,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6876,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6875, 6874])).
% 2.35/2.51 tff(6877,plain,
% 2.35/2.51 (~r(elem!1, s(s(z)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6876, 163, 6863, 3272, 257])).
% 2.35/2.51 tff(6878,plain,
% 2.35/2.51 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[105])).
% 2.35/2.51 tff(6879,plain,
% 2.35/2.51 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.35/2.51 inference(symmetry,[status(thm)],[6878])).
% 2.35/2.51 tff(6880,plain,
% 2.35/2.51 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 2.35/2.51 inference(monotonicity,[status(thm)],[105])).
% 2.35/2.51 tff(6881,plain,
% 2.35/2.51 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(z)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6880, 6631])).
% 2.35/2.51 tff(6882,plain,
% 2.35/2.51 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(z))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6881])).
% 2.35/2.51 tff(6883,plain,
% 2.35/2.51 (~(elem!1 = s(s(z)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[2154, 6882])).
% 2.35/2.51 tff(6884,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 2.35/2.51 tff(6885,plain,
% 2.35/2.51 ((elem!1 = s(s(z))) | b(elem!1, s(s(z)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[5572, 26, 6884])).
% 2.35/2.51 tff(6886,plain,
% 2.35/2.51 (b(elem!1, s(s(z)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6885, 6883])).
% 2.35/2.51 tff(6887,plain,
% 2.35/2.51 (b(s(s(elem!1)), s(s(z)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6886, 6879])).
% 2.35/2.51 tff(6888,plain,
% 2.35/2.51 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(elem!1))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[4013])).
% 2.35/2.51 tff(6889,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 2.35/2.51 tff(6890,plain,
% 2.35/2.51 (~r(s(s(z)), s(s(elem!1)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 2.35/2.51 tff(6891,plain,
% 2.35/2.51 (b(s(s(z)), s(s(elem!1)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2161, 26, 6890, 2154])).
% 2.35/2.51 tff(6892,plain,
% 2.35/2.51 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[90])).
% 2.35/2.51 tff(6893,plain,
% 2.35/2.51 (b(s(z), s(s(elem!1)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[5927, 6892])).
% 2.35/2.51 tff(6894,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4444, 198, 6893, 407, 6891, 6887])).
% 2.35/2.51 tff(6895,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(z)))) | r(elem!1, s(s(z))) | (s(s(z)) = s(s(elem!1))) | r(s(s(z)), elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(6896,plain,
% 2.35/2.51 (~(elem!1 = s(s(elem!1)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6895, 6877, 5927, 2106, 6870, 4201])).
% 2.35/2.51 tff(6897,plain,
% 2.35/2.51 (~(s(s(elem!1)) = elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[118, 6896])).
% 2.35/2.51 tff(6898,plain,
% 2.35/2.51 (r(s(s(elem!1)), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[602, 6897, 597])).
% 2.35/2.51 tff(6899,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6900,plain,
% 2.35/2.51 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6901,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6900])).
% 2.35/2.51 tff(6902,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6901, 6899])).
% 2.35/2.51 tff(6903,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6904,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6903, 6902])).
% 2.35/2.51 tff(6905,plain,
% 2.35/2.51 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6904, 163, 6898, 6860, 257])).
% 2.35/2.51 tff(6906,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~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)))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6907,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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)))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6908,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 2.35/2.51 tff(6909,plain,
% 2.35/2.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6908, 163, 6898, 6860, 257])).
% 2.35/2.51 tff(6910,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4394, 6909, 6905, 560, 6859, 820, 232, 150, 3615, 3272, 95, 6855, 2, 153, 271])).
% 2.35/2.51 tff(6911,plain,(b(elem!1, s(z)) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(elem!1, z)) | b(s(s(elem!1)), elem!1) | (~b(s(z), elem!1)) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(6912,plain,
% 2.35/2.51 (b(elem!1, s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6911, 6854, 820, 232, 150, 6639, 3272, 95, 2, 153, 6797, 6810, 5927, 6809, 6798])).
% 2.35/2.51 tff(6913,plain,
% 2.35/2.51 (~(s(elem!1) = s(s(elem!1)))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[4186, 6798, 150, 2, 6854, 153, 6797, 95])).
% 2.35/2.51 tff(6914,plain,
% 2.35/2.51 (~(s(s(elem!1)) = s(elem!1))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1138, 6913])).
% 2.35/2.51 tff(6915,plain,
% 2.35/2.51 (~(s(elem!1) = elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1762, 6914])).
% 2.35/2.51 tff(6916,plain,
% 2.35/2.51 (~(elem!1 = s(elem!1))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1400, 6915])).
% 2.35/2.51 tff(6917,plain,
% 2.35/2.51 (~b(s(s(z)), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6661, 6912, 5927, 6639])).
% 2.35/2.51 tff(6918,plain,
% 2.35/2.51 (r(s(s(z)), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[2139, 6917, 6635])).
% 2.35/2.51 tff(6919,plain,
% 2.35/2.51 (~b(s(elem!1), s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6683, 1200, 5927, 320])).
% 2.35/2.51 tff(6920,plain,
% 2.35/2.51 (r(s(elem!1), s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1150, 26, 820, 6919])).
% 2.35/2.51 tff(6921,plain,
% 2.35/2.51 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6922,plain,
% 2.35/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6921])).
% 2.35/2.51 tff(6923,plain,
% 2.35/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6922, 1740])).
% 2.35/2.51 tff(6924,plain,
% 2.35/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6925,plain,
% 2.35/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6924, 6923])).
% 2.35/2.51 tff(6926,plain,
% 2.35/2.51 (~b(s(elem!1), z)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6925, 198, 95, 271, 1200])).
% 2.35/2.51 tff(6927,plain,
% 2.35/2.51 (r(s(elem!1), z)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1217, 6926])).
% 2.35/2.51 tff(6928,plain,
% 2.35/2.51 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6929,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 2.35/2.51 inference(monotonicity,[status(thm)],[6928])).
% 2.35/2.51 tff(6930,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 2.35/2.51 inference(transitivity,[status(thm)],[6929, 6686])).
% 2.35/2.51 tff(6931,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6932,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 2.35/2.51 tff(6933,plain,
% 2.35/2.51 ($false),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6932, 163, 6927, 150, 406, 6920])).
% 2.35/2.51 tff(6934,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.51 tff(6935,plain,
% 2.35/2.51 (~b(s(elem!1), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6934, 6797, 406, 820, 95, 150, 5927, 6912])).
% 2.35/2.51 tff(6936,plain,
% 2.35/2.51 (r(s(elem!1), elem!1)),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[856, 6935, 6915])).
% 2.35/2.51 tff(6937,plain,
% 2.35/2.51 (~r(s(elem!1), s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6932, 163, 1221, 150, 406])).
% 2.35/2.51 tff(6938,plain,
% 2.35/2.51 (b(s(elem!1), s(z))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1150, 26, 820, 6937])).
% 2.35/2.51 tff(6939,plain,
% 2.35/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.35/2.51 inference(rewrite,[status(thm)],[])).
% 2.35/2.51 tff(6940,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.35/2.51 inference(quant_inst,[status(thm)],[])).
% 2.35/2.51 tff(6941,plain,
% 2.35/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 2.35/2.51 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 2.35/2.51 tff(6942,plain,
% 2.35/2.51 (~r(s(z), s(elem!1))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[6941, 163, 1221, 150, 406])).
% 2.35/2.51 tff(6943,plain,
% 2.35/2.51 (b(s(z), s(elem!1))),
% 2.35/2.51 inference(unit_resolution,[status(thm)],[1164, 6942, 1157])).
% 2.35/2.51 tff(6944,plain,
% 2.35/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6945,plain,
% 2.35/2.52 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6946,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[6945])).
% 2.35/2.52 tff(6947,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[6946, 6944])).
% 2.35/2.52 tff(6948,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(6949,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 2.35/2.52 tff(6950,plain,
% 2.35/2.52 (~b(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6949, 198, 320, 6943, 6938])).
% 2.35/2.52 tff(6951,plain,
% 2.35/2.52 (r(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1416, 6950, 1409])).
% 2.35/2.52 tff(6952,plain,
% 2.35/2.52 (~r(s(s(z)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2116, 163, 1474, 6951, 2113])).
% 2.35/2.52 tff(6953,plain,
% 2.35/2.52 (b(s(s(z)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2378, 6952, 232])).
% 2.35/2.52 tff(6954,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6955,plain,
% 2.35/2.52 (((~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6956,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[6955])).
% 2.35/2.52 tff(6957,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[6956, 6954])).
% 2.35/2.52 tff(6958,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(6959,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[6958, 6957])).
% 2.35/2.52 tff(6960,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6959, 198, 560, 6943, 6938, 6953])).
% 2.35/2.52 tff(6961,plain,((~r(s(elem!1), z)) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(6962,plain,
% 2.35/2.52 (~r(s(elem!1), z)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6961, 6936, 232, 6639, 6918, 6916, 6912, 820, 150, 406])).
% 2.35/2.52 tff(6963,plain,
% 2.35/2.52 (b(s(elem!1), z)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1217, 6962])).
% 2.35/2.52 tff(6964,plain,
% 2.35/2.52 (~(elem!1 = s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1400, 4373])).
% 2.35/2.52 tff(6965,plain,
% 2.35/2.52 (~b(s(s(elem!1)), elem!1)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1491, 198, 95, 271, 723])).
% 2.35/2.52 tff(6966,plain,
% 2.35/2.52 (r(s(s(elem!1)), elem!1)),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[602, 138, 6965])).
% 2.35/2.52 tff(6967,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6968,plain,
% 2.35/2.52 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6969,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[6968])).
% 2.35/2.52 tff(6970,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[6969, 6967])).
% 2.35/2.52 tff(6971,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(6972,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[6971, 6970])).
% 2.35/2.52 tff(6973,plain,
% 2.35/2.52 (~b(s(s(elem!1)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6972, 198, 95, 271, 1175, 723, 1801])).
% 2.35/2.52 tff(6974,plain,
% 2.35/2.52 (r(s(s(elem!1)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1143, 6973, 1701])).
% 2.35/2.52 tff(6975,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6976,plain,
% 2.35/2.52 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6977,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[6976])).
% 2.35/2.52 tff(6978,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[6977, 6975])).
% 2.35/2.52 tff(6979,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(6980,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[6979, 6978])).
% 2.35/2.52 tff(6981,plain,
% 2.35/2.52 (~b(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6980, 198, 95, 271, 1175, 1801])).
% 2.35/2.52 tff(6982,plain,
% 2.35/2.52 (r(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1416, 6981, 1764])).
% 2.35/2.52 tff(6983,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2341, 163, 1115, 1474, 6982, 6974])).
% 2.35/2.52 tff(6984,plain,((~b(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(6985,plain,
% 2.35/2.52 (~b(z, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6984, 6966, 1474, 2968, 95, 271, 1175, 723])).
% 2.35/2.52 tff(6986,plain,
% 2.35/2.52 (r(z, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1791, 6985])).
% 2.35/2.52 tff(6987,plain,
% 2.35/2.52 (~r(z, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2924, 163, 1474, 791, 1773])).
% 2.35/2.52 tff(6988,plain,
% 2.35/2.52 (b(z, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1096, 6987])).
% 2.35/2.52 tff(6989,plain,
% 2.35/2.52 (~b(elem!1, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1071, 6988, 271, 723])).
% 2.35/2.52 tff(6990,plain,
% 2.35/2.52 (r(elem!1, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[147, 6989, 116])).
% 2.35/2.52 tff(6991,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2349, 163, 1115, 1474, 1773, 6990])).
% 2.35/2.52 tff(6992,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(6993,plain,
% 2.35/2.52 (~r(s(s(elem!1)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[6992, 6966, 1474, 1856, 271, 723, 6986])).
% 2.35/2.52 tff(6994,plain,
% 2.35/2.52 (b(s(s(elem!1)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1143, 6993, 2968])).
% 2.35/2.52 tff(6995,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6996,plain,
% 2.35/2.52 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(6997,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[6996])).
% 2.35/2.52 tff(6998,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[6997, 6995])).
% 2.35/2.52 tff(6999,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7000,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 2.35/2.52 tff(7001,plain,
% 2.35/2.52 (~b(elem!1, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7000, 198, 271, 1175, 1145, 1418])).
% 2.35/2.52 tff(7002,plain,
% 2.35/2.52 (r(elem!1, s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[147, 7001, 116])).
% 2.35/2.52 tff(7003,plain,
% 2.35/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7004,plain,
% 2.35/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7005,plain,
% 2.35/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7004, 7003])).
% 2.35/2.52 tff(7006,plain,
% 2.35/2.52 (~r(s(s(z)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7005, 163, 1474, 7002, 2113])).
% 2.35/2.52 tff(7007,plain,
% 2.35/2.52 (b(s(s(z)), s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2378, 7006, 232])).
% 2.35/2.52 tff(7008,plain,
% 2.35/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7009,plain,
% 2.35/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7010,plain,
% 2.35/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7009, 7008])).
% 2.35/2.52 tff(7011,plain,
% 2.35/2.52 (~r(s(s(z)), s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7010, 163, 1115, 7002, 2113])).
% 2.35/2.52 tff(7012,plain,
% 2.35/2.52 (b(s(s(z)), s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[2161, 26, 7011, 2154])).
% 2.35/2.52 tff(7013,plain,
% 2.35/2.52 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[3043, 163, 1115, 1474, 7002])).
% 2.35/2.52 tff(7014,plain,
% 2.35/2.52 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[901, 7013, 890])).
% 2.35/2.52 tff(7015,plain,
% 2.35/2.52 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(rewrite,[status(thm)],[])).
% 2.35/2.52 tff(7016,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))))),
% 2.35/2.52 inference(monotonicity,[status(thm)],[7015])).
% 2.35/2.52 tff(7017,plain,
% 2.35/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 2.35/2.52 inference(transitivity,[status(thm)],[7016, 2382])).
% 2.35/2.52 tff(7018,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.35/2.52 inference(quant_inst,[status(thm)],[])).
% 2.35/2.52 tff(7019,plain,
% 2.35/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 2.35/2.52 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 2.35/2.52 tff(7020,plain,
% 2.35/2.52 ($false),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7019, 198, 1145, 7014, 7012, 7007])).
% 2.35/2.52 tff(7021,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.52 tff(7022,plain,
% 2.35/2.52 (~b(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[7021, 6994, 232, 890, 1474, 2113, 6966, 1856, 271, 1175, 2154])).
% 2.35/2.52 tff(7023,plain,
% 2.35/2.52 (r(elem!1, s(elem!1))),
% 2.35/2.52 inference(unit_resolution,[status(thm)],[1416, 7022, 6964])).
% 2.35/2.53 tff(7024,plain,
% 2.35/2.53 (~r(s(s(z)), s(elem!1))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2116, 163, 1474, 7023, 2113])).
% 2.35/2.53 tff(7025,plain,
% 2.35/2.53 (b(s(s(z)), s(elem!1))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2378, 7024, 232])).
% 2.35/2.53 tff(7026,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7027,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7028,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7027, 7026])).
% 2.35/2.53 tff(7029,plain,
% 2.35/2.53 (~r(s(s(z)), s(s(elem!1)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7028, 163, 6966, 7023, 2113])).
% 2.35/2.53 tff(7030,plain,
% 2.35/2.53 (b(s(s(z)), s(s(elem!1)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2161, 26, 7029, 2154])).
% 2.35/2.53 tff(7031,plain,
% 2.35/2.53 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3583, 7023, 1474, 6966])).
% 2.35/2.53 tff(7032,plain,
% 2.35/2.53 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[901, 7031, 890])).
% 2.35/2.53 tff(7033,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7019, 198, 6994, 7032, 7030, 7025])).
% 2.35/2.53 tff(7034,plain,((s(s(elem!1)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7035,plain,
% 2.35/2.53 (s(s(elem!1)) = elem!1),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7034, 6936, 232, 2106, 6918, 6913, 6797, 6963, 6800, 95])).
% 2.35/2.53 tff(7036,plain,
% 2.35/2.53 (elem!1 = s(s(elem!1))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[118, 7035])).
% 2.35/2.53 tff(7037,plain,
% 2.35/2.53 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[317, 7036])).
% 2.35/2.53 tff(7038,plain,
% 2.35/2.53 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[256, 7037, 6798])).
% 2.35/2.53 tff(7039,plain,
% 2.35/2.53 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3792, 7037])).
% 2.35/2.53 tff(7040,plain,
% 2.35/2.53 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[703, 7039, 6809])).
% 2.35/2.53 tff(7041,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7042,plain,
% 2.35/2.53 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7043,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7042])).
% 2.35/2.53 tff(7044,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7043, 7041])).
% 2.35/2.53 tff(7045,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7046,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7045, 7044])).
% 2.35/2.53 tff(7047,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7046, 163, 6918, 7040, 7038, 6641])).
% 2.35/2.53 tff(7048,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7049,plain,
% 2.35/2.53 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7048, 6637, 95, 820, 150, 4935, 5927, 2, 153, 330, 5011, 76])).
% 2.35/2.53 tff(7050,plain,
% 2.35/2.53 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[374, 7049])).
% 2.35/2.53 tff(7051,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7052,plain,
% 2.35/2.53 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7053,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7052])).
% 2.35/2.53 tff(7054,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7053, 7051])).
% 2.35/2.53 tff(7055,plain,
% 2.35/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7056,plain,
% 2.35/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7055, 7054])).
% 2.35/2.53 tff(7057,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7056, 198, 95, 5927, 2682, 560, 348, 2, 330])).
% 2.35/2.53 tff(7058,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7059,plain,
% 2.35/2.53 (~b(s(s(z)), elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7058, 6629, 5927, 95, 7050, 2, 330])).
% 2.35/2.53 tff(7060,plain,
% 2.35/2.53 (r(s(s(z)), elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2139, 7059, 6635])).
% 2.35/2.53 tff(7061,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[382, 163, 150, 2113, 328, 153])).
% 2.35/2.53 tff(7062,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7063,plain,
% 2.35/2.53 (~r(s(z), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7062, 7060, 150, 153])).
% 2.35/2.53 tff(7064,plain,
% 2.35/2.53 (b(s(z), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[403, 7063])).
% 2.35/2.53 tff(7065,plain,
% 2.35/2.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3753, 7064, 6629, 2])).
% 2.35/2.53 tff(7066,plain,
% 2.35/2.53 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[420, 7065])).
% 2.35/2.53 tff(7067,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7068,plain,
% 2.35/2.53 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7069,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7068])).
% 2.35/2.53 tff(7070,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7069, 7067])).
% 2.35/2.53 tff(7071,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7072,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7071, 7070])).
% 2.35/2.53 tff(7073,plain,
% 2.35/2.53 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7072, 163, 7060, 153, 7066])).
% 2.35/2.53 tff(7074,plain,
% 2.35/2.53 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[31, 7073])).
% 2.35/2.53 tff(7075,plain,
% 2.35/2.53 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3626, 7050, 2, 6629])).
% 2.35/2.53 tff(7076,plain,
% 2.35/2.53 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3613, 7075])).
% 2.35/2.53 tff(7077,plain,
% 2.35/2.53 (~r(s(s(s(s(s(z))))), s(z))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[456, 7074, 330, 7076, 4935, 7066])).
% 2.35/2.53 tff(7078,plain,
% 2.35/2.53 (b(s(s(s(s(s(z))))), s(z))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[469, 7077])).
% 2.35/2.53 tff(7079,plain,
% 2.35/2.53 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[494, 198, 6629, 7064, 7078])).
% 2.35/2.53 tff(7080,plain,
% 2.35/2.53 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[511, 26, 508, 7079])).
% 2.35/2.53 tff(7081,plain,
% 2.35/2.53 (~r(s(s(s(s(s(z))))), z)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[518, 163, 7060, 153, 7080])).
% 2.35/2.53 tff(7082,plain,
% 2.35/2.53 (b(s(s(s(s(s(z))))), z)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3841, 7081])).
% 2.35/2.53 tff(7083,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7084,plain,
% 2.35/2.53 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7085,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(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)))))))))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7084])).
% 2.35/2.53 tff(7086,plain,
% 2.35/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7085, 7083])).
% 2.35/2.53 tff(7087,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7088,plain,
% 2.35/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7087, 7086])).
% 2.35/2.53 tff(7089,plain,
% 2.35/2.53 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7088, 163, 7060, 7066, 7080])).
% 2.35/2.53 tff(7090,plain,
% 2.35/2.53 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[3098, 7089])).
% 2.35/2.53 tff(7091,plain,
% 2.35/2.53 ($false),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[4174, 7090, 7082, 330, 7074])).
% 2.35/2.53 tff(7092,plain,(b(z, s(z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.53 tff(7093,plain,
% 2.35/2.53 (b(z, s(z))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7092, 6627, 153, 2, 95, 5927, 6619, 820, 5011, 76])).
% 2.35/2.53 tff(7094,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7095,plain,
% 2.35/2.53 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7096,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7095])).
% 2.35/2.53 tff(7097,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(transitivity,[status(thm)],[7096, 7094])).
% 2.35/2.53 tff(7098,plain,
% 2.35/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.53 inference(quant_inst,[status(thm)],[])).
% 2.35/2.53 tff(7099,plain,
% 2.35/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.53 inference(modus_ponens,[status(thm)],[7098, 7097])).
% 2.35/2.53 tff(7100,plain,
% 2.35/2.53 ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7099, 198, 95, 5927, 2])).
% 2.35/2.53 tff(7101,plain,
% 2.35/2.53 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7100, 7093, 6619])).
% 2.35/2.53 tff(7102,plain,
% 2.35/2.53 (~b(s(z), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[4649, 3628, 2, 330, 153, 3615, 150, 595])).
% 2.35/2.53 tff(7103,plain,
% 2.35/2.53 (r(s(z), s(s(z)))),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[403, 7102])).
% 2.35/2.53 tff(7104,plain,
% 2.35/2.53 (~r(s(s(z)), z)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[340, 7103, 150, 153])).
% 2.35/2.53 tff(7105,plain,
% 2.35/2.53 (b(s(s(z)), z)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[345, 7104])).
% 2.35/2.53 tff(7106,plain,
% 2.35/2.53 (~r(s(s(z)), elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[7062, 7103, 150, 153])).
% 2.35/2.53 tff(7107,plain,
% 2.35/2.53 (b(s(s(z)), elem!1)),
% 2.35/2.53 inference(unit_resolution,[status(thm)],[2139, 7106, 2105])).
% 2.35/2.53 tff(7108,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7109,plain,
% 2.35/2.53 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.35/2.53 inference(rewrite,[status(thm)],[])).
% 2.35/2.53 tff(7110,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.35/2.53 inference(monotonicity,[status(thm)],[7109])).
% 2.35/2.53 tff(7111,plain,
% 2.35/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7110, 7108])).
% 2.35/2.54 tff(7112,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7113,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7112, 7111])).
% 2.35/2.54 tff(7114,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7113, 198, 95, 7107, 348, 7105, 330])).
% 2.35/2.54 tff(7115,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(s(z)) = elem!1) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7116,plain,
% 2.35/2.54 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7115, 6619, 95, 6635, 6627, 153, 2, 3615, 7093])).
% 2.35/2.54 tff(7117,plain,
% 2.35/2.54 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[374, 7116])).
% 2.35/2.54 tff(7118,plain,
% 2.35/2.54 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[3701, 7117, 153, 7101, 95])).
% 2.35/2.54 tff(7119,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7120,plain,
% 2.35/2.54 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7121,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7120])).
% 2.35/2.54 tff(7122,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7121, 7119])).
% 2.35/2.54 tff(7123,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7124,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7123, 7122])).
% 2.35/2.54 tff(7125,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7124, 198, 5927, 7093, 7118, 2, 6619])).
% 2.35/2.54 tff(7126,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7127,plain,
% 2.35/2.54 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7126, 5927, 2, 153, 95, 820, 5011, 76])).
% 2.35/2.54 tff(7128,plain,
% 2.35/2.54 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[3613, 7127])).
% 2.35/2.54 tff(7129,plain,
% 2.35/2.54 (~r(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[171, 152, 153, 151])).
% 2.35/2.54 tff(7130,plain,
% 2.35/2.54 (b(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[40, 7129])).
% 2.35/2.54 tff(7131,plain,
% 2.35/2.54 (~b(s(s(z)), s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[5759, 7130, 151, 2, 153, 152])).
% 2.35/2.54 tff(7132,plain,
% 2.35/2.54 (r(s(s(z)), s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[487, 7131])).
% 2.35/2.54 tff(7133,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7134,plain,
% 2.35/2.54 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7135,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7134])).
% 2.35/2.54 tff(7136,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7135, 7133])).
% 2.35/2.54 tff(7137,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7138,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7137, 7136])).
% 2.35/2.54 tff(7139,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7138, 163, 406, 3450, 151, 332])).
% 2.35/2.54 tff(7140,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7141,plain,
% 2.35/2.54 (~r(s(s(z)), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7140, 406, 151, 3450])).
% 2.35/2.54 tff(7142,plain,
% 2.35/2.54 (b(s(s(z)), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[345, 7141])).
% 2.35/2.54 tff(7143,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7144,plain,
% 2.35/2.54 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7145,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7144])).
% 2.35/2.54 tff(7146,plain,
% 2.35/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7145, 7143])).
% 2.35/2.54 tff(7147,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7148,plain,
% 2.35/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), z))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7147, 7146])).
% 2.35/2.54 tff(7149,plain,
% 2.35/2.54 (~b(s(z), s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7148, 198, 95, 5927, 1185, 7142])).
% 2.35/2.54 tff(7150,plain,
% 2.35/2.54 (r(s(z), s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[403, 7149])).
% 2.35/2.54 tff(7151,plain,
% 2.35/2.54 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7152,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7151])).
% 2.35/2.54 tff(7153,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7152, 6560])).
% 2.35/2.54 tff(7154,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7155,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7154, 7153])).
% 2.35/2.54 tff(7156,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7155, 163, 406, 7150, 153, 3450])).
% 2.35/2.54 tff(7157,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7158,plain,
% 2.35/2.54 (~r(z, s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7157, 7132, 153, 95, 5927, 7130, 151])).
% 2.35/2.54 tff(7159,plain,
% 2.35/2.54 (b(z, s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[593, 7158])).
% 2.35/2.54 tff(7160,plain,
% 2.35/2.54 (~b(elem!1, s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6575, 7159, 5927, 95])).
% 2.35/2.54 tff(7161,plain,
% 2.35/2.54 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[251, 7160, 2])).
% 2.35/2.54 tff(7162,plain,
% 2.35/2.54 (r(elem!1, s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[242, 7160, 6596])).
% 2.35/2.54 tff(7163,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7164,plain,
% 2.35/2.54 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7165,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7164])).
% 2.35/2.54 tff(7166,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7165, 7163])).
% 2.35/2.54 tff(7167,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7168,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7167, 7166])).
% 2.35/2.54 tff(7169,plain,
% 2.35/2.54 (~r(elem!1, s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7168, 163, 7162, 7132, 151])).
% 2.35/2.54 tff(7170,plain,
% 2.35/2.54 (b(elem!1, s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 7169])).
% 2.35/2.54 tff(7171,plain,
% 2.35/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4981, 7132, 153, 152])).
% 2.35/2.54 tff(7172,plain,
% 2.35/2.54 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[420, 7171])).
% 2.35/2.54 tff(7173,plain,
% 2.35/2.54 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6611, 198, 5927, 7172, 2, 7170])).
% 2.35/2.54 tff(7174,plain,
% 2.35/2.54 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[256, 7173, 7161])).
% 2.35/2.54 tff(7175,plain,
% 2.35/2.54 (~r(elem!1, z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[5560, 7174, 153, 152])).
% 2.35/2.54 tff(7176,plain,
% 2.35/2.54 (b(elem!1, z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[187, 7175, 76])).
% 2.35/2.54 tff(7177,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2275, 198, 95, 7176, 5927, 7130])).
% 2.35/2.54 tff(7178,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7179,plain,
% 2.35/2.54 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7178, 95, 5927, 76, 153, 2, 5011, 7128])).
% 2.35/2.54 tff(7180,plain,
% 2.35/2.54 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[176, 7179])).
% 2.35/2.54 tff(7181,plain,
% 2.35/2.54 (~r(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7092, 4598, 153, 2, 95, 5927, 330, 820, 5011, 76])).
% 2.35/2.54 tff(7182,plain,
% 2.35/2.54 (b(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[40, 7181])).
% 2.35/2.54 tff(7183,plain,
% 2.35/2.54 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[5847, 7182, 95, 2, 330])).
% 2.35/2.54 tff(7184,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7185,plain,
% 2.35/2.54 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7186,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.54 inference(monotonicity,[status(thm)],[7185])).
% 2.35/2.54 tff(7187,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.54 inference(transitivity,[status(thm)],[7186, 7184])).
% 2.35/2.54 tff(7188,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 2.35/2.54 inference(quant_inst,[status(thm)],[])).
% 2.35/2.54 tff(7189,plain,
% 2.35/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.54 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 2.35/2.54 tff(7190,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7189, 163, 406, 151, 3693, 32])).
% 2.35/2.54 tff(7191,plain,(b(z, s(s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7192,plain,
% 2.35/2.54 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7191, 4935, 7128, 7183, 95])).
% 2.35/2.54 tff(7193,plain,
% 2.35/2.54 (~b(s(s(z)), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[356, 7192, 348, 330])).
% 2.35/2.54 tff(7194,plain,
% 2.35/2.54 (r(s(s(z)), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[345, 7193])).
% 2.35/2.54 tff(7195,plain,
% 2.35/2.54 (~r(s(s(z)), s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7140, 4935, 7128, 7194])).
% 2.35/2.54 tff(7196,plain,
% 2.35/2.54 (b(s(s(z)), s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[487, 7195])).
% 2.35/2.54 tff(7197,plain,
% 2.35/2.54 (~b(s(s(z)), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7058, 7196, 5927, 95, 348, 2, 330])).
% 2.35/2.54 tff(7198,plain,
% 2.35/2.54 (r(s(s(z)), elem!1)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2139, 7197, 6635])).
% 2.35/2.54 tff(7199,plain,
% 2.35/2.54 (~r(elem!1, z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[6761, 7198, 4935, 7194])).
% 2.35/2.54 tff(7200,plain,
% 2.35/2.54 (b(elem!1, z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[187, 7199, 76])).
% 2.35/2.54 tff(7201,plain,
% 2.35/2.54 ($false),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[2275, 198, 95, 7200, 5927, 7182])).
% 2.35/2.54 tff(7202,plain,(b(z, s(z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (s(elem!1) = s(z)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.54 tff(7203,plain,
% 2.35/2.54 (b(z, s(z))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7202, 330, 5927, 76, 348, 2, 95, 153, 820, 5011])).
% 2.35/2.54 tff(7204,plain,
% 2.35/2.54 (~b(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[4953, 7203, 2, 330])).
% 2.35/2.54 tff(7205,plain,
% 2.35/2.54 (r(s(z), z)),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[40, 7204])).
% 2.35/2.54 tff(7206,plain,
% 2.35/2.54 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[7100, 7203, 330])).
% 2.35/2.54 tff(7207,plain,
% 2.35/2.54 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.54 inference(unit_resolution,[status(thm)],[31, 7206])).
% 2.35/2.54 tff(7208,plain,
% 2.35/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7209,plain,
% 2.35/2.54 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.54 inference(rewrite,[status(thm)],[])).
% 2.35/2.54 tff(7210,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7209])).
% 2.35/2.55 tff(7211,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7210, 7208])).
% 2.35/2.55 tff(7212,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7213,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 2.35/2.55 tff(7214,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7213, 163, 150, 151, 33, 423])).
% 2.35/2.55 tff(7215,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7216,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7215, 7205, 7128, 7207])).
% 2.35/2.55 tff(7217,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[420, 7216])).
% 2.35/2.55 tff(7218,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[4647, 198, 595, 407, 3745, 2, 330])).
% 2.35/2.55 tff(7219,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7220,plain,
% 2.35/2.55 (~b(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7219, 7203, 7217, 2, 330])).
% 2.35/2.55 tff(7221,plain,
% 2.35/2.55 (r(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[403, 7220])).
% 2.35/2.55 tff(7222,plain,
% 2.35/2.55 (~r(s(s(z)), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[340, 7221, 7205, 153])).
% 2.35/2.55 tff(7223,plain,
% 2.35/2.55 (b(s(s(z)), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[345, 7222])).
% 2.35/2.55 tff(7224,plain,
% 2.35/2.55 (~r(s(s(z)), elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7062, 7221, 7205, 153])).
% 2.35/2.55 tff(7225,plain,
% 2.35/2.55 (b(s(s(z)), elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[2139, 7224, 6635])).
% 2.35/2.55 tff(7226,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7113, 198, 95, 7225, 348, 7223, 330])).
% 2.35/2.55 tff(7227,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (elem!1 = z) | (s(elem!1) = s(z)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7228,plain,
% 2.35/2.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7227, 7180, 95, 153, 2, 5927, 76, 820, 5011])).
% 2.35/2.55 tff(7229,plain,
% 2.35/2.55 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[374, 7228])).
% 2.35/2.55 tff(7230,plain,
% 2.35/2.55 (~r(s(z), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7092, 4598, 153, 2, 95, 5927, 7180, 820, 5011, 76])).
% 2.35/2.55 tff(7231,plain,
% 2.35/2.55 (b(s(z), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[40, 7230])).
% 2.35/2.55 tff(7232,plain,
% 2.35/2.55 (~b(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5819, 7231, 2, 7128, 153, 7229])).
% 2.35/2.55 tff(7233,plain,
% 2.35/2.55 (~r(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7157, 7231, 153, 95, 5927, 4935, 7128])).
% 2.35/2.55 tff(7234,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[487, 7233, 7232])).
% 2.35/2.55 tff(7235,plain,(b(z, s(z)) | (~r(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7236,plain,
% 2.35/2.55 (b(z, s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7235, 6508, 55, 5926, 2, 6510, 6509, 6507])).
% 2.35/2.55 tff(7237,plain,
% 2.35/2.55 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7126, 5926, 2, 55, 6508, 6510, 6509, 6507])).
% 2.35/2.55 tff(7238,plain,
% 2.35/2.55 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3613, 7237])).
% 2.35/2.55 tff(7239,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7178, 6508, 5926, 6507, 55, 2, 6509, 7238])).
% 2.35/2.55 tff(7240,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[176, 7239])).
% 2.35/2.55 tff(7241,plain,
% 2.35/2.55 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[6526, 198, 6508, 5926, 2])).
% 2.35/2.55 tff(7242,plain,
% 2.35/2.55 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7241, 7236])).
% 2.35/2.55 tff(7243,plain,
% 2.35/2.55 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[31, 7242])).
% 2.35/2.55 tff(7244,plain,
% 2.35/2.55 (~b(s(z), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[4953, 7236, 2, 7240])).
% 2.35/2.55 tff(7245,plain,
% 2.35/2.55 (r(s(z), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[40, 7244])).
% 2.35/2.55 tff(7246,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7215, 7245, 7238, 7243])).
% 2.35/2.55 tff(7247,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[420, 7246])).
% 2.35/2.55 tff(7248,plain,
% 2.35/2.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7227, 7240, 6508, 55, 2, 5926, 6507, 6510, 6509])).
% 2.35/2.55 tff(7249,plain,
% 2.35/2.55 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[374, 7248])).
% 2.35/2.55 tff(7250,plain,
% 2.35/2.55 (~r(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3712, 7245, 55, 7249])).
% 2.35/2.55 tff(7251,plain,
% 2.35/2.55 (b(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[403, 7250])).
% 2.35/2.55 tff(7252,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7219, 7251, 7247, 7240, 2, 7236])).
% 2.35/2.55 tff(7253,plain,(r(z, elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7254,plain,
% 2.35/2.55 (r(z, elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7253, 42, 2])).
% 2.35/2.55 tff(7255,assumption,(~r(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.35/2.55 tff(7256,plain,
% 2.35/2.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[31, 7255])).
% 2.35/2.55 tff(7257,plain,
% 2.35/2.55 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, elem!1)),
% 2.35/2.55 inference(monotonicity,[status(thm)],[245])).
% 2.35/2.55 tff(7258,plain,
% 2.35/2.55 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(symmetry,[status(thm)],[7257])).
% 2.35/2.55 tff(7259,plain,
% 2.35/2.55 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[1475, 7258])).
% 2.35/2.55 tff(7260,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7255, 7259])).
% 2.35/2.55 tff(7261,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | r(z, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7262,plain,
% 2.35/2.55 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7261, 7255, 1475])).
% 2.35/2.55 tff(7263,plain,
% 2.35/2.55 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[171, 152, 153, 150])).
% 2.35/2.55 tff(7264,plain,
% 2.35/2.55 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3613, 7263])).
% 2.35/2.55 tff(7265,plain,
% 2.35/2.55 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3626, 560, 2, 3615])).
% 2.35/2.55 tff(7266,plain,
% 2.35/2.55 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[374, 7265])).
% 2.35/2.55 tff(7267,plain,
% 2.35/2.55 (~b(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3753, 560, 3745, 2])).
% 2.35/2.55 tff(7268,plain,
% 2.35/2.55 (r(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[403, 7267])).
% 2.35/2.55 tff(7269,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5923, 163, 406, 7268, 153, 7266])).
% 2.35/2.55 tff(7270,plain,((~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(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(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7271,plain,
% 2.35/2.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7270, 7264, 153, 406, 2, 6639])).
% 2.35/2.55 tff(7272,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[6516, 7264, 152, 153, 2])).
% 2.35/2.55 tff(7273,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[420, 7272, 7271])).
% 2.35/2.55 tff(7274,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7275,plain,
% 2.35/2.55 (~r(z, s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7274, 152, 2, 153, 150])).
% 2.35/2.55 tff(7276,plain,
% 2.35/2.55 (b(z, s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[593, 7275])).
% 2.35/2.55 tff(7277,plain,
% 2.35/2.55 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7278,plain,
% 2.35/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7277])).
% 2.35/2.55 tff(7279,plain,
% 2.35/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7278, 3664])).
% 2.35/2.55 tff(7280,plain,
% 2.35/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7281,plain,
% 2.35/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7280, 7279])).
% 2.35/2.55 tff(7282,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7281, 198, 7276, 7264, 331, 2])).
% 2.35/2.55 tff(7283,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7284,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7283, 331, 2, 153, 150])).
% 2.35/2.55 tff(7285,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[176, 7284])).
% 2.35/2.55 tff(7286,plain,
% 2.35/2.55 (r(z, elem!1) <=> r(elem!1, elem!1)),
% 2.35/2.55 inference(monotonicity,[status(thm)],[57])).
% 2.35/2.55 tff(7287,plain,
% 2.35/2.55 (r(elem!1, elem!1) <=> r(z, elem!1)),
% 2.35/2.55 inference(symmetry,[status(thm)],[7286])).
% 2.35/2.55 tff(7288,plain,
% 2.35/2.55 ((~r(elem!1, elem!1)) <=> (~r(z, elem!1))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7287])).
% 2.35/2.55 tff(7289,plain,
% 2.35/2.55 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 2.35/2.55 inference(bind,[status(th)],[])).
% 2.35/2.55 tff(7290,plain,
% 2.35/2.55 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.35/2.55 inference(quant_intro,[status(thm)],[7289])).
% 2.35/2.55 tff(7291,plain,
% 2.35/2.55 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7292,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 2.35/2.55 tff(7293,plain,
% 2.35/2.55 (![X: $i] : (~r(X, X))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7292, 7291])).
% 2.35/2.55 tff(7294,plain,(
% 2.35/2.55 ![X: $i] : (~r(X, X))),
% 2.35/2.55 inference(skolemize,[status(sab)],[7293])).
% 2.35/2.55 tff(7295,plain,
% 2.35/2.55 (![X: $i] : (~r(X, X))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7294, 7290])).
% 2.35/2.55 tff(7296,plain,
% 2.35/2.55 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7297,plain,
% 2.35/2.55 (~r(elem!1, elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7296, 7295])).
% 2.35/2.55 tff(7298,plain,
% 2.35/2.55 (~r(z, elem!1)),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7297, 7288])).
% 2.35/2.55 tff(7299,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[1475, 7298])).
% 2.35/2.55 tff(7300,plain,((~(z = elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7301,plain,
% 2.35/2.55 (~(z = elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7300, 1475])).
% 2.35/2.55 tff(7302,plain,
% 2.35/2.55 (~(elem!1 = z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[1079, 7301])).
% 2.35/2.55 tff(7303,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7304,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7305,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7304, 7303])).
% 2.35/2.55 tff(7306,plain,
% 2.35/2.55 ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7305, 163])).
% 2.35/2.55 tff(7307,plain,
% 2.35/2.55 (~r(s(z), elem!1)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7306, 833, 1475, 150])).
% 2.35/2.55 tff(7308,plain,
% 2.35/2.55 (s(z) = elem!1),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[217, 7307, 149])).
% 2.35/2.55 tff(7309,plain,
% 2.35/2.55 (s(s(z)) = s(elem!1)),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.55 tff(7310,plain,
% 2.35/2.55 (s(elem!1) = s(s(z))),
% 2.35/2.55 inference(symmetry,[status(thm)],[7309])).
% 2.35/2.55 tff(7311,plain,
% 2.35/2.55 (r(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7310])).
% 2.35/2.55 tff(7312,plain,
% 2.35/2.55 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.35/2.55 inference(symmetry,[status(thm)],[7311])).
% 2.35/2.55 tff(7313,plain,
% 2.35/2.55 (r(z, s(z)) <=> r(z, elem!1)),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.55 tff(7314,plain,
% 2.35/2.55 (r(z, elem!1) <=> r(z, s(z))),
% 2.35/2.55 inference(symmetry,[status(thm)],[7313])).
% 2.35/2.55 tff(7315,plain,
% 2.35/2.55 (r(z, s(z))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[1475, 7314])).
% 2.35/2.55 tff(7316,plain,
% 2.35/2.55 (~r(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[6539, 7315, 150, 153])).
% 2.35/2.55 tff(7317,plain,
% 2.35/2.55 (b(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[487, 7316])).
% 2.35/2.55 tff(7318,plain,
% 2.35/2.55 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.55 tff(7319,plain,
% 2.35/2.55 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7318, 113])).
% 2.35/2.55 tff(7320,plain,
% 2.35/2.55 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7319])).
% 2.35/2.55 tff(7321,plain,
% 2.35/2.55 (~(elem!1 = s(s(elem!1)))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[620, 7320])).
% 2.35/2.55 tff(7322,plain,
% 2.35/2.55 (r(z, s(z))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[1475, 1106])).
% 2.35/2.55 tff(7323,plain,
% 2.35/2.55 (~r(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[6539, 7322, 150, 153])).
% 2.35/2.55 tff(7324,plain,
% 2.35/2.55 (b(s(s(z)), s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[487, 7323])).
% 2.35/2.55 tff(7325,plain,
% 2.35/2.55 (~r(s(s(elem!1)), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[1823, 405, 1475, 833])).
% 2.35/2.55 tff(7326,plain,
% 2.35/2.55 (b(s(s(elem!1)), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[801, 7325])).
% 2.35/2.55 tff(7327,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7328,plain,
% 2.35/2.55 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7329,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7328])).
% 2.35/2.55 tff(7330,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7329, 7327])).
% 2.35/2.55 tff(7331,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7332,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7331, 7330])).
% 2.35/2.55 tff(7333,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7332, 163, 791, 150, 151, 152])).
% 2.35/2.55 tff(7334,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7335,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7334, 151, 842, 150])).
% 2.35/2.55 tff(7336,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[176, 7335])).
% 2.35/2.55 tff(7337,plain,
% 2.35/2.55 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[423, 828])).
% 2.35/2.55 tff(7338,plain,
% 2.35/2.55 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[2841])).
% 2.35/2.55 tff(7339,plain,
% 2.35/2.55 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.35/2.55 inference(transitivity,[status(thm)],[276, 7338, 134])).
% 2.35/2.55 tff(7340,plain,
% 2.35/2.55 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7339])).
% 2.35/2.55 tff(7341,plain,
% 2.35/2.55 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.35/2.55 inference(symmetry,[status(thm)],[5022])).
% 2.35/2.55 tff(7342,plain,
% 2.35/2.55 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7341])).
% 2.35/2.55 tff(7343,plain,
% 2.35/2.55 (s(s(s(s(elem!1)))) = elem!1),
% 2.35/2.55 inference(transitivity,[status(thm)],[7342, 281, 7340, 129])).
% 2.35/2.55 tff(7344,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5032, 7343])).
% 2.35/2.55 tff(7345,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7346,plain,
% 2.35/2.55 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7345, 206])).
% 2.35/2.55 tff(7347,plain,
% 2.35/2.55 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7215, 423, 150, 151])).
% 2.35/2.55 tff(7348,plain,
% 2.35/2.55 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[31, 7347])).
% 2.35/2.55 tff(7349,plain,
% 2.35/2.55 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[2877, 198, 723, 7348, 330])).
% 2.35/2.55 tff(7350,plain,
% 2.35/2.55 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[934, 26, 7349, 7346])).
% 2.35/2.55 tff(7351,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7352,plain,
% 2.35/2.55 (((~r(s(s(s(s(s(s(s(z))))))), s(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))))))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7353,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(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))))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7352])).
% 2.35/2.55 tff(7354,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(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))))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(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))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7353, 7351])).
% 2.35/2.55 tff(7355,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(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))))))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7356,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7355, 7354])).
% 2.35/2.55 tff(7357,plain,
% 2.35/2.55 ($false),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7356, 163, 405, 2836, 7350, 7337])).
% 2.35/2.55 tff(7358,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.55 tff(7359,plain,
% 2.35/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[7358, 7336, 206, 7326, 405, 150, 151])).
% 2.35/2.55 tff(7360,plain,
% 2.35/2.55 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[420, 7359])).
% 2.35/2.55 tff(7361,plain,
% 2.35/2.55 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[6545, 7360, 2, 153, 150, 7322])).
% 2.35/2.55 tff(7362,plain,
% 2.35/2.55 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[374, 7361])).
% 2.35/2.55 tff(7363,plain,
% 2.35/2.55 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7362, 5124])).
% 2.35/2.55 tff(7364,plain,
% 2.35/2.55 (~(s(elem!1) = s(z))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[814, 7301])).
% 2.35/2.55 tff(7365,plain,
% 2.35/2.55 (~(s(s(z)) = s(s(elem!1)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[822, 7364])).
% 2.35/2.55 tff(7366,plain,
% 2.35/2.55 (~(s(elem!1) = s(s(elem!1)))),
% 2.35/2.55 inference(modus_ponens,[status(thm)],[7365, 5225])).
% 2.35/2.55 tff(7367,plain,
% 2.35/2.55 (~b(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[3753, 7360, 7324, 2])).
% 2.35/2.55 tff(7368,plain,
% 2.35/2.55 (r(s(z), s(s(z)))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[403, 7367])).
% 2.35/2.55 tff(7369,plain,
% 2.35/2.55 (r(elem!1, s(elem!1))),
% 2.35/2.55 inference(unit_resolution,[status(thm)],[5075, 7368, 2915])).
% 2.35/2.55 tff(7370,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7371,plain,
% 2.35/2.55 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.35/2.55 inference(rewrite,[status(thm)],[])).
% 2.35/2.55 tff(7372,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 2.35/2.55 inference(monotonicity,[status(thm)],[7371])).
% 2.35/2.55 tff(7373,plain,
% 2.35/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.35/2.55 inference(transitivity,[status(thm)],[7372, 7370])).
% 2.35/2.55 tff(7374,plain,
% 2.35/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 2.35/2.55 inference(quant_inst,[status(thm)],[])).
% 2.35/2.55 tff(7375,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7374, 7373])).
% 2.35/2.56 tff(7376,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7375, 163, 1475, 791, 1473, 1220])).
% 2.35/2.56 tff(7377,plain,((~r(z, s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7378,plain,
% 2.35/2.56 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7377, 7369, 1475, 842])).
% 2.35/2.56 tff(7379,plain,
% 2.35/2.56 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[901, 7378, 7366])).
% 2.35/2.56 tff(7380,plain,
% 2.35/2.56 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[5021, 825])).
% 2.35/2.56 tff(7381,plain,
% 2.35/2.56 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.35/2.56 inference(symmetry,[status(thm)],[7380])).
% 2.35/2.56 tff(7382,plain,
% 2.35/2.56 (~(s(s(elem!1)) = s(elem!1))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[2154, 5179])).
% 2.35/2.56 tff(7383,plain,
% 2.35/2.56 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.35/2.56 inference(symmetry,[status(thm)],[1272])).
% 2.35/2.56 tff(7384,plain,
% 2.35/2.56 (r(s(z), s(s(elem!1)))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[405, 7383])).
% 2.35/2.56 tff(7385,plain,
% 2.35/2.56 (~b(s(z), s(s(z)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[3753, 3745, 6639, 2])).
% 2.35/2.56 tff(7386,plain,
% 2.35/2.56 (r(s(z), s(s(z)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[403, 7385])).
% 2.35/2.56 tff(7387,plain,
% 2.35/2.56 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7388,plain,
% 2.35/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7387])).
% 2.35/2.56 tff(7389,plain,
% 2.35/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7388, 4034])).
% 2.35/2.56 tff(7390,plain,
% 2.35/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7391,plain,
% 2.35/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7390, 7389])).
% 2.35/2.56 tff(7392,plain,
% 2.35/2.56 (~b(s(s(z)), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7391, 198, 723, 83, 346])).
% 2.35/2.56 tff(7393,plain,
% 2.35/2.56 (r(s(s(z)), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[2161, 26, 2154, 7392])).
% 2.35/2.56 tff(7394,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7395,plain,
% 2.35/2.56 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7396,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7395])).
% 2.35/2.56 tff(7397,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7396, 7394])).
% 2.35/2.56 tff(7398,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7399,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7398, 7397])).
% 2.35/2.56 tff(7400,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7399, 163, 406, 7393, 328, 153])).
% 2.35/2.56 tff(7401,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7402,plain,
% 2.35/2.56 (~b(z, s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7401, 7386, 153, 150, 2154, 406, 723])).
% 2.35/2.56 tff(7403,plain,
% 2.35/2.56 (r(z, s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[1096, 7402])).
% 2.35/2.56 tff(7404,plain,
% 2.35/2.56 (~r(s(s(elem!1)), elem!1)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[1123, 7403, 833, 405])).
% 2.35/2.56 tff(7405,plain,
% 2.35/2.56 (b(s(s(elem!1)), elem!1)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[602, 7404, 978])).
% 2.35/2.56 tff(7406,plain,
% 2.35/2.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[2989, 198, 7405, 1328, 2834, 5123])).
% 2.35/2.56 tff(7407,plain,
% 2.35/2.56 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[945, 7406, 7346, 7384, 151])).
% 2.35/2.56 tff(7408,plain,
% 2.35/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7409,plain,
% 2.35/2.56 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~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(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(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7410,plain,
% 2.35/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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)))))))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7409])).
% 2.35/2.56 tff(7411,plain,
% 2.35/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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))))))))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7410, 7408])).
% 2.35/2.56 tff(7412,plain,
% 2.35/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7413,plain,
% 2.35/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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)))))))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7412, 7411])).
% 2.35/2.56 tff(7414,plain,
% 2.35/2.56 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7413, 198, 723, 7336, 4703])).
% 2.35/2.56 tff(7415,plain,
% 2.35/2.56 (~b(s(s(elem!1)), s(elem!1))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7414, 7407])).
% 2.35/2.56 tff(7416,plain,
% 2.35/2.56 (r(s(s(elem!1)), s(elem!1))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[1143, 7415, 7382])).
% 2.35/2.56 tff(7417,plain,
% 2.35/2.56 (r(s(s(s(z))), s(s(z)))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7416, 7381])).
% 2.35/2.56 tff(7418,plain,
% 2.35/2.56 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[206, 5021])).
% 2.35/2.56 tff(7419,plain,
% 2.35/2.56 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.35/2.56 inference(symmetry,[status(thm)],[7418])).
% 2.35/2.56 tff(7420,plain,
% 2.35/2.56 (r(s(z), s(s(s(z))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[405, 7419])).
% 2.35/2.56 tff(7421,plain,
% 2.35/2.56 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[2441])).
% 2.35/2.56 tff(7422,plain,
% 2.35/2.56 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.35/2.56 inference(symmetry,[status(thm)],[7421])).
% 2.35/2.56 tff(7423,plain,
% 2.35/2.56 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7422])).
% 2.35/2.56 tff(7424,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 2.35/2.56 tff(7425,plain,
% 2.35/2.56 (~r(z, s(s(elem!1)))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7424, 7423])).
% 2.35/2.56 tff(7426,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[1098, 7425])).
% 2.35/2.56 tff(7427,plain,(r(z, s(s(s(z)))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7428,plain,
% 2.35/2.56 (r(z, s(s(s(z))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7427, 7403, 2915])).
% 2.35/2.56 tff(7429,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 2.35/2.56 tff(7430,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.35/2.56 tff(7431,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7432,plain,
% 2.35/2.56 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7433,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7432])).
% 2.35/2.56 tff(7434,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7433, 7431])).
% 2.35/2.56 tff(7435,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7436,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7435, 7434])).
% 2.35/2.56 tff(7437,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7436, 163, 406, 7430, 2666, 7429])).
% 2.35/2.56 tff(7438,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7439,plain,
% 2.35/2.56 (~r(s(s(s(z))), s(s(z)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7438, 7428, 406, 7420])).
% 2.35/2.56 tff(7440,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7439, 7417])).
% 2.35/2.56 tff(7441,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7442,plain,
% 2.35/2.56 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7441, 7379, 7326, 7360, 151, 206, 7322, 833, 405, 153, 150, 7365, 2])).
% 2.35/2.56 tff(7443,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7442, 7363])).
% 2.35/2.56 tff(7444,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7445,plain,
% 2.35/2.56 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7444, 405, 833, 206, 153, 150, 2, 1475])).
% 2.35/2.56 tff(7446,plain,
% 2.35/2.56 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[3613, 7445])).
% 2.35/2.56 tff(7447,plain,
% 2.35/2.56 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[3626, 7446, 2, 7324])).
% 2.35/2.56 tff(7448,plain,
% 2.35/2.56 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[374, 7447])).
% 2.35/2.56 tff(7449,plain,
% 2.35/2.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7270, 7446, 153, 7322, 2, 7324])).
% 2.35/2.56 tff(7450,plain,
% 2.35/2.56 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[420, 7449])).
% 2.35/2.56 tff(7451,plain,
% 2.35/2.56 ($false),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[5817, 163, 153, 3272, 33, 423])).
% 2.35/2.56 tff(7452,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.56 tff(7453,plain,
% 2.35/2.56 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7452, 7450, 7448, 153])).
% 2.35/2.56 tff(7454,plain,
% 2.35/2.56 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[31, 7453])).
% 2.35/2.56 tff(7455,plain,
% 2.35/2.56 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[6516, 7450, 7446, 153, 2])).
% 2.35/2.56 tff(7456,plain,
% 2.35/2.56 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[176, 7455])).
% 2.35/2.56 tff(7457,plain,
% 2.35/2.56 (~r(s(s(s(s(s(z))))), z)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[6822, 7448, 150, 7324, 153])).
% 2.35/2.56 tff(7458,plain,
% 2.35/2.56 (b(s(s(s(s(s(z))))), z)),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[3841, 7457])).
% 2.35/2.56 tff(7459,plain,
% 2.35/2.56 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[4174, 7458, 7456, 7454])).
% 2.35/2.56 tff(7460,plain,
% 2.35/2.56 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[3098, 7459])).
% 2.35/2.56 tff(7461,plain,
% 2.35/2.56 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7460, 5096])).
% 2.35/2.56 tff(7462,plain,
% 2.35/2.56 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7450, 828])).
% 2.35/2.56 tff(7463,plain,
% 2.35/2.56 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[2877, 198, 7326, 7454, 7456])).
% 2.35/2.56 tff(7464,plain,
% 2.35/2.56 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[934, 26, 7463, 7346])).
% 2.35/2.56 tff(7465,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7466,plain,
% 2.35/2.56 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))) | (~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(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7467,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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)))))))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7466])).
% 2.35/2.56 tff(7468,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7467, 7465])).
% 2.35/2.56 tff(7469,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7470,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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)))))))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7469, 7468])).
% 2.35/2.56 tff(7471,plain,
% 2.35/2.56 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7470, 163, 7464, 7462, 7461])).
% 2.35/2.56 tff(7472,plain,
% 2.35/2.56 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[2654, 7471, 5094])).
% 2.35/2.56 tff(7473,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7474,plain,
% 2.35/2.56 (((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7475,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7474])).
% 2.35/2.56 tff(7476,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7475, 7473])).
% 2.35/2.56 tff(7477,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7478,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7477, 7476])).
% 2.35/2.56 tff(7479,plain,
% 2.35/2.56 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[7478, 163, 7464, 7462, 7461])).
% 2.35/2.56 tff(7480,plain,
% 2.35/2.56 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.35/2.56 inference(unit_resolution,[status(thm)],[5274, 7479, 5093])).
% 2.35/2.56 tff(7481,plain,
% 2.35/2.56 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[825])).
% 2.35/2.56 tff(7482,plain,
% 2.35/2.56 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.56 inference(modus_ponens,[status(thm)],[7448, 7481])).
% 2.35/2.56 tff(7483,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7484,plain,
% 2.35/2.56 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.56 inference(rewrite,[status(thm)],[])).
% 2.35/2.56 tff(7485,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.56 inference(monotonicity,[status(thm)],[7484])).
% 2.35/2.56 tff(7486,plain,
% 2.35/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.56 inference(transitivity,[status(thm)],[7485, 7483])).
% 2.35/2.56 tff(7487,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.35/2.56 inference(quant_inst,[status(thm)],[])).
% 2.35/2.56 tff(7488,plain,
% 2.35/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 2.35/2.57 tff(7489,plain,
% 2.35/2.57 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7488, 163, 7464, 7482, 7462])).
% 2.35/2.57 tff(7490,plain,
% 2.35/2.57 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[901, 7489, 7366])).
% 2.35/2.57 tff(7491,plain,
% 2.35/2.57 (~(s(s(elem!1)) = s(elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7365, 5179])).
% 2.35/2.57 tff(7492,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7493,plain,
% 2.35/2.57 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7494,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7493])).
% 2.35/2.57 tff(7495,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7494, 7492])).
% 2.35/2.57 tff(7496,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.35/2.57 inference(quant_inst,[status(thm)],[])).
% 2.35/2.57 tff(7497,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7496, 7495])).
% 2.35/2.57 tff(7498,plain,
% 2.35/2.57 (~r(s(s(elem!1)), s(elem!1))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7497, 163, 7464, 7482, 7462])).
% 2.35/2.57 tff(7499,plain,
% 2.35/2.57 (b(s(s(elem!1)), s(elem!1))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[1143, 7498, 7491])).
% 2.35/2.57 tff(7500,plain,
% 2.35/2.57 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[5326, 198, 7499, 7490, 7480, 7472])).
% 2.35/2.57 tff(7501,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7502,plain,
% 2.35/2.57 (((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7503,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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)))))))))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7502])).
% 2.35/2.57 tff(7504,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7503, 7501])).
% 2.35/2.57 tff(7505,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.35/2.57 inference(quant_inst,[status(thm)],[])).
% 2.35/2.57 tff(7506,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7505, 7504])).
% 2.35/2.57 tff(7507,plain,
% 2.35/2.57 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7506, 163, 7482])).
% 2.35/2.57 tff(7508,plain,
% 2.35/2.57 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7507, 7462, 7461])).
% 2.35/2.57 tff(7509,plain,
% 2.35/2.57 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[5089, 26, 7508])).
% 2.35/2.57 tff(7510,plain,
% 2.35/2.57 ($false),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7509, 7500, 5029])).
% 2.35/2.57 tff(7511,plain,((~r(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.57 tff(7512,plain,
% 2.35/2.57 (~r(elem!1, s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7511, 7308, 153, 2, 150, 833, 1475])).
% 2.35/2.57 tff(7513,plain,
% 2.35/2.57 (b(elem!1, s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[147, 7512, 7321])).
% 2.35/2.57 tff(7514,plain,
% 2.35/2.57 (~(s(elem!1) = elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[778, 7308, 7301])).
% 2.35/2.57 tff(7515,plain,
% 2.35/2.57 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7309])).
% 2.35/2.57 tff(7516,plain,
% 2.35/2.57 (r(z, s(elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[153, 7515])).
% 2.35/2.57 tff(7517,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7518,plain,
% 2.35/2.57 (((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7519,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7518])).
% 2.35/2.57 tff(7520,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7519, 7517])).
% 2.35/2.57 tff(7521,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 2.35/2.57 inference(quant_inst,[status(thm)],[])).
% 2.35/2.57 tff(7522,plain,
% 2.35/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7521, 7520])).
% 2.35/2.57 tff(7523,plain,
% 2.35/2.57 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, z))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7522, 163])).
% 2.35/2.57 tff(7524,plain,
% 2.35/2.57 (~r(s(elem!1), elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7523, 7516, 1475, 833])).
% 2.35/2.57 tff(7525,plain,
% 2.35/2.57 (b(s(elem!1), elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[856, 7524, 7514])).
% 2.35/2.57 tff(7526,plain,
% 2.35/2.57 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7318])).
% 2.35/2.57 tff(7527,plain,
% 2.35/2.57 (~(s(s(elem!1)) = elem!1)),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[620, 7526])).
% 2.35/2.57 tff(7528,plain,
% 2.35/2.57 (elem!1 = s(z)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[2914, 7308])).
% 2.35/2.57 tff(7529,plain,
% 2.35/2.57 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7309])).
% 2.35/2.57 tff(7530,plain,
% 2.35/2.57 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7529, 803])).
% 2.35/2.57 tff(7531,plain,
% 2.35/2.57 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7530, 804])).
% 2.35/2.57 tff(7532,plain,
% 2.35/2.57 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7531])).
% 2.35/2.57 tff(7533,plain,
% 2.35/2.57 (~(s(elem!1) = s(s(elem!1)))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7365, 7532])).
% 2.35/2.57 tff(7534,plain,
% 2.35/2.57 (~b(s(z), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[3739, 790, 150, 153, 7365, 406, 6639])).
% 2.35/2.57 tff(7535,plain,
% 2.35/2.57 (r(s(z), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[403, 7534])).
% 2.35/2.57 tff(7536,plain,
% 2.35/2.57 (r(elem!1, s(elem!1))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[5075, 7535, 229])).
% 2.35/2.57 tff(7537,plain,
% 2.35/2.57 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7377, 7536, 1475, 791])).
% 2.35/2.57 tff(7538,plain,
% 2.35/2.57 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[901, 7537, 890])).
% 2.35/2.57 tff(7539,plain,
% 2.35/2.57 (~r(s(s(elem!1)), elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[2858, 790, 833, 791])).
% 2.35/2.57 tff(7540,plain,
% 2.35/2.57 (b(s(s(elem!1)), elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[602, 7539, 138])).
% 2.35/2.57 tff(7541,plain,
% 2.35/2.57 ($false),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[1470, 198, 7540, 7538, 1200, 68])).
% 2.35/2.57 tff(7542,plain,((~r(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~(elem!1 = s(z))) | (s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.57 tff(7543,plain,
% 2.35/2.57 (~r(s(s(elem!1)), z)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7542, 7525, 7513, 7533, 1475, 7516, 7528, 7527, 833, 150, 153, 7315])).
% 2.35/2.57 tff(7544,plain,
% 2.35/2.57 (b(s(s(elem!1)), z)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[801, 7543])).
% 2.35/2.57 tff(7545,plain,
% 2.35/2.57 (r(elem!1, s(elem!1))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[5075, 328, 2915])).
% 2.35/2.57 tff(7546,plain,
% 2.35/2.57 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7377, 7545, 1475, 842])).
% 2.35/2.57 tff(7547,plain,
% 2.35/2.57 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[901, 7546, 7366])).
% 2.35/2.57 tff(7548,plain,
% 2.35/2.57 (b(s(elem!1), z)),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[346, 832])).
% 2.35/2.57 tff(7549,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7550,plain,
% 2.35/2.57 (((~b(s(s(elem!1)), z)) | (~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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), 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)) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7551,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7550])).
% 2.35/2.57 tff(7552,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7551, 7549])).
% 2.35/2.57 tff(7553,plain,
% 2.35/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.35/2.57 inference(quant_inst,[status(thm)],[])).
% 2.35/2.57 tff(7554,plain,
% 2.35/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7553, 7552])).
% 2.35/2.57 tff(7555,plain,
% 2.35/2.57 ($false),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7554, 198, 7548, 723, 7547, 1200, 68])).
% 2.35/2.57 tff(7556,plain,((~r(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.57 tff(7557,plain,
% 2.35/2.57 (~r(s(z), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7556, 7544, 7525, 7513, 7308, 1475, 150, 153])).
% 2.35/2.57 tff(7558,plain,
% 2.35/2.57 (b(s(z), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[403, 7557])).
% 2.35/2.57 tff(7559,plain,
% 2.35/2.57 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[3753, 7558, 7317, 2])).
% 2.35/2.57 tff(7560,plain,
% 2.35/2.57 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[420, 7559])).
% 2.35/2.57 tff(7561,plain,
% 2.35/2.57 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7560, 7312])).
% 2.35/2.57 tff(7562,plain,
% 2.35/2.57 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7345, 7308])).
% 2.35/2.57 tff(7563,plain,
% 2.35/2.57 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[3249, 7562])).
% 2.35/2.57 tff(7564,plain,
% 2.35/2.57 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7274, 7315, 2, 153, 150])).
% 2.35/2.57 tff(7565,plain,
% 2.35/2.57 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[176, 7564])).
% 2.35/2.57 tff(7566,plain,
% 2.35/2.57 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[2833, 7308, 2])).
% 2.35/2.57 tff(7567,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7568,plain,
% 2.35/2.57 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.57 inference(rewrite,[status(thm)],[])).
% 2.35/2.57 tff(7569,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7568])).
% 2.35/2.57 tff(7570,plain,
% 2.35/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7569, 7567])).
% 2.35/2.57 tff(7571,plain,
% 2.35/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.57 inference(quant_inst,[status(thm)],[])).
% 2.35/2.57 tff(7572,plain,
% 2.35/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7571, 7570])).
% 2.35/2.57 tff(7573,plain,
% 2.35/2.57 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7572, 198, 7544, 7513, 7566, 7565])).
% 2.35/2.57 tff(7574,plain,
% 2.35/2.57 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[4221, 7573, 7563])).
% 2.35/2.57 tff(7575,plain,
% 2.35/2.57 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7530])).
% 2.35/2.57 tff(7576,plain,
% 2.35/2.57 (~(s(s(elem!1)) = s(elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7365, 7575])).
% 2.35/2.57 tff(7577,plain,
% 2.35/2.57 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.57 tff(7578,plain,
% 2.35/2.57 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 2.35/2.57 inference(symmetry,[status(thm)],[7577])).
% 2.35/2.57 tff(7579,plain,
% 2.35/2.57 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7309])).
% 2.35/2.57 tff(7580,plain,
% 2.35/2.57 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.57 tff(7581,plain,
% 2.35/2.57 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 2.35/2.57 inference(transitivity,[status(thm)],[7580, 7579, 7578])).
% 2.35/2.57 tff(7582,plain,
% 2.35/2.57 (b(s(z), s(elem!1))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7558, 7581])).
% 2.35/2.57 tff(7583,plain,
% 2.35/2.57 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.35/2.57 inference(monotonicity,[status(thm)],[7308])).
% 2.35/2.57 tff(7584,plain,
% 2.35/2.57 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.35/2.57 inference(symmetry,[status(thm)],[7583])).
% 2.35/2.57 tff(7585,plain,
% 2.35/2.57 (b(s(z), s(s(elem!1)))),
% 2.35/2.57 inference(modus_ponens,[status(thm)],[7513, 7584])).
% 2.35/2.57 tff(7586,plain,
% 2.35/2.57 ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[908, 163, 791, 1220])).
% 2.35/2.57 tff(7587,plain,
% 2.35/2.57 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[7586, 7337])).
% 2.35/2.57 tff(7588,plain,
% 2.35/2.57 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[31, 7587])).
% 2.35/2.57 tff(7589,plain,
% 2.35/2.57 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[2877, 198, 723, 7588, 330])).
% 2.35/2.57 tff(7590,plain,
% 2.35/2.57 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.57 inference(unit_resolution,[status(thm)],[934, 26, 7589, 7346])).
% 2.35/2.57 tff(7591,plain,
% 2.35/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7592,plain,
% 2.35/2.58 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7593,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.35/2.58 inference(monotonicity,[status(thm)],[7592])).
% 2.35/2.58 tff(7594,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(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)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7593, 7591])).
% 2.35/2.58 tff(7595,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(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(s(s(s(z))))))), s(elem!1))))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7596,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 2.35/2.58 tff(7597,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7596, 163, 1220, 7590, 680, 7337])).
% 2.35/2.58 tff(7598,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7599,plain,
% 2.35/2.58 (~r(s(elem!1), s(s(elem!1)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7598, 7574, 7544, 7565, 7516, 7560, 7308])).
% 2.35/2.58 tff(7600,plain,
% 2.35/2.58 (b(s(elem!1), s(s(elem!1)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[901, 7599, 7533])).
% 2.35/2.58 tff(7601,plain,
% 2.35/2.58 (~b(s(s(elem!1)), s(elem!1))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[1552, 7600, 7585, 7582])).
% 2.35/2.58 tff(7602,plain,
% 2.35/2.58 (r(s(s(elem!1)), s(elem!1))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[1143, 7601, 7576])).
% 2.35/2.58 tff(7603,plain,
% 2.35/2.58 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7580, 7579])).
% 2.35/2.58 tff(7604,plain,
% 2.35/2.58 (b(elem!1, s(elem!1))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7558, 7603])).
% 2.35/2.58 tff(7605,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7606,plain,
% 2.35/2.58 (((~b(s(s(elem!1)), z)) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), 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)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7607,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 2.35/2.58 inference(monotonicity,[status(thm)],[7606])).
% 2.35/2.58 tff(7608,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7607, 7605])).
% 2.35/2.58 tff(7609,plain,
% 2.35/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7610,plain,
% 2.35/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7609, 7608])).
% 2.35/2.58 tff(7611,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7610, 198, 1175, 723, 1328, 1200, 68, 1418])).
% 2.35/2.58 tff(7612,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7613,plain,
% 2.35/2.58 (~b(s(elem!1), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7612, 7600, 7513, 7525, 7544, 7604])).
% 2.35/2.58 tff(7614,plain,
% 2.35/2.58 (r(s(elem!1), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[1217, 7613])).
% 2.35/2.58 tff(7615,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~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)))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7616,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~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)))))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7617,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7616, 7615])).
% 2.35/2.58 tff(7618,plain,
% 2.35/2.58 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7617, 163, 7614, 7602, 7574])).
% 2.35/2.58 tff(7619,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7618, 7561])).
% 2.35/2.58 tff(7620,plain,((~r(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7621,plain,
% 2.35/2.58 (~r(elem!1, z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7620, 149, 1475, 150, 153, 2])).
% 2.35/2.58 tff(7622,plain,
% 2.35/2.58 (b(elem!1, z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[187, 7621, 7302])).
% 2.35/2.58 tff(7623,plain,
% 2.35/2.58 (~(s(z) = elem!1)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[212, 7621, 150])).
% 2.35/2.58 tff(7624,plain,
% 2.35/2.58 (r(s(z), elem!1)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[217, 7623, 149])).
% 2.35/2.58 tff(7625,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7626,plain,
% 2.35/2.58 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7627,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 2.35/2.58 inference(monotonicity,[status(thm)],[7626])).
% 2.35/2.58 tff(7628,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7627, 7625])).
% 2.35/2.58 tff(7629,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7630,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7629, 7628])).
% 2.35/2.58 tff(7631,plain,
% 2.35/2.58 ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7630, 163])).
% 2.35/2.58 tff(7632,plain,
% 2.35/2.58 (~r(elem!1, s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7631, 7624, 1475, 150])).
% 2.35/2.58 tff(7633,plain,
% 2.35/2.58 (~(s(s(z)) = s(elem!1))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[227, 7623])).
% 2.35/2.58 tff(7634,plain,
% 2.35/2.58 (~(elem!1 = s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[234, 7633])).
% 2.35/2.58 tff(7635,plain,
% 2.35/2.58 (b(elem!1, s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[242, 7634, 7632])).
% 2.35/2.58 tff(7636,plain,
% 2.35/2.58 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3689, 7264, 153, 150, 2, 236])).
% 2.35/2.58 tff(7637,plain,
% 2.35/2.58 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[374, 7636])).
% 2.35/2.58 tff(7638,plain,
% 2.35/2.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[4548, 7637, 153, 152])).
% 2.35/2.58 tff(7639,plain,
% 2.35/2.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[31, 7638])).
% 2.35/2.58 tff(7640,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7281, 198, 595, 7264, 7639, 2])).
% 2.35/2.58 tff(7641,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7642,plain,
% 2.35/2.58 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7641, 595, 2, 153, 150, 236])).
% 2.35/2.58 tff(7643,plain,
% 2.35/2.58 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[176, 7642])).
% 2.35/2.58 tff(7644,plain,
% 2.35/2.58 (~b(s(z), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7219, 3745, 595, 2, 330])).
% 2.35/2.58 tff(7645,plain,
% 2.35/2.58 (r(s(z), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[403, 7644])).
% 2.35/2.58 tff(7646,plain,
% 2.35/2.58 (~r(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[340, 7645, 150, 153])).
% 2.35/2.58 tff(7647,plain,
% 2.35/2.58 (b(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[345, 7646])).
% 2.35/2.58 tff(7648,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3961, 198, 595, 7647, 3745, 2, 330])).
% 2.35/2.58 tff(7649,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7650,plain,
% 2.35/2.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7649, 7643, 2, 595, 150, 153])).
% 2.35/2.58 tff(7651,plain,
% 2.35/2.58 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[420, 7650])).
% 2.35/2.58 tff(7652,plain,
% 2.35/2.58 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3689, 3615, 153, 150, 2, 236])).
% 2.35/2.58 tff(7653,plain,
% 2.35/2.58 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[374, 7652])).
% 2.35/2.58 tff(7654,plain,
% 2.35/2.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7452, 7653, 7651, 153])).
% 2.35/2.58 tff(7655,plain,
% 2.35/2.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[31, 7654])).
% 2.35/2.58 tff(7656,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7281, 198, 595, 3615, 7655, 2])).
% 2.35/2.58 tff(7657,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7658,plain,
% 2.35/2.58 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7657, 595, 2, 153, 150, 236])).
% 2.35/2.58 tff(7659,plain,
% 2.35/2.58 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3613, 7658])).
% 2.35/2.58 tff(7660,plain,
% 2.35/2.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7215, 7659, 150, 7651])).
% 2.35/2.58 tff(7661,plain,
% 2.35/2.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[31, 7660])).
% 2.35/2.58 tff(7662,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7663,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7664,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7663, 7662])).
% 2.35/2.58 tff(7665,plain,
% 2.35/2.58 (~r(s(s(elem!1)), s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7664, 163, 1475, 790, 150])).
% 2.35/2.58 tff(7666,plain,
% 2.35/2.58 (b(s(s(elem!1)), s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[626, 7665])).
% 2.35/2.58 tff(7667,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7668,plain,
% 2.35/2.58 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7669,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.58 inference(monotonicity,[status(thm)],[7668])).
% 2.35/2.58 tff(7670,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7669, 7667])).
% 2.35/2.58 tff(7671,plain,
% 2.35/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7672,plain,
% 2.35/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7671, 7670])).
% 2.35/2.58 tff(7673,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7672, 198, 1544, 722, 595, 7264, 7639, 2])).
% 2.35/2.58 tff(7674,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7675,plain,
% 2.35/2.58 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7674, 1053, 7666, 595, 2, 153, 150, 236])).
% 2.35/2.58 tff(7676,plain,
% 2.35/2.58 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[176, 7675])).
% 2.35/2.58 tff(7677,plain,
% 2.35/2.58 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7649, 7676, 2, 595, 150, 153])).
% 2.35/2.58 tff(7678,plain,
% 2.35/2.58 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[420, 7677])).
% 2.35/2.58 tff(7679,plain,
% 2.35/2.58 (~b(z, s(s(elem!1)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[649, 198, 1053, 7666, 595])).
% 2.35/2.58 tff(7680,plain,
% 2.35/2.58 (r(z, s(s(elem!1)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[1096, 7679])).
% 2.35/2.58 tff(7681,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3462, 163, 1098, 150, 3450, 332])).
% 2.35/2.58 tff(7682,plain,((~r(s(s(z)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7683,plain,
% 2.35/2.58 (~r(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7682, 3450, 150, 1098])).
% 2.35/2.58 tff(7684,plain,
% 2.35/2.58 (b(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[345, 7683])).
% 2.35/2.58 tff(7685,plain,
% 2.35/2.58 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3671, 3450, 153, 150, 423, 595])).
% 2.35/2.58 tff(7686,plain,
% 2.35/2.58 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3613, 7685])).
% 2.35/2.58 tff(7687,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7688,plain,
% 2.35/2.58 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7689,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.58 inference(monotonicity,[status(thm)],[7688])).
% 2.35/2.58 tff(7690,plain,
% 2.35/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.58 inference(transitivity,[status(thm)],[7689, 7687])).
% 2.35/2.58 tff(7691,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 2.35/2.58 inference(quant_inst,[status(thm)],[])).
% 2.35/2.58 tff(7692,plain,
% 2.35/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.58 inference(modus_ponens,[status(thm)],[7691, 7690])).
% 2.35/2.58 tff(7693,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7692, 163, 3450, 151, 3272, 423])).
% 2.35/2.58 tff(7694,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7695,plain,
% 2.35/2.58 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7694, 7686, 423, 3450])).
% 2.35/2.58 tff(7696,plain,
% 2.35/2.58 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[374, 7695])).
% 2.35/2.58 tff(7697,plain,
% 2.35/2.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7215, 7686, 150, 423])).
% 2.35/2.58 tff(7698,plain,
% 2.35/2.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[31, 7697])).
% 2.35/2.58 tff(7699,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[356, 7698, 7696, 330, 7684])).
% 2.35/2.58 tff(7700,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7701,plain,
% 2.35/2.58 (~r(s(s(z)), s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7700, 7676, 150, 7678, 7680, 153, 595])).
% 2.35/2.58 tff(7702,plain,
% 2.35/2.58 (b(s(s(z)), s(z))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[487, 7701])).
% 2.35/2.58 tff(7703,plain,
% 2.35/2.58 (~b(s(z), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3500, 7702, 7365, 7666, 153, 1053, 7680])).
% 2.35/2.58 tff(7704,plain,
% 2.35/2.58 (r(s(z), s(s(z)))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[403, 7703])).
% 2.35/2.58 tff(7705,plain,
% 2.35/2.58 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3712, 7704, 153, 150])).
% 2.35/2.58 tff(7706,plain,
% 2.35/2.58 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[374, 7705])).
% 2.35/2.58 tff(7707,plain,
% 2.35/2.58 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3689, 7706, 153, 150, 2, 236])).
% 2.35/2.58 tff(7708,plain,
% 2.35/2.58 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[3613, 7707])).
% 2.35/2.58 tff(7709,plain,
% 2.35/2.58 (~r(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[340, 7704, 150, 153])).
% 2.35/2.58 tff(7710,plain,
% 2.35/2.58 (b(s(s(z)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[345, 7709])).
% 2.35/2.58 tff(7711,plain,
% 2.35/2.58 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[356, 7706, 7676, 7710])).
% 2.35/2.58 tff(7712,plain,
% 2.35/2.58 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[31, 7711])).
% 2.35/2.58 tff(7713,plain,
% 2.35/2.58 ($false),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7215, 7712, 7708, 150, 7678])).
% 2.35/2.58 tff(7714,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.58 tff(7715,plain,
% 2.35/2.58 (~r(s(s(elem!1)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[7714, 595, 153, 2, 236, 150, 1475])).
% 2.35/2.58 tff(7716,plain,
% 2.35/2.58 (b(s(s(elem!1)), z)),
% 2.35/2.58 inference(unit_resolution,[status(thm)],[801, 7715])).
% 2.35/2.58 tff(7717,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7718,plain,
% 2.35/2.58 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.35/2.58 inference(rewrite,[status(thm)],[])).
% 2.35/2.58 tff(7719,plain,
% 2.35/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7718])).
% 2.35/2.59 tff(7720,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7719, 7717])).
% 2.35/2.59 tff(7721,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7722,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7721, 7720])).
% 2.35/2.59 tff(7723,plain,
% 2.35/2.59 (~b(elem!1, s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7722, 198, 271, 7716, 320, 595])).
% 2.35/2.59 tff(7724,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7725,plain,
% 2.35/2.59 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7726,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7725])).
% 2.35/2.59 tff(7727,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7726, 7724])).
% 2.35/2.59 tff(7728,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7729,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7728, 7727])).
% 2.35/2.59 tff(7730,plain,
% 2.35/2.59 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7729, 198, 271, 595, 2])).
% 2.35/2.59 tff(7731,plain,
% 2.35/2.59 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7730, 7643])).
% 2.35/2.59 tff(7732,plain,
% 2.35/2.59 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7261, 7660, 1475])).
% 2.35/2.59 tff(7733,plain,
% 2.35/2.59 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[256, 7732, 7731])).
% 2.35/2.59 tff(7734,plain,
% 2.35/2.59 (~r(elem!1, s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3441, 7733, 236, 7659])).
% 2.35/2.59 tff(7735,plain,
% 2.35/2.59 (elem!1 = s(s(elem!1))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[147, 7734, 7723])).
% 2.35/2.59 tff(7736,plain,
% 2.35/2.59 (s(s(elem!1)) = elem!1),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[676, 7735])).
% 2.35/2.59 tff(7737,plain,
% 2.35/2.59 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.35/2.59 inference(monotonicity,[status(thm)],[114])).
% 2.35/2.59 tff(7738,plain,
% 2.35/2.59 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.35/2.59 inference(symmetry,[status(thm)],[7737])).
% 2.35/2.59 tff(7739,plain,
% 2.35/2.59 (r(z, s(s(elem!1)))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[1475, 7738])).
% 2.35/2.59 tff(7740,plain,
% 2.35/2.59 ($false),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[1091, 7739])).
% 2.35/2.59 tff(7741,plain,((~(s(s(elem!1)) = elem!1)) | r(z, s(s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.59 tff(7742,plain,
% 2.35/2.59 (r(z, s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7741, 7736, 1475])).
% 2.35/2.59 tff(7743,plain,
% 2.35/2.59 (~r(s(s(z)), s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7700, 7742, 150, 7643, 7651, 153, 595])).
% 2.35/2.59 tff(7744,plain,
% 2.35/2.59 (b(s(s(z)), s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[487, 7743])).
% 2.35/2.59 tff(7745,plain,
% 2.35/2.59 (b(s(s(elem!1)), s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[717, 7736, 320])).
% 2.35/2.59 tff(7746,plain,
% 2.35/2.59 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[671, 7735, 7733])).
% 2.35/2.59 tff(7747,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7748,plain,
% 2.35/2.59 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7749,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7748])).
% 2.35/2.59 tff(7750,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7749, 7747])).
% 2.35/2.59 tff(7751,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7752,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7751, 7750])).
% 2.35/2.59 tff(7753,plain,
% 2.35/2.59 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7752, 198, 271, 320, 595, 7643])).
% 2.35/2.59 tff(7754,plain,
% 2.35/2.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3792, 7732])).
% 2.35/2.59 tff(7755,plain,
% 2.35/2.59 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[703, 7754, 7753])).
% 2.35/2.59 tff(7756,plain,
% 2.35/2.59 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[698, 7736, 7755])).
% 2.35/2.59 tff(7757,plain,
% 2.35/2.59 (~r(s(z), s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[690, 7756, 7746, 7659])).
% 2.35/2.59 tff(7758,plain,
% 2.35/2.59 (b(s(z), s(s(elem!1)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[642, 7757])).
% 2.35/2.59 tff(7759,plain,
% 2.35/2.59 (~b(s(z), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3500, 7758, 7365, 7745, 153, 7744, 7742])).
% 2.35/2.59 tff(7760,plain,
% 2.35/2.59 (r(s(z), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[403, 7759])).
% 2.35/2.59 tff(7761,plain,
% 2.35/2.59 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3712, 7760, 153, 150])).
% 2.35/2.59 tff(7762,plain,
% 2.35/2.59 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[374, 7761])).
% 2.35/2.59 tff(7763,plain,
% 2.35/2.59 (~r(s(s(z)), z)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[340, 7760, 150, 153])).
% 2.35/2.59 tff(7764,plain,
% 2.35/2.59 (b(s(s(z)), z)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[345, 7763])).
% 2.35/2.59 tff(7765,plain,
% 2.35/2.59 ($false),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[356, 7764, 7762, 7643, 7661])).
% 2.35/2.59 tff(7766,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.59 tff(7767,plain,
% 2.35/2.59 (~b(z, s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7766, 7635, 153, 150, 1475, 7624, 2, 7622])).
% 2.35/2.59 tff(7768,plain,
% 2.35/2.59 (r(z, s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[593, 7767])).
% 2.35/2.59 tff(7769,plain,
% 2.35/2.59 (~r(s(s(z)), s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[6539, 7768, 150, 153])).
% 2.35/2.59 tff(7770,plain,
% 2.35/2.59 (b(s(s(z)), s(z))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[487, 7769])).
% 2.35/2.59 tff(7771,plain,
% 2.35/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7772,plain,
% 2.35/2.59 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7773,plain,
% 2.35/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7772])).
% 2.35/2.59 tff(7774,plain,
% 2.35/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7773, 7771])).
% 2.35/2.59 tff(7775,plain,
% 2.35/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7776,plain,
% 2.35/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7775, 7774])).
% 2.35/2.59 tff(7777,plain,
% 2.35/2.59 ($false),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7776, 163, 1475, 236, 150, 694])).
% 2.35/2.59 tff(7778,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.59 tff(7779,plain,
% 2.35/2.59 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7778, 236, 1475, 150])).
% 2.35/2.59 tff(7780,plain,
% 2.35/2.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7270, 3615, 153, 406, 2, 6639])).
% 2.35/2.59 tff(7781,plain,
% 2.35/2.59 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[420, 7780])).
% 2.35/2.59 tff(7782,plain,
% 2.35/2.59 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7452, 7653, 7781, 153])).
% 2.35/2.59 tff(7783,plain,
% 2.35/2.59 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7261, 7782, 1475])).
% 2.35/2.59 tff(7784,plain,
% 2.35/2.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3792, 7783])).
% 2.35/2.59 tff(7785,plain,
% 2.35/2.59 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[703, 7784, 7779])).
% 2.35/2.59 tff(7786,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7787,plain,
% 2.35/2.59 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7788,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7787])).
% 2.35/2.59 tff(7789,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7788, 7786])).
% 2.35/2.59 tff(7790,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7791,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7790, 7789])).
% 2.35/2.59 tff(7792,plain,
% 2.35/2.59 ($false),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7791, 198, 320, 7785, 3615, 2])).
% 2.35/2.59 tff(7793,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.59 tff(7794,plain,
% 2.35/2.59 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7793, 7635, 2, 1475, 153, 7768, 150, 7624])).
% 2.35/2.59 tff(7795,plain,
% 2.35/2.59 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3613, 7794])).
% 2.35/2.59 tff(7796,plain,
% 2.35/2.59 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7778, 7624, 1475, 150])).
% 2.35/2.59 tff(7797,assumption,(~r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.35/2.59 tff(7798,plain,
% 2.35/2.59 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3792, 7262])).
% 2.35/2.59 tff(7799,plain,
% 2.35/2.59 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[703, 7798, 7797])).
% 2.35/2.59 tff(7800,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7801,plain,
% 2.35/2.59 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(rewrite,[status(thm)],[])).
% 2.35/2.59 tff(7802,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.35/2.59 inference(monotonicity,[status(thm)],[7801])).
% 2.35/2.59 tff(7803,plain,
% 2.35/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.35/2.59 inference(transitivity,[status(thm)],[7802, 7800])).
% 2.35/2.59 tff(7804,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))),
% 2.35/2.59 inference(quant_inst,[status(thm)],[])).
% 2.35/2.59 tff(7805,plain,
% 2.35/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.35/2.59 inference(modus_ponens,[status(thm)],[7804, 7803])).
% 2.35/2.59 tff(7806,plain,
% 2.35/2.59 ($false),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7805, 198, 271, 320, 7799, 7256, 2])).
% 2.35/2.59 tff(7807,plain,(r(z, s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.59 tff(7808,plain,
% 2.35/2.59 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7807, 7622, 7635, 2, 7796, 1475])).
% 2.35/2.59 tff(7809,plain,
% 2.35/2.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[7215, 7808, 150, 7795])).
% 2.35/2.59 tff(7810,plain,
% 2.35/2.59 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[420, 7809])).
% 2.35/2.59 tff(7811,plain,
% 2.35/2.59 (~b(s(z), s(s(z)))),
% 2.35/2.59 inference(unit_resolution,[status(thm)],[3753, 7810, 7770, 2])).
% 2.35/2.59 tff(7812,plain,
% 2.35/2.59 (r(s(z), s(s(z)))),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[403, 7811])).
% 2.35/2.60 tff(7813,plain,
% 2.35/2.60 (~r(s(s(z)), z)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[340, 7812, 150, 153])).
% 2.35/2.60 tff(7814,plain,
% 2.35/2.60 (b(s(s(z)), z)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[345, 7813])).
% 2.35/2.60 tff(7815,plain,
% 2.35/2.60 (~r(s(s(z)), elem!1)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[7062, 7812, 150, 153])).
% 2.35/2.60 tff(7816,plain,
% 2.35/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.60 inference(rewrite,[status(thm)],[])).
% 2.35/2.60 tff(7817,plain,
% 2.35/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.35/2.60 inference(quant_inst,[status(thm)],[])).
% 2.35/2.60 tff(7818,plain,
% 2.35/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 2.35/2.60 inference(modus_ponens,[status(thm)],[7817, 7816])).
% 2.35/2.60 tff(7819,plain,
% 2.35/2.60 ($false),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[7818, 163, 1475, 236, 405, 150])).
% 2.35/2.60 tff(7820,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.60 tff(7821,plain,
% 2.35/2.60 (~r(elem!1, s(s(elem!1)))),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[7820, 7624, 1475, 150])).
% 2.35/2.60 tff(7822,plain,
% 2.35/2.60 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[7274, 7768, 2, 153, 150])).
% 2.35/2.60 tff(7823,plain,
% 2.35/2.60 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[176, 7822])).
% 2.35/2.60 tff(7824,plain,
% 2.35/2.60 ($false),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[749, 163, 406, 151, 33, 680])).
% 2.35/2.60 tff(7825,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.35/2.60 tff(7826,plain,
% 2.35/2.60 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[7825, 7768, 7795, 7808])).
% 2.35/2.60 tff(7827,plain,
% 2.35/2.60 (b(s(s(elem!1)), z)),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[4228, 7826, 150, 2, 7768, 7823, 153])).
% 2.35/2.60 tff(7828,plain,
% 2.35/2.60 (s(s(s(z))) = s(elem!1)),
% 2.35/2.60 inference(monotonicity,[status(thm)],[2082])).
% 2.35/2.60 tff(7829,plain,
% 2.35/2.60 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.35/2.60 inference(monotonicity,[status(thm)],[7828])).
% 2.35/2.60 tff(7830,plain,
% 2.35/2.60 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.35/2.60 inference(monotonicity,[status(thm)],[7829])).
% 2.35/2.60 tff(7831,plain,
% 2.35/2.60 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.35/2.60 inference(symmetry,[status(thm)],[7830])).
% 2.35/2.60 tff(7832,plain,
% 2.35/2.60 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 2.35/2.60 inference(monotonicity,[status(thm)],[7831])).
% 2.35/2.60 tff(7833,plain,
% 2.35/2.60 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 2.35/2.60 inference(symmetry,[status(thm)],[7832])).
% 2.35/2.60 tff(7834,plain,
% 2.35/2.60 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.60 inference(monotonicity,[status(thm)],[2082])).
% 2.35/2.60 tff(7835,plain,
% 2.35/2.60 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.35/2.60 inference(modus_ponens,[status(thm)],[3745, 7834])).
% 2.35/2.60 tff(7836,plain,
% 2.35/2.60 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.35/2.60 inference(monotonicity,[status(thm)],[2082])).
% 2.35/2.60 tff(7837,plain,
% 2.35/2.60 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.35/2.60 inference(transitivity,[status(thm)],[7836, 112])).
% 2.35/2.60 tff(7838,plain,
% 2.35/2.60 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.35/2.60 inference(transitivity,[status(thm)],[7837, 113])).
% 2.35/2.60 tff(7839,plain,
% 2.35/2.60 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.35/2.60 inference(monotonicity,[status(thm)],[7838])).
% 2.35/2.60 tff(7840,plain,
% 2.35/2.60 (~(elem!1 = s(s(elem!1)))),
% 2.35/2.60 inference(modus_ponens,[status(thm)],[2154, 7839])).
% 2.35/2.60 tff(7841,plain,
% 2.35/2.60 (b(elem!1, s(s(elem!1)))),
% 2.35/2.60 inference(unit_resolution,[status(thm)],[147, 7840, 142])).
% 2.45/2.60 tff(7842,plain,
% 2.45/2.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7572, 198, 723, 7841, 7835, 330])).
% 2.45/2.60 tff(7843,plain,
% 2.45/2.60 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[4221, 7842, 669])).
% 2.45/2.60 tff(7844,plain,
% 2.45/2.60 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7843])).
% 2.45/2.60 tff(7845,plain,
% 2.45/2.60 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(symmetry,[status(thm)],[7844])).
% 2.45/2.60 tff(7846,plain,
% 2.45/2.60 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.45/2.60 inference(transitivity,[status(thm)],[135, 7845, 275, 7833])).
% 2.45/2.60 tff(7847,plain,
% 2.45/2.60 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7846])).
% 2.45/2.60 tff(7848,plain,
% 2.45/2.60 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.45/2.60 inference(symmetry,[status(thm)],[7847])).
% 2.45/2.60 tff(7849,plain,
% 2.45/2.60 (s(s(s(elem!1))) = elem!1),
% 2.45/2.60 inference(transitivity,[status(thm)],[965, 7848, 129])).
% 2.45/2.60 tff(7850,plain,
% 2.45/2.60 (~(s(s(s(elem!1))) = elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[2088, 2082])).
% 2.45/2.60 tff(7851,plain,
% 2.45/2.60 ($false),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7850, 7849])).
% 2.45/2.60 tff(7852,plain,((~(s(s(z)) = elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(elem!1, s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.60 tff(7853,plain,
% 2.45/2.60 (~(s(s(z)) = elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7852, 7826, 7827, 7823, 7821, 7810, 7365])).
% 2.45/2.60 tff(7854,plain,
% 2.45/2.60 (b(s(s(z)), elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[2139, 7853, 7815])).
% 2.45/2.60 tff(7855,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7856,plain,
% 2.45/2.60 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7857,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7856])).
% 2.45/2.60 tff(7858,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.60 inference(transitivity,[status(thm)],[7857, 7855])).
% 2.45/2.60 tff(7859,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.45/2.60 inference(quant_inst,[status(thm)],[])).
% 2.45/2.60 tff(7860,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.45/2.60 inference(modus_ponens,[status(thm)],[7859, 7858])).
% 2.45/2.60 tff(7861,plain,
% 2.45/2.60 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7860, 198, 7622, 7854, 7810, 7823])).
% 2.45/2.60 tff(7862,plain,
% 2.45/2.60 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[317, 90])).
% 2.45/2.60 tff(7863,plain,
% 2.45/2.60 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[671, 90, 669])).
% 2.45/2.60 tff(7864,plain,
% 2.45/2.60 ($false),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[256, 7863, 7862, 244])).
% 2.45/2.60 tff(7865,plain,((~(elem!1 = s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.60 tff(7866,plain,
% 2.45/2.60 (~(elem!1 = s(s(elem!1)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7865, 7861, 7826])).
% 2.45/2.60 tff(7867,plain,
% 2.45/2.60 (b(elem!1, s(s(elem!1)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[147, 7866, 7821])).
% 2.45/2.60 tff(7868,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7869,plain,
% 2.45/2.60 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7870,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7869])).
% 2.45/2.60 tff(7871,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.45/2.60 inference(transitivity,[status(thm)],[7870, 7868])).
% 2.45/2.60 tff(7872,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.45/2.60 inference(quant_inst,[status(thm)],[])).
% 2.45/2.60 tff(7873,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 2.45/2.60 inference(modus_ponens,[status(thm)],[7872, 7871])).
% 2.45/2.60 tff(7874,plain,
% 2.45/2.60 (~b(s(s(z)), s(s(elem!1)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7873, 198, 7827, 7867, 7854, 7814])).
% 2.45/2.60 tff(7875,plain,
% 2.45/2.60 (r(s(s(z)), s(s(elem!1)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[2161, 26, 7365, 7874])).
% 2.45/2.60 tff(7876,plain,
% 2.45/2.60 ($false),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7399, 163, 7768, 7875, 7812, 153])).
% 2.45/2.60 tff(7877,plain,(b(s(z), elem!1) | (~r(z, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.60 tff(7878,plain,
% 2.45/2.60 (b(s(z), elem!1)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7877, 150, 1475, 153, 2])).
% 2.45/2.60 tff(7879,plain,
% 2.45/2.60 (~r(s(s(z)), s(z))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[6539, 4193, 150, 153])).
% 2.45/2.60 tff(7880,plain,
% 2.45/2.60 (b(s(s(z)), s(z))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[487, 7879])).
% 2.45/2.60 tff(7881,plain,
% 2.45/2.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7270, 7880, 153, 3615, 2, 4193])).
% 2.45/2.60 tff(7882,plain,
% 2.45/2.60 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[420, 7881])).
% 2.45/2.60 tff(7883,plain,
% 2.45/2.60 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3626, 7880, 2, 3615])).
% 2.45/2.60 tff(7884,plain,
% 2.45/2.60 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[374, 7883])).
% 2.45/2.60 tff(7885,plain,
% 2.45/2.60 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[4494, 3615, 2, 153, 150, 7285, 331])).
% 2.45/2.60 tff(7886,plain,
% 2.45/2.60 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3098, 7885])).
% 2.45/2.60 tff(7887,plain,
% 2.45/2.60 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[4502, 163, 7886, 7884, 7882])).
% 2.45/2.60 tff(7888,plain,
% 2.45/2.60 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[511, 26, 508, 7887])).
% 2.45/2.60 tff(7889,plain,
% 2.45/2.60 (~r(s(z), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3712, 7884, 153, 150])).
% 2.45/2.60 tff(7890,plain,
% 2.45/2.60 (b(s(z), s(s(z)))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[403, 7889])).
% 2.45/2.60 tff(7891,plain,
% 2.45/2.60 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3792, 3790])).
% 2.45/2.60 tff(7892,plain,
% 2.45/2.60 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[6822, 7884, 150, 7880, 153])).
% 2.45/2.60 tff(7893,plain,
% 2.45/2.60 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3841, 7892])).
% 2.45/2.60 tff(7894,plain,
% 2.45/2.60 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[6834, 163, 7886, 7884, 7882])).
% 2.45/2.60 tff(7895,plain,
% 2.45/2.60 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[2715, 26, 507, 7894])).
% 2.45/2.60 tff(7896,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.45/2.60 tff(7897,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7898,plain,
% 2.45/2.60 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7899,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7898])).
% 2.45/2.60 tff(7900,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(transitivity,[status(thm)],[7899, 7897])).
% 2.45/2.60 tff(7901,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.45/2.60 inference(quant_inst,[status(thm)],[])).
% 2.45/2.60 tff(7902,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.45/2.60 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 2.45/2.60 tff(7903,plain,
% 2.45/2.60 (~b(s(z), s(s(s(s(s(z))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7902, 198, 560, 407, 7896, 4049])).
% 2.45/2.60 tff(7904,plain,
% 2.45/2.60 (r(s(z), s(s(s(s(s(z))))))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[3301, 7903])).
% 2.45/2.60 tff(7905,plain,
% 2.45/2.60 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7906,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7905])).
% 2.45/2.60 tff(7907,plain,
% 2.45/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.45/2.60 inference(transitivity,[status(thm)],[7906, 489])).
% 2.45/2.60 tff(7908,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.45/2.60 inference(quant_inst,[status(thm)],[])).
% 2.45/2.60 tff(7909,plain,
% 2.45/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.45/2.60 inference(modus_ponens,[status(thm)],[7908, 7907])).
% 2.45/2.60 tff(7910,plain,
% 2.45/2.60 (~b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[7909, 198, 560, 407, 4049])).
% 2.45/2.60 tff(7911,plain,
% 2.45/2.60 (r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.60 inference(unit_resolution,[status(thm)],[469, 7910])).
% 2.45/2.60 tff(7912,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.45/2.60 tff(7913,plain,
% 2.45/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7914,plain,
% 2.45/2.60 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(rewrite,[status(thm)],[])).
% 2.45/2.60 tff(7915,plain,
% 2.45/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.45/2.60 inference(monotonicity,[status(thm)],[7914])).
% 2.45/2.60 tff(7916,plain,
% 2.45/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.45/2.60 inference(transitivity,[status(thm)],[7915, 7913])).
% 2.45/2.60 tff(7917,plain,
% 2.45/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 2.45/2.60 inference(quant_inst,[status(thm)],[])).
% 2.45/2.60 tff(7918,plain,
% 2.45/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7917, 7916])).
% 2.45/2.61 tff(7919,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7918, 163, 406, 6249, 422, 7912])).
% 2.45/2.61 tff(7920,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(7921,plain,
% 2.45/2.61 (~r(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7920, 7911, 7904, 406])).
% 2.45/2.61 tff(7922,plain,
% 2.45/2.61 (b(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[4110, 7921])).
% 2.45/2.61 tff(7923,plain,
% 2.45/2.61 (~b(s(s(z)), z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[4296, 198, 7922, 4167, 7896])).
% 2.45/2.61 tff(7924,plain,
% 2.45/2.61 (r(s(s(z)), z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[345, 7923])).
% 2.45/2.61 tff(7925,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.45/2.61 tff(7926,plain,
% 2.45/2.61 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.61 inference(symmetry,[status(thm)],[7834])).
% 2.45/2.61 tff(7927,plain,
% 2.45/2.61 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[831, 7926])).
% 2.45/2.61 tff(7928,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7925, 7927])).
% 2.45/2.61 tff(7929,plain,((~(s(s(z)) = elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(7930,plain,
% 2.45/2.61 (~(s(s(z)) = elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7929, 831, 7925])).
% 2.45/2.61 tff(7931,plain,
% 2.45/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7932,plain,
% 2.45/2.61 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7933,plain,
% 2.45/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7932])).
% 2.45/2.61 tff(7934,plain,
% 2.45/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.45/2.61 inference(transitivity,[status(thm)],[7933, 7931])).
% 2.45/2.61 tff(7935,plain,
% 2.45/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(7936,plain,
% 2.45/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7935, 7934])).
% 2.45/2.61 tff(7937,plain,
% 2.45/2.61 ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7936, 163])).
% 2.45/2.61 tff(7938,plain,
% 2.45/2.61 (~r(elem!1, s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7937, 833, 1475, 150])).
% 2.45/2.61 tff(7939,plain,
% 2.45/2.61 (b(elem!1, s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[242, 7938, 6596])).
% 2.45/2.61 tff(7940,plain,
% 2.45/2.61 (~r(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[6761, 833, 332, 406])).
% 2.45/2.61 tff(7941,plain,
% 2.45/2.61 (b(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[2139, 7940, 2105])).
% 2.45/2.61 tff(7942,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[6661, 7941, 7939, 5927, 560])).
% 2.45/2.61 tff(7943,plain,((~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(7944,plain,
% 2.45/2.61 (~r(elem!1, z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7943, 7930, 560, 5927, 7924, 406, 1475, 150])).
% 2.45/2.61 tff(7945,plain,
% 2.45/2.61 (b(elem!1, z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[187, 7944, 7302])).
% 2.45/2.61 tff(7946,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7947,plain,
% 2.45/2.61 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7948,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7947])).
% 2.45/2.61 tff(7949,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.61 inference(transitivity,[status(thm)],[7948, 7946])).
% 2.45/2.61 tff(7950,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(7951,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7950, 7949])).
% 2.45/2.61 tff(7952,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7951, 198, 7945, 5927, 831, 2, 330])).
% 2.45/2.61 tff(7953,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), z)) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(7954,plain,
% 2.45/2.61 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7953, 7880, 2, 7285, 7878, 4193, 1475, 150, 7881, 7893, 7895, 7890, 7888])).
% 2.45/2.61 tff(7955,plain,
% 2.45/2.61 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[256, 7954, 3790])).
% 2.45/2.61 tff(7956,plain,
% 2.45/2.61 (r(elem!1, z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[187, 6643, 7302])).
% 2.45/2.61 tff(7957,plain,
% 2.45/2.61 (~r(elem!1, s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7937, 7956, 1475, 150])).
% 2.45/2.61 tff(7958,plain,
% 2.45/2.61 (b(elem!1, s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[242, 7957, 6596])).
% 2.45/2.61 tff(7959,plain,
% 2.45/2.61 (~b(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[6661, 7958, 5927, 560])).
% 2.45/2.61 tff(7960,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7961,plain,
% 2.45/2.61 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7962,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7961])).
% 2.45/2.61 tff(7963,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(transitivity,[status(thm)],[7962, 7960])).
% 2.45/2.61 tff(7964,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(7965,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7964, 7963])).
% 2.45/2.61 tff(7966,plain,
% 2.45/2.61 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7965, 198, 5927, 7958, 3615, 2])).
% 2.45/2.61 tff(7967,plain,
% 2.45/2.61 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[703, 7966, 673])).
% 2.45/2.61 tff(7968,plain,
% 2.45/2.61 (~r(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[6869, 163, 7967, 7266, 258])).
% 2.45/2.61 tff(7969,plain,
% 2.45/2.61 (s(s(z)) = elem!1),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[2139, 7968, 7959])).
% 2.45/2.61 tff(7970,plain,
% 2.45/2.61 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7969])).
% 2.45/2.61 tff(7971,plain,
% 2.45/2.61 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.45/2.61 inference(symmetry,[status(thm)],[7970])).
% 2.45/2.61 tff(7972,plain,
% 2.45/2.61 ((~b(elem!1, z)) <=> (~b(s(s(z)), z))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7971])).
% 2.45/2.61 tff(7973,plain,
% 2.45/2.61 (~b(s(s(z)), z)),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[6643, 7972])).
% 2.45/2.61 tff(7974,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[347, 7973])).
% 2.45/2.61 tff(7975,plain,(b(elem!1, z) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(7976,plain,
% 2.45/2.61 (b(elem!1, z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7975, 347, 258, 673, 5927, 3615, 2, 560, 1475, 150])).
% 2.45/2.61 tff(7977,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7978,plain,
% 2.45/2.61 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7979,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7978])).
% 2.45/2.61 tff(7980,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.45/2.61 inference(transitivity,[status(thm)],[7979, 7977])).
% 2.45/2.61 tff(7981,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(7982,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7981, 7980])).
% 2.45/2.61 tff(7983,plain,
% 2.45/2.61 (~b(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7982, 198, 7976, 5927, 560, 347])).
% 2.45/2.61 tff(7984,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7985,plain,
% 2.45/2.61 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(7986,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7985])).
% 2.45/2.61 tff(7987,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.61 inference(transitivity,[status(thm)],[7986, 7984])).
% 2.45/2.61 tff(7988,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(7989,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7988, 7987])).
% 2.45/2.61 tff(7990,plain,
% 2.45/2.61 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7989, 198, 7976, 331, 330])).
% 2.45/2.61 tff(7991,plain,
% 2.45/2.61 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[703, 7990, 673])).
% 2.45/2.61 tff(7992,plain,
% 2.45/2.61 (~r(s(s(z)), elem!1)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[6869, 163, 7991, 7266, 258])).
% 2.45/2.61 tff(7993,plain,
% 2.45/2.61 (s(s(z)) = elem!1),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[2139, 7992, 7983])).
% 2.45/2.61 tff(7994,plain,
% 2.45/2.61 (s(s(s(z))) = s(elem!1)),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7993])).
% 2.45/2.61 tff(7995,plain,
% 2.45/2.61 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7994])).
% 2.45/2.61 tff(7996,plain,
% 2.45/2.61 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7995])).
% 2.45/2.61 tff(7997,plain,
% 2.45/2.61 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.45/2.61 inference(symmetry,[status(thm)],[7996])).
% 2.45/2.61 tff(7998,plain,
% 2.45/2.61 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7997])).
% 2.45/2.61 tff(7999,plain,
% 2.45/2.61 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.45/2.61 inference(symmetry,[status(thm)],[7998])).
% 2.45/2.61 tff(8000,plain,
% 2.45/2.61 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7993])).
% 2.45/2.61 tff(8001,plain,
% 2.45/2.61 (b(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[7896, 8000])).
% 2.45/2.61 tff(8002,plain,
% 2.45/2.61 (b(elem!1, s(s(s(elem!1))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[8001, 7999])).
% 2.45/2.61 tff(8003,plain,
% 2.45/2.61 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7996])).
% 2.45/2.61 tff(8004,plain,
% 2.45/2.61 (~r(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7920, 7911, 7904, 4193])).
% 2.45/2.61 tff(8005,plain,
% 2.45/2.61 (b(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[4110, 8004])).
% 2.45/2.61 tff(8006,plain,
% 2.45/2.61 (b(z, s(s(s(elem!1))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[8005, 8003])).
% 2.45/2.61 tff(8007,plain,
% 2.45/2.61 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.45/2.61 inference(monotonicity,[status(thm)],[7996])).
% 2.45/2.61 tff(8008,plain,
% 2.45/2.61 (b(s(s(s(elem!1))), z)),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[4167, 8007])).
% 2.45/2.61 tff(8009,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(8010,plain,
% 2.45/2.61 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(8011,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[8010])).
% 2.45/2.61 tff(8012,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.45/2.61 inference(transitivity,[status(thm)],[8011, 8009])).
% 2.45/2.61 tff(8013,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 2.45/2.61 inference(quant_inst,[status(thm)],[])).
% 2.45/2.61 tff(8014,plain,
% 2.45/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[8013, 8012])).
% 2.45/2.61 tff(8015,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[8014, 198, 7976, 8008, 8006, 8002])).
% 2.45/2.61 tff(8016,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(8017,plain,
% 2.45/2.61 (~b(s(s(z)), z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[8016, 7955, 7895, 7893, 7891, 7880, 7890, 7888, 7878, 331, 7285, 3615, 2, 1475, 150])).
% 2.45/2.61 tff(8018,plain,
% 2.45/2.61 (r(s(s(z)), z)),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[345, 8017])).
% 2.45/2.61 tff(8019,plain,
% 2.45/2.61 (~b(s(z), s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7902, 198, 7880, 7890, 7895, 7888])).
% 2.45/2.61 tff(8020,plain,
% 2.45/2.61 (r(s(z), s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[3301, 8019])).
% 2.45/2.61 tff(8021,plain,
% 2.45/2.61 (~b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7909, 198, 7880, 7890, 7888])).
% 2.45/2.61 tff(8022,plain,
% 2.45/2.61 (r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[469, 8021])).
% 2.45/2.61 tff(8023,plain,
% 2.45/2.61 (~r(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[7920, 8022, 8020, 4193])).
% 2.45/2.61 tff(8024,plain,
% 2.45/2.61 (b(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[4110, 8023])).
% 2.45/2.61 tff(8025,plain,
% 2.45/2.61 (r(z, elem!1) <=> r(z, s(s(s(s(s(z))))))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[5376])).
% 2.45/2.61 tff(8026,plain,
% 2.45/2.61 (r(z, s(s(s(s(s(z)))))) <=> r(z, elem!1)),
% 2.45/2.61 inference(symmetry,[status(thm)],[8025])).
% 2.45/2.61 tff(8027,plain,
% 2.45/2.61 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(z, elem!1))),
% 2.45/2.61 inference(monotonicity,[status(thm)],[8026])).
% 2.45/2.61 tff(8028,plain,
% 2.45/2.61 (~r(z, elem!1)),
% 2.45/2.61 inference(modus_ponens,[status(thm)],[4104, 8027])).
% 2.45/2.61 tff(8029,plain,
% 2.45/2.61 ($false),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[1475, 8028])).
% 2.45/2.61 tff(8030,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~r(z, elem!1)) | r(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.61 tff(8031,plain,
% 2.45/2.61 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.45/2.61 inference(unit_resolution,[status(thm)],[8030, 8023, 1475])).
% 2.45/2.61 tff(8032,plain,
% 2.45/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.61 inference(rewrite,[status(thm)],[])).
% 2.45/2.61 tff(8033,plain,
% 2.45/2.61 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8034,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8033])).
% 2.45/2.62 tff(8035,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(transitivity,[status(thm)],[8034, 8032])).
% 2.45/2.62 tff(8036,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)))),
% 2.45/2.62 inference(quant_inst,[status(thm)],[])).
% 2.45/2.62 tff(8037,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8036, 8035])).
% 2.45/2.62 tff(8038,plain,
% 2.45/2.62 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8037, 198, 271, 331, 330, 5428, 4167])).
% 2.45/2.62 tff(8039,plain,
% 2.45/2.62 (r(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[4810, 8038, 5530])).
% 2.45/2.62 tff(8040,plain,
% 2.45/2.62 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[7989, 198, 271, 331, 330])).
% 2.45/2.62 tff(8041,plain,
% 2.45/2.62 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[703, 8040, 673])).
% 2.45/2.62 tff(8042,plain,
% 2.45/2.62 ($false),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[6117, 163, 3066, 8041, 258, 8039])).
% 2.45/2.62 tff(8043,plain,((~b(elem!1, 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))))))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.62 tff(8044,plain,
% 2.45/2.62 (~b(elem!1, z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8043, 7886, 7955, 8031, 7891, 331, 7285, 8024, 7893])).
% 2.45/2.62 tff(8045,plain,
% 2.45/2.62 (r(elem!1, z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[187, 8044, 7302])).
% 2.45/2.62 tff(8046,plain,
% 2.45/2.62 (s(s(z)) = elem!1),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[7943, 8045, 7880, 7878, 8018, 4193, 1475, 150])).
% 2.45/2.62 tff(8047,plain,
% 2.45/2.62 (s(s(s(z))) = s(elem!1)),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8046])).
% 2.45/2.62 tff(8048,plain,
% 2.45/2.62 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8047])).
% 2.45/2.62 tff(8049,plain,
% 2.45/2.62 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8048])).
% 2.45/2.62 tff(8050,plain,
% 2.45/2.62 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8049])).
% 2.45/2.62 tff(8051,plain,
% 2.45/2.62 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8050])).
% 2.45/2.62 tff(8052,plain,
% 2.45/2.62 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8051])).
% 2.45/2.62 tff(8053,plain,
% 2.45/2.62 (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(s(z))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8050])).
% 2.45/2.62 tff(8054,plain,
% 2.45/2.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8053])).
% 2.45/2.62 tff(8055,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8056,plain,
% 2.45/2.62 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8057,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8056])).
% 2.45/2.62 tff(8058,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.62 inference(transitivity,[status(thm)],[8057, 8055])).
% 2.45/2.62 tff(8059,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.45/2.62 inference(quant_inst,[status(thm)],[])).
% 2.45/2.62 tff(8060,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8059, 8058])).
% 2.45/2.62 tff(8061,plain,
% 2.45/2.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8060, 198, 331, 7285, 8024, 7893])).
% 2.45/2.62 tff(8062,plain,
% 2.45/2.62 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[3328, 26, 8061])).
% 2.45/2.62 tff(8063,plain,
% 2.45/2.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8062, 2935])).
% 2.45/2.62 tff(8064,plain,
% 2.45/2.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8063, 8054])).
% 2.45/2.62 tff(8065,plain,
% 2.45/2.62 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8049])).
% 2.45/2.62 tff(8066,plain,
% 2.45/2.62 (r(s(s(s(elem!1))), s(z))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8022, 8065])).
% 2.45/2.62 tff(8067,plain,
% 2.45/2.62 (~r(s(s(elem!1)), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[3739, 7890, 150, 153, 7365, 4193, 7880])).
% 2.45/2.62 tff(8068,plain,
% 2.45/2.62 (b(s(s(elem!1)), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[801, 8067])).
% 2.45/2.62 tff(8069,plain,
% 2.45/2.62 (~(s(s(elem!1)) = elem!1)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[6671, 8044, 8068])).
% 2.45/2.62 tff(8070,plain,
% 2.45/2.62 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[1250, 8069])).
% 2.45/2.62 tff(8071,plain,
% 2.45/2.62 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[1263, 8070])).
% 2.45/2.62 tff(8072,plain,
% 2.45/2.62 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8049])).
% 2.45/2.62 tff(8073,plain,
% 2.45/2.62 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8072])).
% 2.45/2.62 tff(8074,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8075,plain,
% 2.45/2.62 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8076,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8075])).
% 2.45/2.62 tff(8077,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(transitivity,[status(thm)],[8076, 8074])).
% 2.45/2.62 tff(8078,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), z)))),
% 2.45/2.62 inference(quant_inst,[status(thm)],[])).
% 2.45/2.62 tff(8079,plain,
% 2.45/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 2.45/2.62 tff(8080,plain,
% 2.45/2.62 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8079, 198, 8068, 331, 7285, 8024, 7893])).
% 2.45/2.62 tff(8081,plain,
% 2.45/2.62 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8080, 8073])).
% 2.45/2.62 tff(8082,plain,
% 2.45/2.62 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[1377, 8081, 8071])).
% 2.45/2.62 tff(8083,plain,
% 2.45/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8084,plain,
% 2.45/2.62 (((~r(s(s(s(elem!1))), s(z))) | (~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(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8085,plain,
% 2.45/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8084])).
% 2.45/2.62 tff(8086,plain,
% 2.45/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.45/2.62 inference(transitivity,[status(thm)],[8085, 8083])).
% 2.45/2.62 tff(8087,plain,
% 2.45/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.62 inference(quant_inst,[status(thm)],[])).
% 2.45/2.62 tff(8088,plain,
% 2.45/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8087, 8086])).
% 2.45/2.62 tff(8089,plain,
% 2.45/2.62 ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8088, 163, 8082, 8066])).
% 2.45/2.62 tff(8090,plain,
% 2.45/2.62 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8089, 8064])).
% 2.45/2.62 tff(8091,plain,
% 2.45/2.62 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[2877, 198, 8068, 331, 7285])).
% 2.45/2.62 tff(8092,plain,
% 2.45/2.62 ((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))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[934, 26, 8091])).
% 2.45/2.62 tff(8093,plain,
% 2.45/2.62 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8092, 8090])).
% 2.45/2.62 tff(8094,plain,
% 2.45/2.62 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8093])).
% 2.45/2.62 tff(8095,plain,
% 2.45/2.62 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8094])).
% 2.45/2.62 tff(8096,plain,
% 2.45/2.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8095])).
% 2.45/2.62 tff(8097,plain,
% 2.45/2.62 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.45/2.62 inference(transitivity,[status(thm)],[135, 8096, 275, 8052])).
% 2.45/2.62 tff(8098,plain,
% 2.45/2.62 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8097])).
% 2.45/2.62 tff(8099,plain,
% 2.45/2.62 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.45/2.62 inference(symmetry,[status(thm)],[8098])).
% 2.45/2.62 tff(8100,plain,
% 2.45/2.62 (s(s(s(elem!1))) = elem!1),
% 2.45/2.62 inference(transitivity,[status(thm)],[965, 8099, 129])).
% 2.45/2.62 tff(8101,plain,
% 2.45/2.62 (~(s(s(s(elem!1))) = elem!1)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[2088, 8046])).
% 2.45/2.62 tff(8102,plain,
% 2.45/2.62 ($false),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8101, 8100])).
% 2.45/2.62 tff(8103,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.62 tff(8104,plain,
% 2.45/2.62 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8103, 331, 150, 1475, 2, 3790, 153])).
% 2.45/2.62 tff(8105,plain,
% 2.45/2.62 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[3613, 8104])).
% 2.45/2.62 tff(8106,plain,
% 2.45/2.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[7649, 595, 2, 7285, 150, 153])).
% 2.45/2.62 tff(8107,plain,
% 2.45/2.62 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[420, 8106])).
% 2.45/2.62 tff(8108,plain,
% 2.45/2.62 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[7694, 3450, 423, 151])).
% 2.45/2.62 tff(8109,plain,
% 2.45/2.62 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[374, 8108])).
% 2.45/2.62 tff(8110,plain,
% 2.45/2.62 (~b(s(s(z)), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[356, 8109, 331, 330])).
% 2.45/2.62 tff(8111,plain,
% 2.45/2.62 (r(s(s(z)), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[345, 8110])).
% 2.45/2.62 tff(8112,plain,
% 2.45/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8113,plain,
% 2.45/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.45/2.62 inference(quant_inst,[status(thm)],[])).
% 2.45/2.62 tff(8114,plain,
% 2.45/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 2.45/2.62 inference(modus_ponens,[status(thm)],[8113, 8112])).
% 2.45/2.62 tff(8115,plain,
% 2.45/2.62 ($false),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8114, 163, 1475, 150, 3450, 8111])).
% 2.45/2.62 tff(8116,plain,((~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.62 tff(8117,plain,
% 2.45/2.62 (~r(s(s(z)), s(z))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[8116, 8107, 150, 331, 7285, 1475, 8105])).
% 2.45/2.62 tff(8118,plain,
% 2.45/2.62 (b(s(s(z)), s(z))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[487, 8117])).
% 2.45/2.62 tff(8119,plain,
% 2.45/2.62 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[356, 347, 331, 330])).
% 2.45/2.62 tff(8120,plain,
% 2.45/2.62 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[374, 8119])).
% 2.45/2.62 tff(8121,plain,
% 2.45/2.62 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[6822, 8120, 150, 560, 153])).
% 2.45/2.62 tff(8122,plain,
% 2.45/2.62 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[3841, 8121])).
% 2.45/2.62 tff(8123,plain,
% 2.45/2.62 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[4174, 8122, 330, 331])).
% 2.45/2.62 tff(8124,plain,
% 2.45/2.62 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[3098, 8123])).
% 2.45/2.62 tff(8125,plain,
% 2.45/2.62 (~r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[453, 163, 8124, 151, 423])).
% 2.45/2.62 tff(8126,plain,
% 2.45/2.62 (b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.62 inference(unit_resolution,[status(thm)],[469, 8125])).
% 2.45/2.62 tff(8127,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8128,plain,
% 2.45/2.62 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(z, 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(s(s(s(z))))), s(z))))),
% 2.45/2.62 inference(rewrite,[status(thm)],[])).
% 2.45/2.62 tff(8129,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.45/2.62 inference(monotonicity,[status(thm)],[8128])).
% 2.45/2.62 tff(8130,plain,
% 2.45/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8129, 8127])).
% 2.45/2.63 tff(8131,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8132,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8131, 8130])).
% 2.45/2.63 tff(8133,plain,
% 2.45/2.63 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8132, 198, 595, 347, 8126, 8122])).
% 2.45/2.63 tff(8134,plain,
% 2.45/2.63 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[4502, 163, 8124, 8120, 423])).
% 2.45/2.63 tff(8135,plain,
% 2.45/2.63 ($false),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[511, 26, 508, 8134, 8133])).
% 2.45/2.63 tff(8136,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.63 tff(8137,plain,
% 2.45/2.63 (~b(s(s(z)), z)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8136, 595, 8105, 8107, 7285, 331, 150, 8118, 153])).
% 2.45/2.63 tff(8138,plain,
% 2.45/2.63 (r(s(s(z)), z)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[345, 8137])).
% 2.45/2.63 tff(8139,plain,
% 2.45/2.63 (~(elem!1 = s(z))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[6595, 7878])).
% 2.45/2.63 tff(8140,plain,
% 2.45/2.63 (b(elem!1, s(z))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[242, 7938, 8139])).
% 2.45/2.63 tff(8141,plain,
% 2.45/2.63 (~b(s(s(z)), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[6661, 8140, 7878, 8118])).
% 2.45/2.63 tff(8142,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8143,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8144,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8143, 8142])).
% 2.45/2.63 tff(8145,plain,
% 2.45/2.63 (~r(s(s(z)), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8144, 163, 1475, 833, 8138])).
% 2.45/2.63 tff(8146,plain,
% 2.45/2.63 (s(s(z)) = elem!1),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[2139, 8145, 8141])).
% 2.45/2.63 tff(8147,plain,
% 2.45/2.63 (s(s(s(z))) = s(elem!1)),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8146])).
% 2.45/2.63 tff(8148,plain,
% 2.45/2.63 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8147])).
% 2.45/2.63 tff(8149,plain,
% 2.45/2.63 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8148])).
% 2.45/2.63 tff(8150,plain,
% 2.45/2.63 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.45/2.63 inference(symmetry,[status(thm)],[8149])).
% 2.45/2.63 tff(8151,plain,
% 2.45/2.63 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8150])).
% 2.45/2.63 tff(8152,plain,
% 2.45/2.63 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.63 inference(symmetry,[status(thm)],[8151])).
% 2.45/2.63 tff(8153,plain,
% 2.45/2.63 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 2.45/2.63 inference(monotonicity,[status(thm)],[7830])).
% 2.45/2.63 tff(8154,plain,
% 2.45/2.63 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(z))))), z)),
% 2.45/2.63 inference(symmetry,[status(thm)],[8153])).
% 2.45/2.63 tff(8155,plain,
% 2.45/2.63 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8154])).
% 2.45/2.63 tff(8156,plain,
% 2.45/2.63 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[7830])).
% 2.45/2.63 tff(8157,plain,
% 2.45/2.63 (b(s(s(s(elem!1))), s(z))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[6812, 8156])).
% 2.45/2.63 tff(8158,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8159,plain,
% 2.45/2.63 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8160,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8159])).
% 2.45/2.63 tff(8161,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8160, 8158])).
% 2.45/2.63 tff(8162,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8163,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8162, 8161])).
% 2.45/2.63 tff(8164,plain,
% 2.45/2.63 (~b(s(s(s(elem!1))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8163, 198, 5927, 8157, 7939])).
% 2.45/2.63 tff(8165,plain,
% 2.45/2.63 (r(s(s(s(elem!1))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[1308, 8164, 7850])).
% 2.45/2.63 tff(8166,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8167,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8168,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8167, 8166])).
% 2.45/2.63 tff(8169,plain,
% 2.45/2.63 (~r(s(s(s(elem!1))), z)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8168, 163, 1475, 833, 8165])).
% 2.45/2.63 tff(8170,plain,
% 2.45/2.63 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8169, 8155])).
% 2.45/2.63 tff(8171,plain,
% 2.45/2.63 ($false),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[3828, 8170])).
% 2.45/2.63 tff(8172,plain,((~r(s(s(s(s(s(z))))), z)) | (~(s(s(z)) = elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.63 tff(8173,plain,
% 2.45/2.63 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8172, 8146, 1475, 833, 7878, 153, 150])).
% 2.45/2.63 tff(8174,plain,
% 2.45/2.63 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[3841, 8173])).
% 2.45/2.63 tff(8175,plain,
% 2.45/2.63 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[4174, 8174, 7285, 331])).
% 2.45/2.63 tff(8176,plain,
% 2.45/2.63 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[3098, 8175])).
% 2.45/2.63 tff(8177,plain,
% 2.45/2.63 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8176, 8152])).
% 2.45/2.63 tff(8178,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8179,plain,
% 2.45/2.63 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8180,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8179])).
% 2.45/2.63 tff(8181,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8180, 8178])).
% 2.45/2.63 tff(8182,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8183,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 2.45/2.63 tff(8184,plain,
% 2.45/2.63 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8183, 198, 7878, 8140, 2])).
% 2.45/2.63 tff(8185,plain,
% 2.45/2.63 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[256, 8184, 3790])).
% 2.45/2.63 tff(8186,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8187,plain,
% 2.45/2.63 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8188,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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)))))))))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8187])).
% 2.45/2.63 tff(8189,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8188, 8186])).
% 2.45/2.63 tff(8190,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8191,plain,
% 2.45/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~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)))))))))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8190, 8189])).
% 2.45/2.63 tff(8192,plain,
% 2.45/2.63 ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8191, 163, 8105, 8185])).
% 2.45/2.63 tff(8193,plain,
% 2.45/2.63 (~r(s(s(s(elem!1))), s(z))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8192, 8177])).
% 2.45/2.63 tff(8194,plain,
% 2.45/2.63 (b(s(s(s(elem!1))), s(z))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[1633, 26, 1282, 8193])).
% 2.45/2.63 tff(8195,plain,
% 2.45/2.63 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(elem!1))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8149])).
% 2.45/2.63 tff(8196,plain,
% 2.45/2.63 (~r(s(z), s(s(s(s(s(z))))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[6852, 8176, 8105, 8107])).
% 2.45/2.63 tff(8197,plain,
% 2.45/2.63 (b(s(z), s(s(s(s(s(z))))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[3301, 8196])).
% 2.45/2.63 tff(8198,plain,
% 2.45/2.63 (b(s(z), s(s(s(elem!1))))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8197, 8195])).
% 2.45/2.63 tff(8199,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8200,plain,
% 2.45/2.63 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8201,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8200])).
% 2.45/2.63 tff(8202,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8201, 8199])).
% 2.45/2.63 tff(8203,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8204,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8203, 8202])).
% 2.45/2.63 tff(8205,plain,
% 2.45/2.63 (~b(z, s(s(s(elem!1))))),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8204, 198, 8198, 8194, 595])).
% 2.45/2.63 tff(8206,plain,
% 2.45/2.63 (~(s(s(s(elem!1))) = elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[2088, 8146])).
% 2.45/2.63 tff(8207,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8208,plain,
% 2.45/2.63 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(rewrite,[status(thm)],[])).
% 2.45/2.63 tff(8209,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.45/2.63 inference(monotonicity,[status(thm)],[8208])).
% 2.45/2.63 tff(8210,plain,
% 2.45/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.45/2.63 inference(transitivity,[status(thm)],[8209, 8207])).
% 2.45/2.63 tff(8211,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.45/2.63 inference(quant_inst,[status(thm)],[])).
% 2.45/2.63 tff(8212,plain,
% 2.45/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.45/2.63 inference(modus_ponens,[status(thm)],[8211, 8210])).
% 2.45/2.63 tff(8213,plain,
% 2.45/2.63 (~b(s(s(s(elem!1))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[8212, 198, 7878, 8198, 8194, 8140])).
% 2.45/2.63 tff(8214,plain,
% 2.45/2.63 (r(s(s(s(elem!1))), elem!1)),
% 2.45/2.63 inference(unit_resolution,[status(thm)],[1308, 8213, 8206])).
% 2.45/2.63 tff(8215,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.45/2.63 tff(8216,plain,
% 2.45/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8217,plain,
% 2.45/2.64 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8218,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8217])).
% 2.45/2.64 tff(8219,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8218, 8216])).
% 2.45/2.64 tff(8220,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8221,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8220, 8219])).
% 2.45/2.64 tff(8222,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8221, 163, 1475, 833, 8215, 1363])).
% 2.45/2.64 tff(8223,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8224,plain,
% 2.45/2.64 (~r(z, s(s(s(elem!1))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8223, 8214, 833, 1475])).
% 2.45/2.64 tff(8225,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[1350, 26, 8224, 8205, 1255])).
% 2.45/2.64 tff(8226,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8227,plain,
% 2.45/2.64 (~r(elem!1, z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8226, 595, 1475, 331, 153, 150, 3790, 2])).
% 2.45/2.64 tff(8228,plain,
% 2.45/2.64 (b(elem!1, z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[187, 8227, 7302])).
% 2.45/2.64 tff(8229,plain,
% 2.45/2.64 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7989, 198, 8228, 331, 7285])).
% 2.45/2.64 tff(8230,plain,
% 2.45/2.64 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[703, 8229, 7891])).
% 2.45/2.64 tff(8231,plain,
% 2.45/2.64 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.45/2.64 inference(monotonicity,[status(thm)],[2082])).
% 2.45/2.64 tff(8232,plain,
% 2.45/2.64 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.45/2.64 inference(symmetry,[status(thm)],[8231])).
% 2.45/2.64 tff(8233,plain,
% 2.45/2.64 (b(s(s(z)), z)),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[271, 8232])).
% 2.45/2.64 tff(8234,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 2.45/2.64 tff(8235,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8234, 8233])).
% 2.45/2.64 tff(8236,plain,((~(s(s(z)) = elem!1)) | b(s(s(z)), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8237,plain,
% 2.45/2.64 (~(s(s(z)) = elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8236, 8228, 8137])).
% 2.45/2.64 tff(8238,plain,
% 2.45/2.64 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7729, 198, 8228, 595, 2, 7285])).
% 2.45/2.64 tff(8239,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[256, 8238, 3790])).
% 2.45/2.64 tff(8240,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8241,plain,
% 2.45/2.64 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8242,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8241])).
% 2.45/2.64 tff(8243,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8242, 8240])).
% 2.45/2.64 tff(8244,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8245,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 2.45/2.64 tff(8246,plain,
% 2.45/2.64 (~r(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8245, 163, 8230, 8105, 8239])).
% 2.45/2.64 tff(8247,plain,
% 2.45/2.64 (b(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[242, 8246, 8139])).
% 2.45/2.64 tff(8248,plain,
% 2.45/2.64 (~b(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6661, 8247, 7878, 8118])).
% 2.45/2.64 tff(8249,plain,
% 2.45/2.64 (r(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[2139, 8248, 8237])).
% 2.45/2.64 tff(8250,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8251,plain,
% 2.45/2.64 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8252,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8251])).
% 2.45/2.64 tff(8253,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8252, 8250])).
% 2.45/2.64 tff(8254,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8255,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8254, 8253])).
% 2.45/2.64 tff(8256,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8255, 163, 1475, 8249, 8230, 8138])).
% 2.45/2.64 tff(8257,plain,((~b(z, s(z))) | (~r(z, elem!1)) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8258,plain,
% 2.45/2.64 (~b(z, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8257, 7262, 1475, 7256, 2, 153, 150])).
% 2.45/2.64 tff(8259,plain,
% 2.45/2.64 (r(z, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[593, 8258])).
% 2.45/2.64 tff(8260,plain,
% 2.45/2.64 (~r(s(s(z)), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6539, 8259, 150, 153])).
% 2.45/2.64 tff(8261,plain,
% 2.45/2.64 (b(s(s(z)), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[487, 8260])).
% 2.45/2.64 tff(8262,plain,
% 2.45/2.64 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7283, 7256, 2, 153, 150])).
% 2.45/2.64 tff(8263,plain,
% 2.45/2.64 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[176, 8262])).
% 2.45/2.64 tff(8264,plain,
% 2.45/2.64 (~b(z, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8257, 3790, 1475, 331, 2, 153, 150])).
% 2.45/2.64 tff(8265,plain,
% 2.45/2.64 (r(z, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[593, 8264])).
% 2.45/2.64 tff(8266,plain,
% 2.45/2.64 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7951, 198, 271, 7878, 2, 7285])).
% 2.45/2.64 tff(8267,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[256, 8266, 3790])).
% 2.45/2.64 tff(8268,plain,
% 2.45/2.64 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7989, 198, 271, 331, 7285])).
% 2.45/2.64 tff(8269,plain,
% 2.45/2.64 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[703, 8268, 7891])).
% 2.45/2.64 tff(8270,plain,
% 2.45/2.64 (~r(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8245, 163, 694, 151, 258])).
% 2.45/2.64 tff(8271,plain,
% 2.45/2.64 (b(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[242, 8270, 6596])).
% 2.45/2.64 tff(8272,plain,
% 2.45/2.64 (~b(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6661, 8271, 5927, 6639])).
% 2.45/2.64 tff(8273,plain,
% 2.45/2.64 (~r(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6869, 163, 694, 3272, 258])).
% 2.45/2.64 tff(8274,plain,
% 2.45/2.64 (s(s(z)) = elem!1),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[2139, 8273, 8272])).
% 2.45/2.64 tff(8275,plain,
% 2.45/2.64 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8274])).
% 2.45/2.64 tff(8276,plain,
% 2.45/2.64 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.45/2.64 inference(symmetry,[status(thm)],[8275])).
% 2.45/2.64 tff(8277,plain,
% 2.45/2.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6545, 3272, 2, 153, 150, 406])).
% 2.45/2.64 tff(8278,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[420, 8277])).
% 2.45/2.64 tff(8279,plain,
% 2.45/2.64 (~r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[456, 8278, 151, 7285, 406, 331])).
% 2.45/2.64 tff(8280,plain,
% 2.45/2.64 (b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[469, 8279])).
% 2.45/2.64 tff(8281,plain,
% 2.45/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8282,plain,
% 2.45/2.64 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8283,plain,
% 2.45/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8282])).
% 2.45/2.64 tff(8284,plain,
% 2.45/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8283, 8281])).
% 2.45/2.64 tff(8285,plain,
% 2.45/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8286,plain,
% 2.45/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8285, 8284])).
% 2.45/2.64 tff(8287,plain,
% 2.45/2.64 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8286, 198, 5927, 8271, 8280])).
% 2.45/2.64 tff(8288,plain,
% 2.45/2.64 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6822, 3272, 150, 6639, 153])).
% 2.45/2.64 tff(8289,plain,
% 2.45/2.64 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[3841, 8288])).
% 2.45/2.64 tff(8290,plain,
% 2.45/2.64 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[4174, 8289, 7285, 331])).
% 2.45/2.64 tff(8291,plain,
% 2.45/2.64 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[3098, 8290])).
% 2.45/2.64 tff(8292,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8293,plain,
% 2.45/2.64 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8294,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8293])).
% 2.45/2.64 tff(8295,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8294, 8292])).
% 2.45/2.64 tff(8296,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8297,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8296, 8295])).
% 2.45/2.64 tff(8298,plain,
% 2.45/2.64 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8297, 163, 8291, 694, 8278])).
% 2.45/2.64 tff(8299,plain,
% 2.45/2.64 (s(s(s(s(s(z))))) = elem!1),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[528, 8298, 8287])).
% 2.45/2.64 tff(8300,plain,
% 2.45/2.64 (s(s(s(s(s(z))))) = s(s(z))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8299, 8276])).
% 2.45/2.64 tff(8301,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[508, 8300])).
% 2.45/2.64 tff(8302,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8303,plain,
% 2.45/2.64 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8302, 8269, 8267, 7878, 8105, 8265, 331, 2, 153, 150])).
% 2.45/2.64 tff(8304,plain,
% 2.45/2.64 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[374, 8303])).
% 2.45/2.64 tff(8305,plain,
% 2.45/2.64 (~b(s(s(z)), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[356, 8304, 331, 7285])).
% 2.45/2.64 tff(8306,plain,
% 2.45/2.64 (r(s(s(z)), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[345, 8305])).
% 2.45/2.64 tff(8307,plain,
% 2.45/2.64 (~r(s(s(z)), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6539, 8265, 150, 153])).
% 2.45/2.64 tff(8308,plain,
% 2.45/2.64 (b(s(s(z)), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[487, 8307])).
% 2.45/2.64 tff(8309,plain,
% 2.45/2.64 (~r(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8245, 163, 8269, 8105, 8267])).
% 2.45/2.64 tff(8310,plain,
% 2.45/2.64 (b(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[242, 8309, 8139])).
% 2.45/2.64 tff(8311,plain,
% 2.45/2.64 (~b(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6661, 8310, 7878, 8308])).
% 2.45/2.64 tff(8312,plain,
% 2.45/2.64 (~(s(s(z)) = elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8236, 8305, 271])).
% 2.45/2.64 tff(8313,plain,
% 2.45/2.64 (r(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[2139, 8312, 8311])).
% 2.45/2.64 tff(8314,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8255, 163, 1475, 8313, 8269, 8306])).
% 2.45/2.64 tff(8315,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8316,plain,
% 2.45/2.64 (~b(elem!1, z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8315, 7256, 1475, 2, 153, 150, 7262])).
% 2.45/2.64 tff(8317,plain,
% 2.45/2.64 (r(elem!1, z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[187, 8316, 7302])).
% 2.45/2.64 tff(8318,plain,
% 2.45/2.64 (~r(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7937, 8317, 1475, 150])).
% 2.45/2.64 tff(8319,plain,
% 2.45/2.64 (b(elem!1, s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[242, 8318, 8139])).
% 2.45/2.64 tff(8320,plain,
% 2.45/2.64 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8183, 198, 7878, 8319, 2])).
% 2.45/2.64 tff(8321,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[256, 8320, 7262])).
% 2.45/2.64 tff(8322,plain,
% 2.45/2.64 (~r(s(s(z)), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[7943, 2105, 406, 5927, 560, 833, 1475, 150])).
% 2.45/2.64 tff(8323,plain,
% 2.45/2.64 (b(s(s(z)), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[345, 8322])).
% 2.45/2.64 tff(8324,plain,
% 2.45/2.64 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[356, 8323, 331, 330])).
% 2.45/2.64 tff(8325,plain,
% 2.45/2.64 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[374, 8324])).
% 2.45/2.64 tff(8326,plain,
% 2.45/2.64 (~b(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6661, 7939, 5927, 560])).
% 2.45/2.64 tff(8327,plain,
% 2.45/2.64 (r(s(s(z)), elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[2139, 2105, 8326])).
% 2.45/2.64 tff(8328,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8329,plain,
% 2.45/2.64 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(rewrite,[status(thm)],[])).
% 2.45/2.64 tff(8330,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8329])).
% 2.45/2.64 tff(8331,plain,
% 2.45/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(transitivity,[status(thm)],[8330, 8328])).
% 2.45/2.64 tff(8332,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.64 inference(quant_inst,[status(thm)],[])).
% 2.45/2.64 tff(8333,plain,
% 2.45/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 2.45/2.64 tff(8334,plain,
% 2.45/2.64 ($false),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8333, 163, 833, 8327, 8325, 258])).
% 2.45/2.64 tff(8335,plain,((s(s(z)) = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.64 tff(8336,plain,
% 2.45/2.64 (s(s(z)) = elem!1),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8335, 8317, 8321, 7256, 8263, 8259, 7878, 8261, 1475, 150])).
% 2.45/2.64 tff(8337,plain,
% 2.45/2.64 (s(s(s(z))) = s(elem!1)),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8336])).
% 2.45/2.64 tff(8338,plain,
% 2.45/2.64 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8337])).
% 2.45/2.64 tff(8339,plain,
% 2.45/2.64 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8338])).
% 2.45/2.64 tff(8340,plain,
% 2.45/2.64 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.45/2.64 inference(symmetry,[status(thm)],[8339])).
% 2.45/2.64 tff(8341,plain,
% 2.45/2.64 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8340])).
% 2.45/2.64 tff(8342,plain,
% 2.45/2.64 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(symmetry,[status(thm)],[8341])).
% 2.45/2.64 tff(8343,plain,
% 2.45/2.64 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8172, 8336, 1475, 8317, 7878, 153, 150])).
% 2.45/2.64 tff(8344,plain,
% 2.45/2.64 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[3841, 8343])).
% 2.45/2.64 tff(8345,plain,
% 2.45/2.64 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[4174, 8344, 8263, 7256])).
% 2.45/2.64 tff(8346,plain,
% 2.45/2.64 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[3098, 8345])).
% 2.45/2.64 tff(8347,plain,
% 2.45/2.64 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8346, 8342])).
% 2.45/2.64 tff(8348,plain,
% 2.45/2.64 (~(s(s(s(elem!1))) = elem!1)),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[2088, 8336])).
% 2.45/2.64 tff(8349,plain,
% 2.45/2.64 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8339])).
% 2.45/2.64 tff(8350,plain,
% 2.45/2.64 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[8103, 7256, 150, 1475, 2, 7262, 153])).
% 2.45/2.64 tff(8351,plain,
% 2.45/2.64 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[3613, 8350])).
% 2.45/2.64 tff(8352,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8336])).
% 2.45/2.64 tff(8353,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.64 inference(symmetry,[status(thm)],[8352])).
% 2.45/2.64 tff(8354,plain,
% 2.45/2.64 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8321, 8353])).
% 2.45/2.64 tff(8355,plain,
% 2.45/2.64 (~r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[456, 8354, 8351, 8263, 8259, 7256])).
% 2.45/2.64 tff(8356,plain,
% 2.45/2.64 (b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[469, 8355])).
% 2.45/2.64 tff(8357,plain,
% 2.45/2.64 (b(s(s(s(elem!1))), s(z))),
% 2.45/2.64 inference(modus_ponens,[status(thm)],[8356, 8349])).
% 2.45/2.64 tff(8358,plain,
% 2.45/2.64 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(elem!1))))),
% 2.45/2.64 inference(monotonicity,[status(thm)],[8339])).
% 2.45/2.64 tff(8359,plain,
% 2.45/2.64 (~r(s(z), s(s(s(s(s(z))))))),
% 2.45/2.64 inference(unit_resolution,[status(thm)],[6852, 8354, 8351, 8346])).
% 2.45/2.65 tff(8360,plain,
% 2.45/2.65 (b(s(z), s(s(s(s(s(z))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3301, 8359])).
% 2.45/2.65 tff(8361,plain,
% 2.45/2.65 (b(s(z), s(s(s(elem!1))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8360, 8358])).
% 2.45/2.65 tff(8362,plain,
% 2.45/2.65 (~b(s(s(s(elem!1))), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8212, 198, 7878, 8361, 8357, 8319])).
% 2.45/2.65 tff(8363,plain,
% 2.45/2.65 (r(s(s(s(elem!1))), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[1308, 8362, 8348])).
% 2.45/2.65 tff(8364,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8365,plain,
% 2.45/2.65 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, 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))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8366,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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)))))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8365])).
% 2.45/2.65 tff(8367,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, 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))))))))))),
% 2.45/2.65 inference(transitivity,[status(thm)],[8366, 8364])).
% 2.45/2.65 tff(8368,plain,
% 2.45/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(quant_inst,[status(thm)],[])).
% 2.45/2.65 tff(8369,plain,
% 2.45/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8368, 8367])).
% 2.45/2.65 tff(8370,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8369, 163, 8317, 8363, 8321, 8347])).
% 2.45/2.65 tff(8371,plain,(r(z, s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8372,plain,
% 2.45/2.65 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8371, 150, 153, 1475, 2])).
% 2.45/2.65 tff(8373,plain,
% 2.45/2.65 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[4548, 152, 153, 33])).
% 2.45/2.65 tff(8374,plain,
% 2.45/2.65 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[374, 8373])).
% 2.45/2.65 tff(8375,plain,
% 2.45/2.65 (~b(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3626, 8374, 2, 7264])).
% 2.45/2.65 tff(8376,plain,
% 2.45/2.65 (r(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[487, 8375])).
% 2.45/2.65 tff(8377,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[420, 7272])).
% 2.45/2.65 tff(8378,plain,
% 2.45/2.65 (~b(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3679, 198, 7264, 8374, 8377, 2])).
% 2.45/2.65 tff(8379,plain,
% 2.45/2.65 (r(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[403, 8378])).
% 2.45/2.65 tff(8380,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3687, 163, 150, 8379, 153, 8376])).
% 2.45/2.65 tff(8381,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8382,plain,
% 2.45/2.65 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8381, 150, 153, 2, 33])).
% 2.45/2.65 tff(8383,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[176, 8382])).
% 2.45/2.65 tff(8384,plain,
% 2.45/2.65 (~r(z, s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[6539, 3450, 150, 153])).
% 2.45/2.65 tff(8385,plain,
% 2.45/2.65 (b(z, s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[593, 8384])).
% 2.45/2.65 tff(8386,plain,
% 2.45/2.65 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7649, 8385, 2, 8383, 150, 153])).
% 2.45/2.65 tff(8387,plain,
% 2.45/2.65 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[420, 8386])).
% 2.45/2.65 tff(8388,plain,
% 2.45/2.65 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7215, 8387, 150, 33])).
% 2.45/2.65 tff(8389,plain,
% 2.45/2.65 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3671, 8387, 153, 150, 3450, 8385])).
% 2.45/2.65 tff(8390,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3613, 8389, 8388])).
% 2.45/2.65 tff(8391,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8392,plain,
% 2.45/2.65 (~r(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8391, 150, 153, 8372, 2])).
% 2.45/2.65 tff(8393,plain,
% 2.45/2.65 (b(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[487, 8392])).
% 2.45/2.65 tff(8394,plain,
% 2.45/2.65 (~r(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8391, 150, 153, 33, 2])).
% 2.45/2.65 tff(8395,plain,
% 2.45/2.65 (b(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[487, 8394])).
% 2.45/2.65 tff(8396,plain,
% 2.45/2.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7452, 3272, 33, 153])).
% 2.45/2.65 tff(8397,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[420, 8396])).
% 2.45/2.65 tff(8398,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3753, 8397, 4201, 8395, 2])).
% 2.45/2.65 tff(8399,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8400,plain,
% 2.45/2.65 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8399, 8372, 2, 153, 150])).
% 2.45/2.65 tff(8401,plain,
% 2.45/2.65 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[374, 8400])).
% 2.45/2.65 tff(8402,plain,
% 2.45/2.65 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3626, 8401, 2, 8393])).
% 2.45/2.65 tff(8403,plain,
% 2.45/2.65 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3613, 8402])).
% 2.45/2.65 tff(8404,plain,
% 2.45/2.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7215, 8403, 150, 8372])).
% 2.45/2.65 tff(8405,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[420, 8404])).
% 2.45/2.65 tff(8406,plain,
% 2.45/2.65 (~b(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3753, 8405, 8393, 2])).
% 2.45/2.65 tff(8407,plain,
% 2.45/2.65 (r(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[403, 8406])).
% 2.45/2.65 tff(8408,plain,
% 2.45/2.65 (~r(s(s(z)), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7062, 8407, 150, 153])).
% 2.45/2.65 tff(8409,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8410,plain,
% 2.45/2.65 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8411,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8410])).
% 2.45/2.65 tff(8412,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.45/2.65 inference(transitivity,[status(thm)],[8411, 8409])).
% 2.45/2.65 tff(8413,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(quant_inst,[status(thm)],[])).
% 2.45/2.65 tff(8414,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8413, 8412])).
% 2.45/2.65 tff(8415,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8414, 198, 5927, 2682, 560, 348, 2])).
% 2.45/2.65 tff(8416,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8417,plain,
% 2.45/2.65 (~b(s(s(z)), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8416, 7878, 8393, 8401, 2])).
% 2.45/2.65 tff(8418,plain,
% 2.45/2.65 (s(s(z)) = elem!1),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[2139, 8417, 8408])).
% 2.45/2.65 tff(8419,plain,
% 2.45/2.65 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8418])).
% 2.45/2.65 tff(8420,plain,
% 2.45/2.65 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.45/2.65 inference(symmetry,[status(thm)],[8419])).
% 2.45/2.65 tff(8421,plain,
% 2.45/2.65 (b(s(z), s(s(z)))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[7878, 8420])).
% 2.45/2.65 tff(8422,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8406, 8421])).
% 2.45/2.65 tff(8423,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8424,plain,
% 2.45/2.65 (~r(s(z), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8423, 153, 2, 1475])).
% 2.45/2.65 tff(8425,plain,
% 2.45/2.65 (b(s(z), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[40, 8424])).
% 2.45/2.65 tff(8426,plain,
% 2.45/2.65 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[4981, 152, 153, 4934])).
% 2.45/2.65 tff(8427,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[420, 8426])).
% 2.45/2.65 tff(8428,plain,
% 2.45/2.65 (~b(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[7270, 6518, 153, 406, 2, 3615])).
% 2.45/2.65 tff(8429,plain,
% 2.45/2.65 (r(s(s(z)), s(z))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[487, 8428])).
% 2.45/2.65 tff(8430,plain,
% 2.45/2.65 (~r(s(z), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3636, 8429, 153, 406])).
% 2.45/2.65 tff(8431,plain,
% 2.45/2.65 (s(z) = elem!1),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[217, 8430, 149])).
% 2.45/2.65 tff(8432,plain,
% 2.45/2.65 (s(s(z)) = s(elem!1)),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8431])).
% 2.45/2.65 tff(8433,plain,
% 2.45/2.65 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8432])).
% 2.45/2.65 tff(8434,plain,
% 2.45/2.65 (elem!1 = s(z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[2914, 8431])).
% 2.45/2.65 tff(8435,plain,
% 2.45/2.65 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8432])).
% 2.45/2.65 tff(8436,plain,
% 2.45/2.65 (r(z, s(elem!1))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[153, 8435])).
% 2.45/2.65 tff(8437,plain,
% 2.45/2.65 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8431])).
% 2.45/2.65 tff(8438,plain,
% 2.45/2.65 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.45/2.65 inference(symmetry,[status(thm)],[8437])).
% 2.45/2.65 tff(8439,plain,
% 2.45/2.65 (~b(s(elem!1), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[4570, 8434, 8428])).
% 2.45/2.65 tff(8440,plain,
% 2.45/2.65 (~(z = elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[4923, 149, 1185])).
% 2.45/2.65 tff(8441,plain,
% 2.45/2.65 (~(s(elem!1) = elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[778, 8431, 8440])).
% 2.45/2.65 tff(8442,plain,
% 2.45/2.65 (r(s(elem!1), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[856, 8441, 8439])).
% 2.45/2.65 tff(8443,plain,
% 2.45/2.65 (r(s(elem!1), s(z))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8442, 8438])).
% 2.45/2.65 tff(8444,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8445,plain,
% 2.45/2.65 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8446,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8445])).
% 2.45/2.65 tff(8447,plain,
% 2.45/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))))),
% 2.45/2.65 inference(transitivity,[status(thm)],[8446, 8444])).
% 2.45/2.65 tff(8448,plain,
% 2.45/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 2.45/2.65 inference(quant_inst,[status(thm)],[])).
% 2.45/2.65 tff(8449,plain,
% 2.45/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1)))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 2.45/2.65 tff(8450,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8449, 163, 791, 406, 1637, 3920])).
% 2.45/2.65 tff(8451,plain,((~r(s(elem!1), s(z))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8452,plain,
% 2.45/2.65 (~r(s(z), s(elem!1))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8451, 8443, 406, 8436])).
% 2.45/2.65 tff(8453,plain,
% 2.45/2.65 (~r(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[5120, 8452, 8434])).
% 2.45/2.65 tff(8454,plain,
% 2.45/2.65 (b(s(z), s(s(z)))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[403, 8453])).
% 2.45/2.65 tff(8455,plain,
% 2.45/2.65 (~b(s(s(z)), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[6226, 8454, 3615, 1185, 6518])).
% 2.45/2.65 tff(8456,plain,
% 2.45/2.65 (r(s(s(z)), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[345, 8455])).
% 2.45/2.65 tff(8457,plain,
% 2.45/2.65 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[4031, 8456, 406, 152])).
% 2.45/2.65 tff(8458,plain,
% 2.45/2.65 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[374, 8457])).
% 2.45/2.65 tff(8459,plain,
% 2.45/2.65 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8458, 8433])).
% 2.45/2.65 tff(8460,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8432])).
% 2.45/2.65 tff(8461,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[6518, 8460])).
% 2.45/2.65 tff(8462,plain,
% 2.45/2.65 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8431])).
% 2.45/2.65 tff(8463,plain,
% 2.45/2.65 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[3615, 8462])).
% 2.45/2.65 tff(8464,plain,
% 2.45/2.65 (~(elem!1 = s(elem!1))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[1400, 8441])).
% 2.45/2.65 tff(8465,plain,
% 2.45/2.65 (~r(elem!1, s(elem!1))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[1483, 8436, 1475, 8442])).
% 2.45/2.65 tff(8466,plain,
% 2.45/2.65 (b(elem!1, s(elem!1))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[1416, 8465, 8464])).
% 2.45/2.65 tff(8467,plain,
% 2.45/2.65 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8468,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8467])).
% 2.45/2.65 tff(8469,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(transitivity,[status(thm)],[8468, 4585])).
% 2.45/2.65 tff(8470,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))),
% 2.45/2.65 inference(quant_inst,[status(thm)],[])).
% 2.45/2.65 tff(8471,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8470, 8469])).
% 2.45/2.65 tff(8472,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8471, 198, 8466, 8463, 8461, 8459])).
% 2.45/2.65 tff(8473,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8474,plain,
% 2.45/2.65 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8473, 149, 3615, 1185, 1475, 153, 406, 2])).
% 2.45/2.65 tff(8475,plain,
% 2.45/2.65 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[176, 8474])).
% 2.45/2.65 tff(8476,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8477,plain,
% 2.45/2.65 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8478,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8477])).
% 2.45/2.65 tff(8479,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(transitivity,[status(thm)],[8478, 8476])).
% 2.45/2.65 tff(8480,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)))),
% 2.45/2.65 inference(quant_inst,[status(thm)],[])).
% 2.45/2.65 tff(8481,plain,
% 2.45/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[8480, 8479])).
% 2.45/2.65 tff(8482,plain,
% 2.45/2.65 ($false),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8481, 198, 1185, 3615, 331, 330])).
% 2.45/2.65 tff(8483,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.65 tff(8484,plain,
% 2.45/2.65 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[8483, 8475, 3615, 1185])).
% 2.45/2.65 tff(8485,plain,
% 2.45/2.65 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[31, 8484])).
% 2.45/2.65 tff(8486,plain,
% 2.45/2.65 (~r(s(z), elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[3636, 3628, 153, 406])).
% 2.45/2.65 tff(8487,plain,
% 2.45/2.65 (s(z) = elem!1),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[217, 8486, 149])).
% 2.45/2.65 tff(8488,plain,
% 2.45/2.65 (~(s(elem!1) = elem!1)),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[778, 8487, 8440])).
% 2.45/2.65 tff(8489,plain,
% 2.45/2.65 (~(elem!1 = s(elem!1))),
% 2.45/2.65 inference(unit_resolution,[status(thm)],[1400, 8488])).
% 2.45/2.65 tff(8490,plain,
% 2.45/2.65 (s(s(z)) = s(elem!1)),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8487])).
% 2.45/2.65 tff(8491,plain,
% 2.45/2.65 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8490])).
% 2.45/2.65 tff(8492,plain,
% 2.45/2.65 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[348, 8491])).
% 2.45/2.65 tff(8493,plain,
% 2.45/2.65 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8487])).
% 2.45/2.65 tff(8494,plain,
% 2.45/2.65 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[3615, 8493])).
% 2.45/2.65 tff(8495,plain,
% 2.45/2.65 (b(s(z), z) <=> b(elem!1, z)),
% 2.45/2.65 inference(monotonicity,[status(thm)],[8487])).
% 2.45/2.65 tff(8496,plain,
% 2.45/2.65 (b(elem!1, z)),
% 2.45/2.65 inference(modus_ponens,[status(thm)],[1185, 8495])).
% 2.45/2.65 tff(8497,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8498,plain,
% 2.45/2.65 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.65 inference(rewrite,[status(thm)],[])).
% 2.45/2.65 tff(8499,plain,
% 2.45/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8498])).
% 2.45/2.66 tff(8500,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8499, 8497])).
% 2.45/2.66 tff(8501,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))),
% 2.45/2.66 inference(quant_inst,[status(thm)],[])).
% 2.45/2.66 tff(8502,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8501, 8500])).
% 2.45/2.66 tff(8503,plain,
% 2.45/2.66 (~b(elem!1, s(elem!1))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8502, 198, 8496, 8494, 8475, 8492])).
% 2.45/2.66 tff(8504,plain,
% 2.45/2.66 (elem!1 = s(z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2914, 8487])).
% 2.45/2.66 tff(8505,plain,
% 2.45/2.66 (~b(s(elem!1), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4570, 8504, 3627])).
% 2.45/2.66 tff(8506,plain,
% 2.45/2.66 (r(s(elem!1), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[856, 8488, 8505])).
% 2.45/2.66 tff(8507,plain,
% 2.45/2.66 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8490])).
% 2.45/2.66 tff(8508,plain,
% 2.45/2.66 (r(z, s(elem!1))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[153, 8507])).
% 2.45/2.66 tff(8509,plain,
% 2.45/2.66 (~r(elem!1, s(elem!1))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1483, 8508, 1475, 8506])).
% 2.45/2.66 tff(8510,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1416, 8509, 8503, 8489])).
% 2.45/2.66 tff(8511,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | b(s(z), elem!1) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8512,plain,
% 2.45/2.66 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8511, 149, 153, 3615, 1185, 1475, 406, 2])).
% 2.45/2.66 tff(8513,plain,
% 2.45/2.66 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[374, 8512])).
% 2.45/2.66 tff(8514,plain,
% 2.45/2.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[7452, 8513, 8485, 153])).
% 2.45/2.66 tff(8515,plain,
% 2.45/2.66 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[420, 8514])).
% 2.45/2.66 tff(8516,plain,
% 2.45/2.66 (~b(s(s(z)), s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[7270, 8515, 153, 406, 2, 3615])).
% 2.45/2.66 tff(8517,plain,
% 2.45/2.66 (r(s(s(z)), s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[487, 8516])).
% 2.45/2.66 tff(8518,plain,
% 2.45/2.66 (~r(s(z), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[3636, 8517, 153, 406])).
% 2.45/2.66 tff(8519,plain,
% 2.45/2.66 (s(z) = elem!1),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[217, 8518, 149])).
% 2.45/2.66 tff(8520,plain,
% 2.45/2.66 (b(s(z), z) <=> b(elem!1, z)),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8519])).
% 2.45/2.66 tff(8521,plain,
% 2.45/2.66 (b(elem!1, z)),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[1185, 8520])).
% 2.45/2.66 tff(8522,plain,
% 2.45/2.66 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8519])).
% 2.45/2.66 tff(8523,plain,
% 2.45/2.66 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8522, 113])).
% 2.45/2.66 tff(8524,plain,
% 2.45/2.66 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8523])).
% 2.45/2.66 tff(8525,plain,
% 2.45/2.66 (~(elem!1 = s(s(elem!1)))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[620, 8524])).
% 2.45/2.66 tff(8526,plain,
% 2.45/2.66 (elem!1 = s(z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2914, 8519])).
% 2.45/2.66 tff(8527,plain,
% 2.45/2.66 (~b(s(elem!1), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4570, 8526, 8516])).
% 2.45/2.66 tff(8528,plain,
% 2.45/2.66 (~(s(elem!1) = elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[778, 8519, 8440])).
% 2.45/2.66 tff(8529,plain,
% 2.45/2.66 (r(s(elem!1), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[856, 8528, 8527])).
% 2.45/2.66 tff(8530,plain,
% 2.45/2.66 (s(s(z)) = s(elem!1)),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8519])).
% 2.45/2.66 tff(8531,plain,
% 2.45/2.66 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8530])).
% 2.45/2.66 tff(8532,plain,
% 2.45/2.66 (r(z, s(elem!1))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[153, 8531])).
% 2.45/2.66 tff(8533,plain,
% 2.45/2.66 (~r(elem!1, s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1899, 8532, 1475, 8529])).
% 2.45/2.66 tff(8534,plain,
% 2.45/2.66 (b(elem!1, s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[147, 8533, 8525])).
% 2.45/2.66 tff(8535,plain,
% 2.45/2.66 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8530])).
% 2.45/2.66 tff(8536,plain,
% 2.45/2.66 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8519])).
% 2.45/2.66 tff(8537,plain,
% 2.45/2.66 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.45/2.66 inference(symmetry,[status(thm)],[8536])).
% 2.45/2.66 tff(8538,plain,
% 2.45/2.66 (r(s(elem!1), s(z))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8529, 8537])).
% 2.45/2.66 tff(8539,plain,
% 2.45/2.66 (~r(s(z), s(elem!1))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8451, 8538, 406, 8532])).
% 2.45/2.66 tff(8540,plain,
% 2.45/2.66 (~r(s(z), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5120, 8539, 8526])).
% 2.45/2.66 tff(8541,plain,
% 2.45/2.66 (b(s(z), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[403, 8540])).
% 2.45/2.66 tff(8542,plain,
% 2.45/2.66 (~b(s(s(z)), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[6226, 8541, 3615, 1185, 8515])).
% 2.45/2.66 tff(8543,plain,
% 2.45/2.66 (r(s(s(z)), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[345, 8542])).
% 2.45/2.66 tff(8544,plain,
% 2.45/2.66 (r(s(elem!1), z)),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8543, 8535])).
% 2.45/2.66 tff(8545,plain,
% 2.45/2.66 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8530])).
% 2.45/2.66 tff(8546,plain,
% 2.45/2.66 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8545, 803])).
% 2.45/2.66 tff(8547,plain,
% 2.45/2.66 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8546])).
% 2.45/2.66 tff(8548,plain,
% 2.45/2.66 (~(s(elem!1) = s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[814, 8440])).
% 2.45/2.66 tff(8549,plain,
% 2.45/2.66 (~(s(s(z)) = s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[822, 8548])).
% 2.45/2.66 tff(8550,plain,
% 2.45/2.66 (~(s(s(elem!1)) = s(elem!1))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8549, 8547])).
% 2.45/2.66 tff(8551,plain,
% 2.45/2.66 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8530])).
% 2.45/2.66 tff(8552,plain,
% 2.45/2.66 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8515, 8551])).
% 2.45/2.66 tff(8553,plain,
% 2.45/2.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[3973, 8513, 8485, 153])).
% 2.45/2.66 tff(8554,plain,
% 2.45/2.66 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[7345, 8519])).
% 2.45/2.66 tff(8555,plain,
% 2.45/2.66 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[3249, 8554])).
% 2.45/2.66 tff(8556,plain,
% 2.45/2.66 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4221, 8555, 8553])).
% 2.45/2.66 tff(8557,plain,
% 2.45/2.66 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2833, 8519, 2])).
% 2.45/2.66 tff(8558,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8559,plain,
% 2.45/2.66 (((~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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8560,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8559])).
% 2.45/2.66 tff(8561,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, 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(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8560, 8558])).
% 2.45/2.66 tff(8562,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.45/2.66 inference(quant_inst,[status(thm)],[])).
% 2.45/2.66 tff(8563,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8562, 8561])).
% 2.45/2.66 tff(8564,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8563, 198, 1145, 68, 831, 6080, 3317])).
% 2.45/2.66 tff(8565,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8566,plain,
% 2.45/2.66 (~b(s(s(elem!1)), s(elem!1))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8565, 8534, 8557, 8556, 8552])).
% 2.45/2.66 tff(8567,plain,
% 2.45/2.66 (r(s(s(elem!1)), s(elem!1))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1143, 8566, 8550])).
% 2.45/2.66 tff(8568,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2184, 163, 1221, 790, 1773, 406])).
% 2.45/2.66 tff(8569,plain,((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8570,plain,
% 2.45/2.66 (~r(s(s(elem!1)), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8569, 8567, 406, 8544])).
% 2.45/2.66 tff(8571,plain,
% 2.45/2.66 (b(s(s(elem!1)), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[801, 8570])).
% 2.45/2.66 tff(8572,plain,
% 2.45/2.66 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[826])).
% 2.45/2.66 tff(8573,plain,
% 2.45/2.66 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(symmetry,[status(thm)],[8572])).
% 2.45/2.66 tff(8574,plain,
% 2.45/2.66 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[3272, 8573])).
% 2.45/2.66 tff(8575,plain,
% 2.45/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8576,plain,
% 2.45/2.66 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8577,plain,
% 2.45/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8576])).
% 2.45/2.66 tff(8578,plain,
% 2.45/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8577, 8575])).
% 2.45/2.66 tff(8579,plain,
% 2.45/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.45/2.66 inference(quant_inst,[status(thm)],[])).
% 2.45/2.66 tff(8580,plain,
% 2.45/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8579, 8578])).
% 2.45/2.66 tff(8581,plain,
% 2.45/2.66 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8580, 163, 791, 1773, 1098])).
% 2.45/2.66 tff(8582,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8581, 8574])).
% 2.45/2.66 tff(8583,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8584,plain,
% 2.45/2.66 (~r(z, s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8583, 8567, 8513, 8519, 8532])).
% 2.45/2.66 tff(8585,plain,
% 2.45/2.66 (b(z, s(s(elem!1)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1096, 8584])).
% 2.45/2.66 tff(8586,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[1071, 8585, 8571, 8534, 8521])).
% 2.45/2.66 tff(8587,plain,(b(s(z), elem!1) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8588,plain,
% 2.45/2.66 (~r(z, s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8587, 3615, 8425, 149, 1475, 153, 2])).
% 2.45/2.66 tff(8589,plain,
% 2.45/2.66 (b(z, s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[593, 8588])).
% 2.45/2.66 tff(8590,plain,
% 2.45/2.66 (b(z, elem!1) <=> b(z, s(z))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[229])).
% 2.45/2.66 tff(8591,plain,
% 2.45/2.66 (b(z, s(z)) <=> b(z, elem!1)),
% 2.45/2.66 inference(symmetry,[status(thm)],[8590])).
% 2.45/2.66 tff(8592,plain,
% 2.45/2.66 (b(z, elem!1)),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[595, 8591])).
% 2.45/2.66 tff(8593,plain,
% 2.45/2.66 (s(s(z)) = s(elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[234, 229])).
% 2.45/2.66 tff(8594,plain,
% 2.45/2.66 (s(z) = elem!1),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[227, 8593])).
% 2.45/2.66 tff(8595,plain,
% 2.45/2.66 (~b(z, elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5328, 8594, 1185, 3615, 3745, 2, 595, 153, 482, 3])).
% 2.45/2.66 tff(8596,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8595, 8592])).
% 2.45/2.66 tff(8597,plain,((~(elem!1 = s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | b(s(s(z)), s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8598,plain,
% 2.45/2.66 (~(elem!1 = s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8597, 8589, 8425, 3615, 8427, 2, 153, 482, 7301])).
% 2.45/2.66 tff(8599,plain,
% 2.45/2.66 (~(s(z) = elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2914, 8598])).
% 2.45/2.66 tff(8600,plain,
% 2.45/2.66 (r(s(z), elem!1)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[217, 8599, 149])).
% 2.45/2.66 tff(8601,plain,
% 2.45/2.66 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4967, 8589, 8425, 3615, 2])).
% 2.45/2.66 tff(8602,plain,
% 2.45/2.66 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[31, 8601])).
% 2.45/2.66 tff(8603,plain,
% 2.45/2.66 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4977, 8589, 8425, 4934, 2, 153])).
% 2.45/2.66 tff(8604,plain,
% 2.45/2.66 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[374, 8603])).
% 2.45/2.66 tff(8605,plain,
% 2.45/2.66 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5337, 8600, 3615, 8604, 2, 4934, 8427])).
% 2.45/2.66 tff(8606,plain,
% 2.45/2.66 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[3098, 8605])).
% 2.45/2.66 tff(8607,plain,
% 2.45/2.66 (~r(z, s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5347, 163, 8606, 8602, 152])).
% 2.45/2.66 tff(8608,plain,
% 2.45/2.66 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8030, 8607, 1475])).
% 2.45/2.66 tff(8609,plain,
% 2.45/2.66 (b(z, s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4110, 8607])).
% 2.45/2.66 tff(8610,plain,
% 2.45/2.66 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[3788])).
% 2.45/2.66 tff(8611,plain,
% 2.45/2.66 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), elem!1)),
% 2.45/2.66 inference(symmetry,[status(thm)],[8610])).
% 2.45/2.66 tff(8612,plain,
% 2.45/2.66 (b(s(z), elem!1)),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[3615, 8611])).
% 2.45/2.66 tff(8613,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[149, 8612])).
% 2.45/2.66 tff(8614,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8615,plain,
% 2.45/2.66 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8614, 3615, 149])).
% 2.45/2.66 tff(8616,plain,
% 2.45/2.66 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[3787])).
% 2.45/2.66 tff(8617,plain,
% 2.45/2.66 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[673, 8616])).
% 2.45/2.66 tff(8618,plain,
% 2.45/2.66 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5001, 348, 3450, 152, 153])).
% 2.45/2.66 tff(8619,plain,
% 2.45/2.66 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[3841, 8618])).
% 2.45/2.66 tff(8620,plain,
% 2.45/2.66 (~b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5008, 198, 1185, 595, 8619])).
% 2.45/2.66 tff(8621,plain,
% 2.45/2.66 (r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[469, 8620])).
% 2.45/2.66 tff(8622,plain,
% 2.45/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8623,plain,
% 2.45/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.45/2.66 inference(quant_inst,[status(thm)],[])).
% 2.45/2.66 tff(8624,plain,
% 2.45/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8623, 8622])).
% 2.45/2.66 tff(8625,plain,
% 2.45/2.66 (~r(elem!1, s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8624, 163, 236, 259, 3450])).
% 2.45/2.66 tff(8626,plain,
% 2.45/2.66 (b(elem!1, s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 8625])).
% 2.45/2.66 tff(8627,plain,
% 2.45/2.66 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5335, 163, 236, 3450, 422])).
% 2.45/2.66 tff(8628,plain,
% 2.45/2.66 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[511, 26, 508, 8627])).
% 2.45/2.66 tff(8629,plain,
% 2.45/2.66 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5361, 163, 236, 3450, 422])).
% 2.45/2.66 tff(8630,plain,
% 2.45/2.66 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[2715, 26, 507, 8629])).
% 2.45/2.66 tff(8631,plain,
% 2.45/2.66 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[5548, 163, 236, 259, 422])).
% 2.45/2.66 tff(8632,plain,
% 2.45/2.66 (b(elem!1, s(s(s(s(s(z))))))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[4810, 8631, 5530])).
% 2.45/2.66 tff(8633,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8634,plain,
% 2.45/2.66 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8635,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8634])).
% 2.45/2.66 tff(8636,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(transitivity,[status(thm)],[8635, 8633])).
% 2.45/2.66 tff(8637,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.45/2.66 inference(quant_inst,[status(thm)],[])).
% 2.45/2.66 tff(8638,plain,
% 2.45/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.45/2.66 inference(modus_ponens,[status(thm)],[8637, 8636])).
% 2.45/2.66 tff(8639,plain,
% 2.45/2.66 ($false),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8638, 198, 8632, 5428, 4167, 8630, 8628, 8626])).
% 2.45/2.66 tff(8640,plain,((~r(elem!1, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.66 tff(8641,plain,
% 2.45/2.66 (~r(elem!1, s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[8640, 5011, 8619, 5428, 5530, 236, 8621, 3450])).
% 2.45/2.66 tff(8642,plain,
% 2.45/2.66 (b(elem!1, s(z))),
% 2.45/2.66 inference(unit_resolution,[status(thm)],[242, 8641, 237])).
% 2.45/2.66 tff(8643,plain,
% 2.45/2.66 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.45/2.66 inference(rewrite,[status(thm)],[])).
% 2.45/2.66 tff(8644,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 2.45/2.66 inference(monotonicity,[status(thm)],[8643])).
% 2.45/2.66 tff(8645,plain,
% 2.45/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8644, 1439])).
% 2.45/2.67 tff(8646,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8647,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8646, 8645])).
% 2.45/2.67 tff(8648,plain,
% 2.45/2.67 (~b(elem!1, z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8647, 198, 1185, 8642, 595])).
% 2.45/2.67 tff(8649,plain,
% 2.45/2.67 (r(elem!1, z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[187, 8648, 76])).
% 2.45/2.67 tff(8650,plain,
% 2.45/2.67 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5560, 8649, 153, 152])).
% 2.45/2.67 tff(8651,plain,
% 2.45/2.67 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5361, 163, 236, 3450, 8621])).
% 2.45/2.67 tff(8652,plain,
% 2.45/2.67 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[2715, 26, 507, 8651])).
% 2.45/2.67 tff(8653,plain,
% 2.45/2.67 (~b(s(s(z)), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[4296, 198, 5428, 8619, 8652])).
% 2.45/2.67 tff(8654,plain,
% 2.45/2.67 (r(s(s(z)), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[345, 8653])).
% 2.45/2.67 tff(8655,plain,
% 2.45/2.67 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5596, 8649, 152, 8654, 673, 153, 5011, 348])).
% 2.45/2.67 tff(8656,plain,
% 2.45/2.67 ($false),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[256, 8655, 8650, 8617])).
% 2.45/2.67 tff(8657,plain,((elem!1 = s(s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~b(z, s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.67 tff(8658,plain,
% 2.45/2.67 (elem!1 = s(s(z))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8657, 8615, 152, 153, 8604, 7302, 8425, 8589, 8598, 8609, 8608, 8600, 4934])).
% 2.45/2.67 tff(8659,plain,
% 2.45/2.67 (s(s(z)) = elem!1),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[4926, 6630])).
% 2.45/2.67 tff(8660,plain,
% 2.45/2.67 ($false),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[2105, 8659])).
% 2.45/2.67 tff(8661,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.45/2.67 tff(8662,plain,
% 2.45/2.67 (s(s(z)) = elem!1),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8661, 8658])).
% 2.45/2.67 tff(8663,plain,
% 2.45/2.67 (s(s(s(z))) = s(elem!1)),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8662])).
% 2.45/2.67 tff(8664,plain,
% 2.45/2.67 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8663])).
% 2.45/2.67 tff(8665,plain,
% 2.45/2.67 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8664])).
% 2.45/2.67 tff(8666,plain,
% 2.45/2.67 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8665])).
% 2.45/2.67 tff(8667,plain,
% 2.45/2.67 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5001, 8604, 4934, 152, 153])).
% 2.45/2.67 tff(8668,plain,
% 2.45/2.67 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[3841, 8667])).
% 2.45/2.67 tff(8669,plain,
% 2.45/2.67 (~b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5008, 198, 8425, 8589, 8668])).
% 2.45/2.67 tff(8670,plain,
% 2.45/2.67 (r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[469, 8669])).
% 2.45/2.67 tff(8671,plain,
% 2.45/2.67 (r(s(s(s(elem!1))), s(z))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8670, 8666])).
% 2.45/2.67 tff(8672,plain,
% 2.45/2.67 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8665])).
% 2.45/2.67 tff(8673,plain,
% 2.45/2.67 (b(z, s(s(s(elem!1))))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8609, 8672])).
% 2.45/2.67 tff(8674,plain,
% 2.45/2.67 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8665])).
% 2.45/2.67 tff(8675,plain,
% 2.45/2.67 (b(s(s(s(elem!1))), z)),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8668, 8674])).
% 2.45/2.67 tff(8676,plain,
% 2.45/2.67 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8662])).
% 2.45/2.67 tff(8677,plain,
% 2.45/2.67 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.45/2.67 inference(transitivity,[status(thm)],[8676, 112])).
% 2.45/2.67 tff(8678,plain,
% 2.45/2.67 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8677, 113])).
% 2.45/2.67 tff(8679,plain,
% 2.45/2.67 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8678])).
% 2.45/2.67 tff(8680,plain,
% 2.45/2.67 (~(elem!1 = s(s(elem!1)))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[7365, 8679])).
% 2.45/2.67 tff(8681,plain,
% 2.45/2.67 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5361, 163, 8600, 4934, 8670])).
% 2.45/2.67 tff(8682,plain,
% 2.45/2.67 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[2715, 26, 507, 8681])).
% 2.45/2.67 tff(8683,plain,
% 2.45/2.67 (~b(s(s(z)), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[4296, 198, 8609, 8668, 8682])).
% 2.45/2.67 tff(8684,plain,
% 2.45/2.67 (~b(elem!1, z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8236, 8662, 8683])).
% 2.45/2.67 tff(8685,plain,
% 2.45/2.67 (r(elem!1, z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[187, 8684, 7302])).
% 2.45/2.67 tff(8686,plain,
% 2.45/2.67 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8677])).
% 2.45/2.67 tff(8687,plain,
% 2.45/2.67 (~(s(s(elem!1)) = elem!1)),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[7365, 8686])).
% 2.45/2.67 tff(8688,plain,
% 2.45/2.67 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(symmetry,[status(thm)],[7338])).
% 2.45/2.67 tff(8689,plain,
% 2.45/2.67 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.45/2.67 inference(transitivity,[status(thm)],[135, 8688, 275, 7833])).
% 2.45/2.67 tff(8690,plain,
% 2.45/2.67 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8689])).
% 2.45/2.67 tff(8691,plain,
% 2.45/2.67 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.45/2.67 inference(symmetry,[status(thm)],[8690])).
% 2.45/2.67 tff(8692,plain,
% 2.45/2.67 (s(s(s(elem!1))) = elem!1),
% 2.45/2.67 inference(transitivity,[status(thm)],[965, 8691, 129])).
% 2.45/2.67 tff(8693,plain,
% 2.45/2.67 ($false),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[7850, 8692])).
% 2.45/2.67 tff(8694,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.67 tff(8695,plain,
% 2.45/2.67 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8694, 8662])).
% 2.45/2.67 tff(8696,plain,
% 2.45/2.67 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8615, 8616])).
% 2.45/2.67 tff(8697,plain,
% 2.45/2.67 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[5560, 8685, 153, 152])).
% 2.45/2.67 tff(8698,plain,
% 2.45/2.67 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[256, 8697, 8696])).
% 2.45/2.67 tff(8699,plain,
% 2.45/2.67 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8662])).
% 2.45/2.67 tff(8700,plain,
% 2.45/2.67 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8604, 8699])).
% 2.45/2.67 tff(8701,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8702,plain,
% 2.45/2.67 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8703,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8702])).
% 2.45/2.67 tff(8704,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8703, 8701])).
% 2.45/2.67 tff(8705,plain,
% 2.45/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8706,plain,
% 2.45/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8705, 8704])).
% 2.45/2.67 tff(8707,plain,
% 2.45/2.67 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8706, 163, 1475, 790, 152])).
% 2.45/2.67 tff(8708,plain,
% 2.45/2.67 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[934, 26, 8707, 930])).
% 2.45/2.67 tff(8709,plain,
% 2.45/2.67 (~r(elem!1, s(s(elem!1)))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[1823, 790, 1475, 833])).
% 2.45/2.67 tff(8710,plain,
% 2.45/2.67 (b(elem!1, s(s(elem!1)))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[147, 8709, 116])).
% 2.45/2.67 tff(8711,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8712,plain,
% 2.45/2.67 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8713,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8712])).
% 2.45/2.67 tff(8714,plain,
% 2.45/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8713, 8711])).
% 2.45/2.67 tff(8715,plain,
% 2.45/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8716,plain,
% 2.45/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8715, 8714])).
% 2.45/2.67 tff(8717,plain,
% 2.45/2.67 (~r(s(s(elem!1)), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8716, 163, 1475, 833, 790])).
% 2.45/2.67 tff(8718,plain,
% 2.45/2.67 (b(s(s(elem!1)), elem!1)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[602, 8717, 138])).
% 2.45/2.67 tff(8719,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8720,plain,
% 2.45/2.67 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, 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))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8721,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8720])).
% 2.45/2.67 tff(8722,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8721, 8719])).
% 2.45/2.67 tff(8723,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8724,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8723, 8722])).
% 2.45/2.67 tff(8725,plain,
% 2.45/2.67 ($false),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8724, 198, 8718, 8710, 707, 831, 8708])).
% 2.45/2.67 tff(8726,plain,((~r(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.67 tff(8727,plain,
% 2.45/2.67 (~r(s(s(elem!1)), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8726, 8700, 8698, 8695, 8687, 1475, 152, 8685, 8680])).
% 2.45/2.67 tff(8728,plain,
% 2.45/2.67 (b(s(s(elem!1)), z)),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[801, 8727])).
% 2.45/2.67 tff(8729,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8730,plain,
% 2.45/2.67 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8731,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8730])).
% 2.45/2.67 tff(8732,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8731, 8729])).
% 2.45/2.67 tff(8733,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8734,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8733, 8732])).
% 2.45/2.67 tff(8735,plain,
% 2.45/2.67 (~b(s(s(elem!1)), s(z))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8734, 198, 8728, 8675, 8673, 8425, 8589])).
% 2.45/2.67 tff(8736,plain,
% 2.45/2.67 (r(s(s(elem!1)), s(z))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[626, 8735])).
% 2.45/2.67 tff(8737,plain,
% 2.45/2.67 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8665])).
% 2.45/2.67 tff(8738,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8739,plain,
% 2.45/2.67 (((~b(s(s(s(s(s(z))))), z)) | (~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(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))))))))),
% 2.45/2.67 inference(rewrite,[status(thm)],[])).
% 2.45/2.67 tff(8740,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))))),
% 2.45/2.67 inference(monotonicity,[status(thm)],[8739])).
% 2.45/2.67 tff(8741,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 2.45/2.67 inference(transitivity,[status(thm)],[8740, 8738])).
% 2.45/2.67 tff(8742,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.45/2.67 inference(quant_inst,[status(thm)],[])).
% 2.45/2.67 tff(8743,plain,
% 2.45/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8742, 8741])).
% 2.45/2.67 tff(8744,plain,
% 2.45/2.67 (~b(s(z), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[8743, 198, 8425, 8609, 8668])).
% 2.45/2.67 tff(8745,plain,
% 2.45/2.67 (r(s(z), s(s(s(s(s(z))))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[3301, 8744])).
% 2.45/2.67 tff(8746,plain,
% 2.45/2.67 (r(s(z), s(s(s(elem!1))))),
% 2.45/2.67 inference(modus_ponens,[status(thm)],[8745, 8737])).
% 2.45/2.67 tff(8747,plain,
% 2.45/2.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[1250, 8687])).
% 2.45/2.67 tff(8748,plain,
% 2.45/2.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.45/2.67 inference(unit_resolution,[status(thm)],[1263, 8747])).
% 2.45/2.67 tff(8749,plain,
% 2.45/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8750,plain,
% 2.45/2.68 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8751,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8750])).
% 2.45/2.68 tff(8752,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8751, 8749])).
% 2.45/2.68 tff(8753,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8754,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8753, 8752])).
% 2.45/2.68 tff(8755,plain,
% 2.45/2.68 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8754, 198, 8728, 8675, 8673])).
% 2.45/2.68 tff(8756,plain,
% 2.45/2.68 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[1377, 8755, 8748])).
% 2.45/2.68 tff(8757,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8758,plain,
% 2.45/2.68 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8759,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8758])).
% 2.45/2.68 tff(8760,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8759, 8757])).
% 2.45/2.68 tff(8761,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8762,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8761, 8760])).
% 2.45/2.68 tff(8763,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8762, 163, 8756, 8746, 8736, 8671])).
% 2.45/2.68 tff(8764,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8765,plain,
% 2.45/2.68 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8764, 152, 1475, 153, 149, 2, 482])).
% 2.45/2.68 tff(8766,plain,
% 2.45/2.68 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3613, 8765])).
% 2.45/2.68 tff(8767,plain,
% 2.45/2.68 (~b(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[4977, 3272, 1185, 4934, 2, 153])).
% 2.45/2.68 tff(8768,plain,
% 2.45/2.68 (r(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[593, 8767])).
% 2.45/2.68 tff(8769,plain,
% 2.45/2.68 (~r(s(z), elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3636, 8768, 153, 4934])).
% 2.45/2.68 tff(8770,plain,
% 2.45/2.68 (s(z) = elem!1),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[217, 8769, 149])).
% 2.45/2.68 tff(8771,plain,
% 2.45/2.68 (s(s(z)) = s(elem!1)),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8770])).
% 2.45/2.68 tff(8772,plain,
% 2.45/2.68 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8771])).
% 2.45/2.68 tff(8773,plain,
% 2.45/2.68 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[3272, 8772])).
% 2.45/2.68 tff(8774,plain,
% 2.45/2.68 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8770])).
% 2.45/2.68 tff(8775,plain,
% 2.45/2.68 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[151, 8774])).
% 2.45/2.68 tff(8776,plain,
% 2.45/2.68 (~(s(elem!1) = elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[778, 8770, 3])).
% 2.45/2.68 tff(8777,plain,
% 2.45/2.68 (elem!1 = s(z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[2914, 8770])).
% 2.45/2.68 tff(8778,plain,
% 2.45/2.68 (~b(s(elem!1), elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[4570, 8777, 482])).
% 2.45/2.68 tff(8779,plain,
% 2.45/2.68 (r(s(elem!1), elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[856, 8778, 8776])).
% 2.45/2.68 tff(8780,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8781,plain,
% 2.45/2.68 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8782,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8781])).
% 2.45/2.68 tff(8783,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8782, 8780])).
% 2.45/2.68 tff(8784,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), elem!1)))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8785,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8784, 8783])).
% 2.45/2.68 tff(8786,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8785, 163, 8779, 8775, 152, 8773])).
% 2.45/2.68 tff(8787,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(z)) | (z = elem!1) | b(s(z), elem!1) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8788,plain,
% 2.45/2.68 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8787, 152, 8766, 482, 7301, 149, 153, 8425, 2])).
% 2.45/2.68 tff(8789,plain,
% 2.45/2.68 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[374, 8788])).
% 2.45/2.68 tff(8790,plain,
% 2.45/2.68 (~r(s(s(s(s(s(z))))), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[5001, 8789, 4934, 152, 153])).
% 2.45/2.68 tff(8791,plain,
% 2.45/2.68 (b(s(s(s(s(s(z))))), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3841, 8790])).
% 2.45/2.68 tff(8792,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8793,plain,
% 2.45/2.68 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8794,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8793])).
% 2.45/2.68 tff(8795,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8794, 8792])).
% 2.45/2.68 tff(8796,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8797,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 2.45/2.68 tff(8798,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8797, 163, 406, 153, 3450, 151])).
% 2.45/2.68 tff(8799,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8800,plain,
% 2.45/2.68 (~r(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8799, 8766, 4934, 153])).
% 2.45/2.68 tff(8801,plain,
% 2.45/2.68 (b(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[593, 8800])).
% 2.45/2.68 tff(8802,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[2662, 198, 1185, 595, 559, 4167])).
% 2.45/2.68 tff(8803,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8804,plain,
% 2.45/2.68 (~b(s(s(s(s(s(z))))), s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8803, 8801, 8425, 8791])).
% 2.45/2.68 tff(8805,plain,
% 2.45/2.68 (r(s(s(s(s(s(z))))), s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[469, 8804])).
% 2.45/2.68 tff(8806,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8807,plain,
% 2.45/2.68 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8808,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8807])).
% 2.45/2.68 tff(8809,plain,
% 2.45/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8808, 8806])).
% 2.45/2.68 tff(8810,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8811,plain,
% 2.45/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8810, 8809])).
% 2.45/2.68 tff(8812,plain,
% 2.45/2.68 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8811, 163, 4934, 8766, 8805])).
% 2.45/2.68 tff(8813,plain,
% 2.45/2.68 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[511, 26, 508, 8812])).
% 2.45/2.68 tff(8814,plain,
% 2.45/2.68 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[5672, 198, 8789, 8427, 8813])).
% 2.45/2.68 tff(8815,plain,
% 2.45/2.68 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3098, 8814])).
% 2.45/2.68 tff(8816,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[5680, 163, 8815, 8766, 152, 8805])).
% 2.45/2.68 tff(8817,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | b(s(s(z)), s(z)) | b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8818,plain,
% 2.45/2.68 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8817, 149, 482, 153, 2, 1475])).
% 2.45/2.68 tff(8819,plain,
% 2.45/2.68 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[176, 8818])).
% 2.45/2.68 tff(8820,plain,
% 2.45/2.68 (~b(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[4953, 8819, 2, 8425])).
% 2.45/2.68 tff(8821,plain,
% 2.45/2.68 (r(z, s(z))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[593, 8820])).
% 2.45/2.68 tff(8822,plain,
% 2.45/2.68 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8587, 8821, 8425, 149, 1475, 153, 2])).
% 2.45/2.68 tff(8823,plain,
% 2.45/2.68 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8799, 8821, 4934, 153])).
% 2.45/2.68 tff(8824,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3613, 8823, 8822])).
% 2.45/2.68 tff(8825,plain,(b(s(z), elem!1) | (~r(z, s(s(z)))) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8826,plain,
% 2.45/2.68 (b(s(z), elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8825, 482, 1475, 2, 153])).
% 2.45/2.68 tff(8827,plain,
% 2.45/2.68 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8799, 406, 3450, 153])).
% 2.45/2.68 tff(8828,plain,
% 2.45/2.68 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3613, 8827])).
% 2.45/2.68 tff(8829,plain,
% 2.45/2.68 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8483, 6210, 1185, 3615])).
% 2.45/2.68 tff(8830,plain,
% 2.45/2.68 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[31, 8829])).
% 2.45/2.68 tff(8831,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[3661, 163, 153, 3450, 8830, 423])).
% 2.45/2.68 tff(8832,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8833,plain,
% 2.45/2.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8832, 8828, 3450, 8425, 153])).
% 2.45/2.68 tff(8834,plain,
% 2.45/2.68 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[420, 8833])).
% 2.45/2.68 tff(8835,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[6565, 163, 406, 328, 153, 3450])).
% 2.45/2.68 tff(8836,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8837,plain,
% 2.45/2.68 (~r(s(z), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8836, 406, 153, 3450])).
% 2.45/2.68 tff(8838,plain,
% 2.45/2.68 (b(s(z), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[403, 8837])).
% 2.45/2.68 tff(8839,plain,
% 2.45/2.68 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8840,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8839])).
% 2.45/2.68 tff(8841,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8840, 3946])).
% 2.45/2.68 tff(8842,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8843,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8842, 8841])).
% 2.45/2.68 tff(8844,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8843, 198, 407, 3615, 348, 3745])).
% 2.45/2.68 tff(8845,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8846,plain,
% 2.45/2.68 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8845, 8838, 8828, 8834])).
% 2.45/2.68 tff(8847,plain,
% 2.45/2.68 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[374, 8846])).
% 2.45/2.68 tff(8848,plain,
% 2.45/2.68 (~b(s(s(z)), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[6226, 8838, 8425, 8828, 8834])).
% 2.45/2.68 tff(8849,plain,
% 2.45/2.68 (r(s(s(z)), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[345, 8848])).
% 2.45/2.68 tff(8850,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8851,plain,
% 2.45/2.68 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(rewrite,[status(thm)],[])).
% 2.45/2.68 tff(8852,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.68 inference(monotonicity,[status(thm)],[8851])).
% 2.45/2.68 tff(8853,plain,
% 2.45/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(transitivity,[status(thm)],[8852, 8850])).
% 2.45/2.68 tff(8854,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.68 inference(quant_inst,[status(thm)],[])).
% 2.45/2.68 tff(8855,plain,
% 2.45/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.68 inference(modus_ponens,[status(thm)],[8854, 8853])).
% 2.45/2.68 tff(8856,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8855, 198, 5927, 2682, 407, 3615, 3745])).
% 2.45/2.68 tff(8857,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8858,plain,
% 2.45/2.68 (~b(s(s(z)), elem!1)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8857, 8838, 5927, 8828, 8834])).
% 2.45/2.68 tff(8859,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[5923, 163, 406, 328, 153, 3272])).
% 2.45/2.68 tff(8860,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8861,plain,
% 2.45/2.68 (~r(s(z), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[8860, 3272, 153, 406])).
% 2.45/2.68 tff(8862,plain,
% 2.45/2.68 (b(s(z), s(s(z)))),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[403, 8861])).
% 2.45/2.68 tff(8863,plain,
% 2.45/2.68 (~r(s(s(z)), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[4031, 152, 406, 3272])).
% 2.45/2.68 tff(8864,plain,
% 2.45/2.68 (b(s(s(z)), z)),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[345, 8863])).
% 2.45/2.68 tff(8865,plain,
% 2.45/2.68 ($false),
% 2.45/2.68 inference(unit_resolution,[status(thm)],[6226, 8864, 6518, 3615, 1185, 8862])).
% 2.45/2.68 tff(8866,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.68 tff(8867,plain,
% 2.45/2.69 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8866, 8847, 8425, 406, 8828, 153, 2])).
% 2.45/2.69 tff(8868,plain,
% 2.45/2.69 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[176, 8867])).
% 2.45/2.69 tff(8869,plain,
% 2.45/2.69 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8483, 330, 3615, 1185])).
% 2.45/2.69 tff(8870,plain,
% 2.45/2.69 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[31, 8869])).
% 2.45/2.69 tff(8871,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8872,plain,
% 2.45/2.69 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8873,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8872])).
% 2.45/2.69 tff(8874,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8873, 8871])).
% 2.45/2.69 tff(8875,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8876,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8875, 8874])).
% 2.45/2.69 tff(8877,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8876, 163, 3272, 332, 258, 33])).
% 2.45/2.69 tff(8878,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8879,plain,
% 2.45/2.69 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8878, 332, 3272, 8870])).
% 2.45/2.69 tff(8880,plain,
% 2.45/2.69 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(elem!1, z)),
% 2.45/2.69 inference(monotonicity,[status(thm)],[245])).
% 2.45/2.69 tff(8881,plain,
% 2.45/2.69 (b(elem!1, z)),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[330, 8880])).
% 2.45/2.69 tff(8882,plain,
% 2.45/2.69 (~(s(s(elem!1)) = elem!1)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[118, 318])).
% 2.45/2.69 tff(8883,plain,
% 2.45/2.69 (~(s(elem!1) = elem!1)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1395, 8882])).
% 2.45/2.69 tff(8884,plain,
% 2.45/2.69 (~(elem!1 = s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1400, 8883])).
% 2.45/2.69 tff(8885,plain,
% 2.45/2.69 (r(s(s(z)), elem!1)),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[3272, 329])).
% 2.45/2.69 tff(8886,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8887,plain,
% 2.45/2.69 (((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8888,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8887])).
% 2.45/2.69 tff(8889,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8888, 8886])).
% 2.45/2.69 tff(8890,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8891,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8890, 8889])).
% 2.45/2.69 tff(8892,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8891, 163, 1475, 1473, 2113, 332])).
% 2.45/2.69 tff(8893,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8894,plain,
% 2.45/2.69 (~r(elem!1, s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8893, 8885, 1475, 332])).
% 2.45/2.69 tff(8895,plain,
% 2.45/2.69 (b(elem!1, s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1416, 8894, 8884])).
% 2.45/2.69 tff(8896,plain,
% 2.45/2.69 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[245])).
% 2.45/2.69 tff(8897,plain,
% 2.45/2.69 ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8896])).
% 2.45/2.69 tff(8898,plain,
% 2.45/2.69 (~r(elem!1, s(s(elem!1)))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[669, 8897])).
% 2.45/2.69 tff(8899,plain,
% 2.45/2.69 (b(elem!1, s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[147, 8898, 318])).
% 2.45/2.69 tff(8900,plain,
% 2.45/2.69 (~(s(elem!1) = s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[140, 8882])).
% 2.45/2.69 tff(8901,plain,
% 2.45/2.69 (~(s(s(elem!1)) = s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1138, 8900])).
% 2.45/2.69 tff(8902,plain,
% 2.45/2.69 (~b(s(elem!1), s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1426, 1145, 68, 1418])).
% 2.45/2.69 tff(8903,plain,
% 2.45/2.69 (r(s(elem!1), s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[901, 8902, 6708])).
% 2.45/2.69 tff(8904,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[7000, 198, 271, 1175, 1145, 68, 1418])).
% 2.45/2.69 tff(8905,plain,((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8906,plain,
% 2.45/2.69 (~b(s(elem!1), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8905, 1145, 271, 68, 1418])).
% 2.45/2.69 tff(8907,plain,
% 2.45/2.69 (r(s(elem!1), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1217, 8906])).
% 2.45/2.69 tff(8908,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8909,plain,
% 2.45/2.69 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8910,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8909])).
% 2.45/2.69 tff(8911,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8910, 8908])).
% 2.45/2.69 tff(8912,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8913,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8912, 8911])).
% 2.45/2.69 tff(8914,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8913, 163, 1475, 1221, 790, 1220])).
% 2.45/2.69 tff(8915,plain,((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8916,plain,
% 2.45/2.69 (~r(s(s(elem!1)), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8915, 8907, 1475, 8903])).
% 2.45/2.69 tff(8917,plain,
% 2.45/2.69 (b(s(s(elem!1)), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[801, 8916])).
% 2.45/2.69 tff(8918,plain,
% 2.45/2.69 (~b(z, s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1071, 8917, 68, 271])).
% 2.45/2.69 tff(8919,plain,
% 2.45/2.69 (r(z, s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1096, 8918])).
% 2.45/2.69 tff(8920,plain,
% 2.45/2.69 (~r(s(s(elem!1)), s(z))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1229, 8919, 8907, 8903])).
% 2.45/2.69 tff(8921,plain,
% 2.45/2.69 (b(s(s(elem!1)), s(z))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[626, 8920])).
% 2.45/2.69 tff(8922,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8923,plain,
% 2.45/2.69 (((~b(elem!1, s(elem!1))) | (~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(z), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8924,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8923])).
% 2.45/2.69 tff(8925,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8924, 8922])).
% 2.45/2.69 tff(8926,plain,
% 2.45/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8927,plain,
% 2.45/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8926, 8925])).
% 2.45/2.69 tff(8928,plain,
% 2.45/2.69 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8927, 198, 5927, 1145, 1418])).
% 2.45/2.69 tff(8929,plain,
% 2.45/2.69 (~b(s(s(elem!1)), elem!1)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8928, 8921])).
% 2.45/2.69 tff(8930,plain,
% 2.45/2.69 (r(s(s(elem!1)), elem!1)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[602, 8929, 138])).
% 2.45/2.69 tff(8931,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8932,plain,
% 2.45/2.69 (((~b(s(s(elem!1)), z)) | (~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(elem!1, s(s(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(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8933,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8932])).
% 2.45/2.69 tff(8934,plain,
% 2.45/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8933, 8931])).
% 2.45/2.69 tff(8935,plain,
% 2.45/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8936,plain,
% 2.45/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8935, 8934])).
% 2.45/2.69 tff(8937,plain,
% 2.45/2.69 (~b(s(z), s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8936, 198, 5927, 8917, 68, 1185])).
% 2.45/2.69 tff(8938,plain,
% 2.45/2.69 (r(s(z), s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[642, 8937])).
% 2.45/2.69 tff(8939,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8940,plain,
% 2.45/2.69 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8941,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8940])).
% 2.45/2.69 tff(8942,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8941, 8939])).
% 2.45/2.69 tff(8943,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8944,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8943, 8942])).
% 2.45/2.69 tff(8945,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8944, 163, 1115, 1220, 682, 1637])).
% 2.45/2.69 tff(8946,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8947,plain,
% 2.45/2.69 (~r(s(z), s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8946, 8938, 8930, 8903])).
% 2.45/2.69 tff(8948,plain,
% 2.45/2.69 (r(s(elem!1), s(z))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1173, 8947, 820, 8921, 1145])).
% 2.45/2.69 tff(8949,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8950,plain,
% 2.45/2.69 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(rewrite,[status(thm)],[])).
% 2.45/2.69 tff(8951,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 2.45/2.69 inference(monotonicity,[status(thm)],[8950])).
% 2.45/2.69 tff(8952,plain,
% 2.45/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.45/2.69 inference(transitivity,[status(thm)],[8951, 8949])).
% 2.45/2.69 tff(8953,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 2.45/2.69 inference(quant_inst,[status(thm)],[])).
% 2.45/2.69 tff(8954,plain,
% 2.45/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))),
% 2.45/2.69 inference(modus_ponens,[status(thm)],[8953, 8952])).
% 2.45/2.69 tff(8955,plain,
% 2.45/2.69 ($false),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8954, 163, 8930, 8903, 8938, 8948])).
% 2.45/2.69 tff(8956,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.69 tff(8957,plain,
% 2.45/2.69 (~b(s(s(elem!1)), s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8956, 8899, 5927, 820, 1185, 8882, 8895, 8881, 1475])).
% 2.45/2.69 tff(8958,plain,
% 2.45/2.69 (r(s(s(elem!1)), s(elem!1))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1143, 8957, 8901])).
% 2.45/2.69 tff(8959,plain,
% 2.45/2.69 (~r(s(s(elem!1)), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[8569, 1221, 406, 1773])).
% 2.45/2.69 tff(8960,plain,
% 2.45/2.69 (b(s(s(elem!1)), z)),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[801, 8959])).
% 2.45/2.69 tff(8961,plain,
% 2.45/2.69 (~b(z, s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1071, 8960, 68, 271])).
% 2.45/2.69 tff(8962,plain,
% 2.45/2.69 (r(z, s(s(elem!1)))),
% 2.45/2.69 inference(unit_resolution,[status(thm)],[1096, 8961])).
% 2.45/2.69 tff(8963,plain,
% 2.45/2.70 (~r(s(z), s(s(elem!1)))),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[5192, 1221, 1637, 1773])).
% 2.45/2.70 tff(8964,plain,
% 2.45/2.70 (b(s(z), s(s(elem!1)))),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[642, 8963])).
% 2.45/2.70 tff(8965,plain,
% 2.45/2.70 ($false),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[8936, 198, 5927, 8960, 8964, 68, 1185])).
% 2.45/2.70 tff(8966,plain,((~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.45/2.70 tff(8967,plain,
% 2.45/2.70 (~r(s(z), s(elem!1))),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[8966, 1221, 68, 1185, 1773, 5927, 406])).
% 2.45/2.70 tff(8968,plain,
% 2.45/2.70 (b(s(z), s(elem!1))),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[1164, 8967, 1158])).
% 2.45/2.70 tff(8969,plain,
% 2.45/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.70 inference(rewrite,[status(thm)],[])).
% 2.45/2.70 tff(8970,plain,
% 2.45/2.70 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.70 inference(rewrite,[status(thm)],[])).
% 2.45/2.70 tff(8971,plain,
% 2.45/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.45/2.70 inference(monotonicity,[status(thm)],[8970])).
% 2.45/2.70 tff(8972,plain,
% 2.45/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.70 inference(transitivity,[status(thm)],[8971, 8969])).
% 2.45/2.70 tff(8973,plain,
% 2.45/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.45/2.70 inference(quant_inst,[status(thm)],[])).
% 2.45/2.70 tff(8974,plain,
% 2.45/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.45/2.70 inference(modus_ponens,[status(thm)],[8973, 8972])).
% 2.45/2.70 tff(8975,plain,
% 2.45/2.70 ($false),
% 2.45/2.70 inference(unit_resolution,[status(thm)],[8974, 198, 1801, 1185, 1543, 3615, 330])).
% 2.55/2.70 tff(8976,plain,((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(8977,plain,
% 2.55/2.70 (~b(z, s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8976, 8968, 3615, 1185, 330])).
% 2.55/2.70 tff(8978,plain,
% 2.55/2.70 (r(z, s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1791, 8977])).
% 2.55/2.70 tff(8979,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(8980,plain,
% 2.55/2.70 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(8981,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[8980])).
% 2.55/2.70 tff(8982,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.55/2.70 inference(transitivity,[status(thm)],[8981, 8979])).
% 2.55/2.70 tff(8983,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(8984,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[8983, 8982])).
% 2.55/2.70 tff(8985,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8984, 163, 8978, 1221, 1773, 8962])).
% 2.55/2.70 tff(8986,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(8987,plain,
% 2.55/2.70 (~r(s(elem!1), z)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8986, 8958, 8899, 8881, 3615, 1185, 330, 1157, 406, 5927])).
% 2.55/2.70 tff(8988,plain,
% 2.55/2.70 (b(s(elem!1), z)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1217, 8987])).
% 2.55/2.70 tff(8989,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1994, 198, 271, 1175, 1801, 1418])).
% 2.55/2.70 tff(8990,plain,((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(8991,plain,
% 2.55/2.70 (~b(z, s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8990, 8988, 8895, 8881])).
% 2.55/2.70 tff(8992,plain,
% 2.55/2.70 (r(z, s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1791, 8991])).
% 2.55/2.70 tff(8993,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(8994,plain,
% 2.55/2.70 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(8995,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[8994])).
% 2.55/2.70 tff(8996,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.70 inference(transitivity,[status(thm)],[8995, 8993])).
% 2.55/2.70 tff(8997,plain,
% 2.55/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(8998,plain,
% 2.55/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[8997, 8996])).
% 2.55/2.70 tff(8999,plain,
% 2.55/2.70 (~b(s(z), s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8998, 198, 5927, 8988, 8895, 1185])).
% 2.55/2.70 tff(9000,plain,
% 2.55/2.70 (r(s(z), s(elem!1))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1164, 8999, 1157])).
% 2.55/2.70 tff(9001,plain,
% 2.55/2.70 (~r(s(elem!1), s(z))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8451, 9000, 406, 8992])).
% 2.55/2.70 tff(9002,plain,
% 2.55/2.70 (b(elem!1, s(z))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[251, 245, 2])).
% 2.55/2.70 tff(9003,plain,
% 2.55/2.70 (~b(s(z), s(s(elem!1)))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[8936, 198, 5927, 723, 68, 1185])).
% 2.55/2.70 tff(9004,plain,
% 2.55/2.70 (r(s(z), s(s(elem!1)))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[642, 9003])).
% 2.55/2.70 tff(9005,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[3595, 198, 271, 723, 1328, 68, 1418])).
% 2.55/2.70 tff(9006,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(9007,plain,
% 2.55/2.70 (~b(s(elem!1), s(s(elem!1)))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9006, 723, 271, 68, 1418])).
% 2.55/2.70 tff(9008,plain,
% 2.55/2.70 (r(s(elem!1), s(s(elem!1)))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[901, 9007, 890])).
% 2.55/2.70 tff(9009,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9010,plain,
% 2.55/2.70 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9011,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[9010])).
% 2.55/2.70 tff(9012,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.55/2.70 inference(transitivity,[status(thm)],[9011, 9009])).
% 2.55/2.70 tff(9013,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(9014,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[9013, 9012])).
% 2.55/2.70 tff(9015,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9014, 163, 1773, 9008, 9004, 1637])).
% 2.55/2.70 tff(9016,plain,((~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(9017,plain,
% 2.55/2.70 (~b(s(s(elem!1)), z)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9016, 8958, 9000, 8900, 8881, 8899, 8895, 5927, 1185])).
% 2.55/2.70 tff(9018,plain,
% 2.55/2.70 (r(s(s(elem!1)), z)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[801, 9017])).
% 2.55/2.70 tff(9019,plain,
% 2.55/2.70 (~r(s(elem!1), elem!1)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1781, 9018, 8958, 8992])).
% 2.55/2.70 tff(9020,plain,
% 2.55/2.70 (b(s(elem!1), elem!1)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[856, 9019, 8883])).
% 2.55/2.70 tff(9021,plain,
% 2.55/2.70 (~b(s(elem!1), s(z))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[6683, 9020, 5927, 9002])).
% 2.55/2.70 tff(9022,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[1150, 26, 820, 9021, 9001])).
% 2.55/2.70 tff(9023,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(9024,plain,
% 2.55/2.70 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9023, 3618, 5927, 1185, 406, 3615, 330, 1475, 332, 669, 3272, 2])).
% 2.55/2.70 tff(9025,plain,
% 2.55/2.70 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[256, 9024, 8879])).
% 2.55/2.70 tff(9026,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9027,plain,
% 2.55/2.70 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9028,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[9027])).
% 2.55/2.70 tff(9029,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.70 inference(transitivity,[status(thm)],[9028, 9026])).
% 2.55/2.70 tff(9030,plain,
% 2.55/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(9031,plain,
% 2.55/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[9030, 9029])).
% 2.55/2.70 tff(9032,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9031, 198, 1185, 320, 831, 2, 330])).
% 2.55/2.70 tff(9033,plain,((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(9034,plain,
% 2.55/2.70 (~b(elem!1, s(z))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9033, 9025, 330, 2, 1185])).
% 2.55/2.70 tff(9035,plain,
% 2.55/2.70 (r(elem!1, s(z))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[242, 9034, 6596])).
% 2.55/2.70 tff(9036,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 2.55/2.70 tff(9037,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9038,plain,
% 2.55/2.70 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9039,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[9038])).
% 2.55/2.70 tff(9040,plain,
% 2.55/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.55/2.70 inference(transitivity,[status(thm)],[9039, 9037])).
% 2.55/2.70 tff(9041,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(9042,plain,
% 2.55/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[9041, 9040])).
% 2.55/2.70 tff(9043,plain,
% 2.55/2.70 ($false),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9042, 163, 1475, 259, 406, 9036])).
% 2.55/2.70 tff(9044,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.70 tff(9045,plain,
% 2.55/2.70 (~r(s(z), s(s(s(elem!1))))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9044, 9035, 1475, 406])).
% 2.55/2.70 tff(9046,plain,
% 2.55/2.70 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.55/2.70 inference(commutativity,[status(thm)],[])).
% 2.55/2.70 tff(9047,plain,
% 2.55/2.70 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 2.55/2.70 inference(symmetry,[status(thm)],[9046])).
% 2.55/2.70 tff(9048,plain,
% 2.55/2.70 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 2.55/2.70 inference(monotonicity,[status(thm)],[9047])).
% 2.55/2.70 tff(9049,plain,
% 2.55/2.70 (~(s(z) = s(s(s(elem!1))))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[1282, 9048])).
% 2.55/2.70 tff(9050,plain,
% 2.55/2.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 2.55/2.70 inference(rewrite,[status(thm)],[])).
% 2.55/2.70 tff(9051,plain,
% 2.55/2.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 2.55/2.70 inference(quant_inst,[status(thm)],[])).
% 2.55/2.70 tff(9052,plain,
% 2.55/2.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.55/2.70 inference(modus_ponens,[status(thm)],[9051, 9050])).
% 2.55/2.70 tff(9053,plain,
% 2.55/2.70 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9052, 26])).
% 2.55/2.70 tff(9054,plain,
% 2.55/2.70 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9053, 9049])).
% 2.55/2.70 tff(9055,plain,
% 2.55/2.70 (b(s(z), s(s(s(elem!1))))),
% 2.55/2.70 inference(unit_resolution,[status(thm)],[9054, 9045])).
% 2.55/2.70 tff(9056,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 2.55/2.70 tff(9057,plain,
% 2.55/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9058,plain,
% 2.55/2.71 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9059,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9058])).
% 2.55/2.71 tff(9060,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9059, 9057])).
% 2.55/2.71 tff(9061,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9062,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9061, 9060])).
% 2.55/2.71 tff(9063,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9062, 198, 271, 5927, 1185, 3615, 831])).
% 2.55/2.71 tff(9064,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9065,plain,
% 2.55/2.71 (~b(elem!1, z)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9064, 9025, 3615, 1185, 5927])).
% 2.55/2.71 tff(9066,plain,
% 2.55/2.71 (r(elem!1, z)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[187, 9065, 3617])).
% 2.55/2.71 tff(9067,plain,
% 2.55/2.71 (~r(s(s(z)), elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[6761, 9066, 406, 332])).
% 2.55/2.71 tff(9068,plain,
% 2.55/2.71 (s(s(z)) = elem!1),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[2139, 9067, 9056])).
% 2.55/2.71 tff(9069,plain,
% 2.55/2.71 (~(s(s(s(elem!1))) = elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[2088, 9068])).
% 2.55/2.71 tff(9070,plain,
% 2.55/2.71 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.55/2.71 inference(commutativity,[status(thm)],[])).
% 2.55/2.71 tff(9071,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.55/2.71 tff(9072,plain,
% 2.55/2.71 (s(s(s(elem!1))) = elem!1),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 2.55/2.71 tff(9073,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1297, 9072])).
% 2.55/2.71 tff(9074,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9075,plain,
% 2.55/2.71 (~(elem!1 = s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9074, 9069])).
% 2.55/2.71 tff(9076,plain,
% 2.55/2.71 (~(elem!1 = s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9074, 1297])).
% 2.55/2.71 tff(9077,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9078,plain,
% 2.55/2.71 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9079,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9078])).
% 2.55/2.71 tff(9080,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9079, 9077])).
% 2.55/2.71 tff(9081,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9082,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9081, 9080])).
% 2.55/2.71 tff(9083,plain,
% 2.55/2.71 (~r(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9082, 163, 1475, 833, 1352])).
% 2.55/2.71 tff(9084,plain,
% 2.55/2.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9085,plain,
% 2.55/2.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9086,plain,
% 2.55/2.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9085, 9084])).
% 2.55/2.71 tff(9087,plain,
% 2.55/2.71 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9086, 26])).
% 2.55/2.71 tff(9088,plain,
% 2.55/2.71 (b(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9087, 9083, 9076])).
% 2.55/2.71 tff(9089,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 2.55/2.71 tff(9090,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9091,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9092,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9091, 9090])).
% 2.55/2.71 tff(9093,plain,
% 2.55/2.71 (~r(s(s(s(elem!1))), elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9092, 163, 1475, 833, 1352])).
% 2.55/2.71 tff(9094,plain,
% 2.55/2.71 (b(s(s(s(elem!1))), elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1308, 9093, 1297])).
% 2.55/2.71 tff(9095,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9096,plain,
% 2.55/2.71 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9097,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9096])).
% 2.55/2.71 tff(9098,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9097, 9095])).
% 2.55/2.71 tff(9099,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9100,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9099, 9098])).
% 2.55/2.71 tff(9101,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9100, 198, 5927, 9094, 9089, 9088])).
% 2.55/2.71 tff(9102,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9103,plain,
% 2.55/2.71 (~r(s(s(s(elem!1))), z)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9102, 9069, 9055, 5927, 1475, 9066])).
% 2.55/2.71 tff(9104,plain,
% 2.55/2.71 (b(s(s(s(elem!1))), z)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1295, 9103])).
% 2.55/2.71 tff(9105,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 2.55/2.71 tff(9106,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9107,plain,
% 2.55/2.71 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9108,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9107])).
% 2.55/2.71 tff(9109,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9108, 9106])).
% 2.55/2.71 tff(9110,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9111,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9110, 9109])).
% 2.55/2.71 tff(9112,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9111, 198, 5927, 1311, 9089, 1185, 9105])).
% 2.55/2.71 tff(9113,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9114,plain,
% 2.55/2.71 (~b(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9113, 9104, 5927, 9055, 1185])).
% 2.55/2.71 tff(9115,plain,
% 2.55/2.71 (r(elem!1, s(s(s(elem!1))))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9087, 9114, 9075])).
% 2.55/2.71 tff(9116,plain,
% 2.55/2.71 (~(s(z) = s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1156, 3618])).
% 2.55/2.71 tff(9117,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9118,plain,
% 2.55/2.71 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9119,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9118])).
% 2.55/2.71 tff(9120,plain,
% 2.55/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1))))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9119, 9117])).
% 2.55/2.71 tff(9121,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9122,plain,
% 2.55/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9121, 9120])).
% 2.55/2.71 tff(9123,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9122, 163, 1475, 259, 406, 1637])).
% 2.55/2.71 tff(9124,plain,((~r(s(z), s(elem!1))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9125,plain,
% 2.55/2.71 (~r(s(z), s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9124, 9035, 1475, 406])).
% 2.55/2.71 tff(9126,plain,
% 2.55/2.71 (b(s(z), s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1164, 9125, 9116])).
% 2.55/2.71 tff(9127,plain,
% 2.55/2.71 (~(s(elem!1) = s(s(elem!1)))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[4002, 9068])).
% 2.55/2.71 tff(9128,plain,
% 2.55/2.71 (~(s(s(elem!1)) = s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1138, 9127])).
% 2.55/2.71 tff(9129,plain,
% 2.55/2.71 (~(s(elem!1) = elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1762, 9128])).
% 2.55/2.71 tff(9130,plain,
% 2.55/2.71 (~b(z, s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[8976, 9126, 3615, 1185, 330])).
% 2.55/2.71 tff(9131,plain,
% 2.55/2.71 (r(z, s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1791, 9130])).
% 2.55/2.71 tff(9132,plain,
% 2.55/2.71 (~r(s(elem!1), elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[7523, 9131, 1475, 9066])).
% 2.55/2.71 tff(9133,plain,
% 2.55/2.71 (b(s(elem!1), elem!1)),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[856, 9132, 9129])).
% 2.55/2.71 tff(9134,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9135,plain,
% 2.55/2.71 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(rewrite,[status(thm)],[])).
% 2.55/2.71 tff(9136,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9135])).
% 2.55/2.71 tff(9137,plain,
% 2.55/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.55/2.71 inference(transitivity,[status(thm)],[9136, 9134])).
% 2.55/2.71 tff(9138,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.55/2.71 inference(quant_inst,[status(thm)],[])).
% 2.55/2.71 tff(9139,plain,
% 2.55/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[9138, 9137])).
% 2.55/2.71 tff(9140,plain,
% 2.55/2.71 ($false),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9139, 198, 1802, 5927, 1200, 9089, 1543])).
% 2.55/2.71 tff(9141,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.71 tff(9142,plain,
% 2.55/2.71 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[9141, 9133, 5927, 9055, 9126])).
% 2.55/2.71 tff(9143,plain,
% 2.55/2.71 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9068])).
% 2.55/2.71 tff(9144,plain,
% 2.55/2.71 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.55/2.71 inference(transitivity,[status(thm)],[9143, 112])).
% 2.55/2.71 tff(9145,plain,
% 2.55/2.71 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.55/2.71 inference(monotonicity,[status(thm)],[9144])).
% 2.55/2.71 tff(9146,plain,
% 2.55/2.71 (~(s(s(elem!1)) = elem!1)),
% 2.55/2.71 inference(modus_ponens,[status(thm)],[5276, 9145])).
% 2.55/2.71 tff(9147,plain,
% 2.55/2.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.55/2.71 inference(unit_resolution,[status(thm)],[1250, 9146])).
% 2.55/2.72 tff(9148,plain,
% 2.55/2.72 (r(s(s(s(elem!1))), s(elem!1))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[1339, 9147, 9142])).
% 2.55/2.72 tff(9149,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 2.55/2.72 tff(9150,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9151,plain,
% 2.55/2.72 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9152,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9151])).
% 2.55/2.72 tff(9153,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9152, 9150])).
% 2.55/2.72 tff(9154,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9155,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9154, 9153])).
% 2.55/2.72 tff(9156,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9155, 163, 1475, 1353, 8215, 9149])).
% 2.55/2.72 tff(9157,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.72 tff(9158,plain,
% 2.55/2.72 (~r(z, s(s(s(elem!1))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9157, 9148, 1475, 9115])).
% 2.55/2.72 tff(9159,plain,
% 2.55/2.72 (b(z, s(s(s(elem!1))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[1350, 26, 9158, 1255])).
% 2.55/2.72 tff(9160,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9161,plain,
% 2.55/2.72 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9162,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9161])).
% 2.55/2.72 tff(9163,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9162, 9160])).
% 2.55/2.72 tff(9164,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9165,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9164, 9163])).
% 2.55/2.72 tff(9166,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9165, 198, 9104, 9159, 9055, 1185])).
% 2.55/2.72 tff(9167,plain,((z = elem!1) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(z)), elem!1) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.72 tff(9168,plain,
% 2.55/2.72 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9167, 8868, 1475, 7301, 8425, 5927, 8828, 406, 8858, 2, 8849, 8847])).
% 2.55/2.72 tff(9169,plain,
% 2.55/2.72 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8483, 8868, 8425, 8828])).
% 2.55/2.72 tff(9170,plain,
% 2.55/2.72 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[31, 9169])).
% 2.55/2.72 tff(9171,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3973, 9170, 9168, 8847, 153])).
% 2.55/2.72 tff(9172,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.72 tff(9173,plain,
% 2.55/2.72 (~r(z, s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9172, 8826, 1475, 153, 2, 4934])).
% 2.55/2.72 tff(9174,plain,
% 2.55/2.72 (b(z, s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[593, 9173])).
% 2.55/2.72 tff(9175,plain,
% 2.55/2.72 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4953, 9174, 2, 8425])).
% 2.55/2.72 tff(9176,plain,
% 2.55/2.72 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[176, 9175])).
% 2.55/2.72 tff(9177,plain,
% 2.55/2.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4981, 9176, 153, 4934])).
% 2.55/2.72 tff(9178,plain,
% 2.55/2.72 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[420, 9177])).
% 2.55/2.72 tff(9179,plain,
% 2.55/2.72 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4977, 9174, 8425, 4934, 2, 153])).
% 2.55/2.72 tff(9180,plain,
% 2.55/2.72 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[374, 9179])).
% 2.55/2.72 tff(9181,plain,
% 2.55/2.72 (~r(s(s(s(s(s(z))))), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5001, 9176, 4934, 9180, 153])).
% 2.55/2.72 tff(9182,plain,
% 2.55/2.72 (b(s(s(s(s(s(z))))), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3841, 9181])).
% 2.55/2.72 tff(9183,plain,
% 2.55/2.72 (~b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8803, 9182, 8425, 9174])).
% 2.55/2.72 tff(9184,plain,
% 2.55/2.72 (r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[469, 9183])).
% 2.55/2.72 tff(9185,plain,
% 2.55/2.72 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8811, 163, 3450, 151, 422])).
% 2.55/2.72 tff(9186,plain,
% 2.55/2.72 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[511, 26, 508, 9185])).
% 2.55/2.72 tff(9187,plain,
% 2.55/2.72 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5672, 198, 348, 3745, 9186])).
% 2.55/2.72 tff(9188,plain,
% 2.55/2.72 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3098, 9187])).
% 2.55/2.72 tff(9189,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5680, 163, 9188, 151, 152, 422])).
% 2.55/2.72 tff(9190,plain,((~r(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))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.72 tff(9191,plain,
% 2.55/2.72 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9190, 9176, 9184, 9180, 9178, 4934])).
% 2.55/2.72 tff(9192,plain,
% 2.55/2.72 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3613, 9191])).
% 2.55/2.72 tff(9193,plain,
% 2.55/2.72 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4967, 9192, 8425, 9174, 2])).
% 2.55/2.72 tff(9194,plain,
% 2.55/2.72 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[31, 9193])).
% 2.55/2.72 tff(9195,plain,
% 2.55/2.72 (~b(s(z), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8845, 9192, 9180, 9178])).
% 2.55/2.72 tff(9196,plain,
% 2.55/2.72 (r(s(z), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[403, 9195])).
% 2.55/2.72 tff(9197,plain,
% 2.55/2.72 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[2720, 163, 9196, 4934, 9184])).
% 2.55/2.72 tff(9198,plain,
% 2.55/2.72 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[511, 26, 508, 9197])).
% 2.55/2.72 tff(9199,plain,
% 2.55/2.72 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4057, 9198, 9192, 9178, 2, 9180])).
% 2.55/2.72 tff(9200,plain,
% 2.55/2.72 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3098, 9199])).
% 2.55/2.72 tff(9201,plain,
% 2.55/2.72 (~r(z, s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5347, 163, 9200, 9194, 9176])).
% 2.55/2.72 tff(9202,plain,
% 2.55/2.72 (b(z, s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4110, 9201])).
% 2.55/2.72 tff(9203,plain,
% 2.55/2.72 (~(elem!1 = s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[6595, 8826])).
% 2.55/2.72 tff(9204,plain,
% 2.55/2.72 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8030, 9201, 1475])).
% 2.55/2.72 tff(9205,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9206,plain,
% 2.55/2.72 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9207,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9206])).
% 2.55/2.72 tff(9208,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9207, 9205])).
% 2.55/2.72 tff(9209,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9210,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9209, 9208])).
% 2.55/2.72 tff(9211,plain,
% 2.55/2.72 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9210, 198, 271, 1185, 595, 5428, 4167])).
% 2.55/2.72 tff(9212,plain,
% 2.55/2.72 (r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4810, 9211, 5530])).
% 2.55/2.72 tff(9213,plain,
% 2.55/2.72 (~b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8803, 4167, 1185, 595])).
% 2.55/2.72 tff(9214,plain,
% 2.55/2.72 (r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[469, 9213])).
% 2.55/2.72 tff(9215,plain,
% 2.55/2.72 (~b(elem!1, s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[1444, 198, 271, 1185, 595])).
% 2.55/2.72 tff(9216,plain,
% 2.55/2.72 (r(elem!1, s(z))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[242, 9215, 237])).
% 2.55/2.72 tff(9217,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9218,plain,
% 2.55/2.72 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9219,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9218])).
% 2.55/2.72 tff(9220,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9219, 9217])).
% 2.55/2.72 tff(9221,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9222,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9221, 9220])).
% 2.55/2.72 tff(9223,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9222, 163, 9216, 328, 9214, 9212])).
% 2.55/2.72 tff(9224,plain,((~b(elem!1, z)) | (~r(s(z), s(s(z)))) | (elem!1 = s(s(s(s(s(z)))))) | (elem!1 = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.72 tff(9225,plain,
% 2.55/2.72 (~b(elem!1, z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9224, 9196, 9204, 9203, 8425, 9174, 9202, 9182])).
% 2.55/2.72 tff(9226,plain,
% 2.55/2.72 (r(elem!1, z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[187, 9225, 7302])).
% 2.55/2.72 tff(9227,plain,
% 2.55/2.72 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5560, 9226, 153, 9176])).
% 2.55/2.72 tff(9228,plain,
% 2.55/2.72 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[2711, 163, 9196, 4934, 9184])).
% 2.55/2.72 tff(9229,plain,
% 2.55/2.72 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[2715, 26, 507, 9228])).
% 2.55/2.72 tff(9230,plain,
% 2.55/2.72 (~b(s(s(z)), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[4296, 198, 9202, 9182, 9229])).
% 2.55/2.72 tff(9231,plain,
% 2.55/2.72 (r(s(s(z)), z)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[345, 9230])).
% 2.55/2.72 tff(9232,plain,
% 2.55/2.72 (~(s(s(elem!1)) = s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[3493, 7365])).
% 2.55/2.72 tff(9233,assumption,(~r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 2.55/2.72 tff(9234,plain,
% 2.55/2.72 (~(elem!1 = s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8661, 2105])).
% 2.55/2.72 tff(9235,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9236,plain,
% 2.55/2.72 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9237,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9236])).
% 2.55/2.72 tff(9238,plain,
% 2.55/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9237, 9235])).
% 2.55/2.72 tff(9239,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9240,plain,
% 2.55/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9239, 9238])).
% 2.55/2.72 tff(9241,plain,
% 2.55/2.72 (~r(elem!1, s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9240, 163, 1475, 833, 332])).
% 2.55/2.72 tff(9242,plain,
% 2.55/2.72 ((elem!1 = s(s(z))) | b(elem!1, s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[5572, 26, 9241])).
% 2.55/2.72 tff(9243,plain,
% 2.55/2.72 (b(elem!1, s(s(z)))),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9242, 9234])).
% 2.55/2.72 tff(9244,plain,
% 2.55/2.72 (~r(s(s(z)), elem!1)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[8144, 163, 1475, 833, 332])).
% 2.55/2.72 tff(9245,plain,
% 2.55/2.72 (b(s(s(z)), elem!1)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[2139, 2105, 9244])).
% 2.55/2.72 tff(9246,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9247,plain,
% 2.55/2.72 (((~b(elem!1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.72 inference(rewrite,[status(thm)],[])).
% 2.55/2.72 tff(9248,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9247])).
% 2.55/2.72 tff(9249,plain,
% 2.55/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.72 inference(transitivity,[status(thm)],[9248, 9246])).
% 2.55/2.72 tff(9250,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.72 inference(quant_inst,[status(thm)],[])).
% 2.55/2.72 tff(9251,plain,
% 2.55/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.55/2.72 inference(modus_ponens,[status(thm)],[9250, 9249])).
% 2.55/2.72 tff(9252,plain,
% 2.55/2.72 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[9251, 198, 9245, 348, 3745, 9243])).
% 2.55/2.72 tff(9253,plain,
% 2.55/2.72 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[256, 9252, 9233])).
% 2.55/2.72 tff(9254,plain,
% 2.55/2.72 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[3381])).
% 2.55/2.72 tff(9255,plain,
% 2.55/2.72 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[3381])).
% 2.55/2.72 tff(9256,plain,
% 2.55/2.72 (s(s(s(s(z)))) = s(elem!1)),
% 2.55/2.72 inference(transitivity,[status(thm)],[289, 9255, 134])).
% 2.55/2.72 tff(9257,plain,
% 2.55/2.72 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9256])).
% 2.55/2.72 tff(9258,plain,
% 2.55/2.72 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 2.55/2.72 inference(transitivity,[status(thm)],[294, 9257, 129, 322])).
% 2.55/2.72 tff(9259,plain,
% 2.55/2.72 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9258])).
% 2.55/2.72 tff(9260,plain,
% 2.55/2.72 (s(s(z)) = s(s(s(elem!1)))),
% 2.55/2.72 inference(transitivity,[status(thm)],[299, 9259, 275, 9254])).
% 2.55/2.72 tff(9261,plain,
% 2.55/2.72 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 2.55/2.72 inference(monotonicity,[status(thm)],[9260])).
% 2.55/2.72 tff(9262,plain,
% 2.55/2.72 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 2.55/2.72 inference(symmetry,[status(thm)],[9261])).
% 2.55/2.72 tff(9263,plain,
% 2.55/2.72 (s(s(elem!1)) = s(z)),
% 2.55/2.72 inference(transitivity,[status(thm)],[1247, 9262, 222])).
% 2.55/2.72 tff(9264,plain,
% 2.55/2.72 ($false),
% 2.55/2.72 inference(unit_resolution,[status(thm)],[620, 9263])).
% 2.55/2.73 tff(9265,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~(s(s(s(s(s(s(s(z))))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9266,plain,
% 2.55/2.73 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9265, 9253])).
% 2.55/2.73 tff(9267,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9268,plain,
% 2.55/2.73 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9269,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9268])).
% 2.55/2.73 tff(9270,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(transitivity,[status(thm)],[9269, 9267])).
% 2.55/2.73 tff(9271,plain,
% 2.55/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9272,plain,
% 2.55/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 2.55/2.73 tff(9273,plain,
% 2.55/2.73 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9272, 198, 723, 1185, 595, 5428, 4167])).
% 2.55/2.73 tff(9274,plain,
% 2.55/2.73 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3400, 9273, 3396])).
% 2.55/2.73 tff(9275,plain,
% 2.55/2.73 (r(s(s(elem!1)), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[626, 1192])).
% 2.55/2.73 tff(9276,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9277,plain,
% 2.55/2.73 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9278,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9277])).
% 2.55/2.73 tff(9279,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(transitivity,[status(thm)],[9278, 9276])).
% 2.55/2.73 tff(9280,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9281,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9280, 9279])).
% 2.55/2.73 tff(9282,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9281, 163, 328, 9275, 9214, 9274])).
% 2.55/2.73 tff(9283,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9284,plain,
% 2.55/2.73 (~b(s(s(elem!1)), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9283, 9266, 328, 1185, 595, 5428, 4167])).
% 2.55/2.73 tff(9285,plain,
% 2.55/2.73 (r(s(s(elem!1)), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[801, 9284])).
% 2.55/2.73 tff(9286,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9287,plain,
% 2.55/2.73 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9288,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9287])).
% 2.55/2.73 tff(9289,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(transitivity,[status(thm)],[9288, 9286])).
% 2.55/2.73 tff(9290,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9291,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9290, 9289])).
% 2.55/2.73 tff(9292,plain,
% 2.55/2.73 (~r(s(s(elem!1)), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9291, 163, 1475, 9285, 332])).
% 2.55/2.73 tff(9293,plain,
% 2.55/2.73 (b(s(s(elem!1)), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3497, 26, 9292, 9232])).
% 2.55/2.73 tff(9294,plain,
% 2.55/2.73 (~(elem!1 = s(s(elem!1)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[317, 9253])).
% 2.55/2.73 tff(9295,plain,
% 2.55/2.73 (~r(elem!1, s(s(elem!1)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[1823, 9285, 1475, 833])).
% 2.55/2.73 tff(9296,plain,
% 2.55/2.73 (b(elem!1, s(s(elem!1)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[147, 9295, 9294])).
% 2.55/2.73 tff(9297,plain,
% 2.55/2.73 (~(s(s(elem!1)) = elem!1)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[118, 9294])).
% 2.55/2.73 tff(9298,plain,
% 2.55/2.73 (~r(s(s(elem!1)), elem!1)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[8716, 163, 1475, 833, 9285])).
% 2.55/2.73 tff(9299,plain,
% 2.55/2.73 (b(s(s(elem!1)), elem!1)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[602, 9298, 9297])).
% 2.55/2.73 tff(9300,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9301,plain,
% 2.55/2.73 (((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9302,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9301])).
% 2.55/2.73 tff(9303,plain,
% 2.55/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.55/2.73 inference(transitivity,[status(thm)],[9302, 9300])).
% 2.55/2.73 tff(9304,plain,
% 2.55/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9305,plain,
% 2.55/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9304, 9303])).
% 2.55/2.73 tff(9306,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9305, 198, 9299, 9296, 9245, 9243, 9293])).
% 2.55/2.73 tff(9307,plain,((s(s(z)) = elem!1) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | r(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9308,plain,
% 2.55/2.73 (s(s(z)) = elem!1),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9307, 9231, 1475, 9226, 9196, 8425, 9174, 9202, 9182, 9227, 9180, 9178])).
% 2.55/2.73 tff(9309,plain,
% 2.55/2.73 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9308])).
% 2.55/2.73 tff(9310,plain,
% 2.55/2.73 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.55/2.73 inference(symmetry,[status(thm)],[9309])).
% 2.55/2.73 tff(9311,plain,
% 2.55/2.73 (b(s(z), s(s(z)))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[8826, 9310])).
% 2.55/2.73 tff(9312,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9195, 9311])).
% 2.55/2.73 tff(9313,plain,(b(s(s(z)), s(z)) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9314,plain,
% 2.55/2.73 (b(s(s(z)), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9313, 7254, 55, 2])).
% 2.55/2.73 tff(9315,plain,
% 2.55/2.73 (~r(s(z), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[8423, 55, 2, 7254])).
% 2.55/2.73 tff(9316,plain,
% 2.55/2.73 (b(s(z), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[40, 9315])).
% 2.55/2.73 tff(9317,plain,
% 2.55/2.73 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5759, 151, 1185, 2, 153, 560])).
% 2.55/2.73 tff(9318,plain,
% 2.55/2.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[176, 9317])).
% 2.55/2.73 tff(9319,plain,
% 2.55/2.73 (~b(z, s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5960, 560, 1185, 2, 153])).
% 2.55/2.73 tff(9320,plain,
% 2.55/2.73 (r(z, s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[593, 9319])).
% 2.55/2.73 tff(9321,plain,
% 2.55/2.73 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5819, 151, 2, 1185, 153, 560])).
% 2.55/2.73 tff(9322,plain,
% 2.55/2.73 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[374, 9321])).
% 2.55/2.73 tff(9323,plain,
% 2.55/2.73 (~b(s(s(z)), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5691, 9322, 1185, 560, 2])).
% 2.55/2.73 tff(9324,plain,
% 2.55/2.73 (r(s(s(z)), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[345, 9323])).
% 2.55/2.73 tff(9325,plain,
% 2.55/2.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5857, 163, 153, 9324, 423])).
% 2.55/2.73 tff(9326,plain,
% 2.55/2.73 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[31, 9325])).
% 2.55/2.73 tff(9327,plain,
% 2.55/2.73 (~r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[456, 9326, 423, 151, 9320, 9318])).
% 2.55/2.73 tff(9328,plain,
% 2.55/2.73 (b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[469, 9327])).
% 2.55/2.73 tff(9329,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5891, 163, 328, 151, 332, 423])).
% 2.55/2.73 tff(9330,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9331,plain,
% 2.55/2.73 (~r(s(z), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9330, 9324, 423, 151])).
% 2.55/2.73 tff(9332,plain,
% 2.55/2.73 (b(s(z), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[403, 9331])).
% 2.55/2.73 tff(9333,plain,
% 2.55/2.73 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[494, 198, 560, 9332, 9328])).
% 2.55/2.73 tff(9334,plain,
% 2.55/2.73 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[511, 26, 508, 9333])).
% 2.55/2.73 tff(9335,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9336,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9337,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9336, 9335])).
% 2.55/2.73 tff(9338,plain,
% 2.55/2.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9337, 163, 9324, 423, 9334])).
% 2.55/2.73 tff(9339,plain,
% 2.55/2.73 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5805, 198, 1185, 2, 9318, 9328])).
% 2.55/2.73 tff(9340,plain,
% 2.55/2.73 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3328, 26, 9339])).
% 2.55/2.73 tff(9341,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9340, 9338, 2935])).
% 2.55/2.73 tff(9342,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9343,plain,
% 2.55/2.73 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9342, 423, 560, 1185, 2, 153])).
% 2.55/2.73 tff(9344,plain,
% 2.55/2.73 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3613, 9343])).
% 2.55/2.73 tff(9345,plain,
% 2.55/2.73 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3626, 9344, 2, 560])).
% 2.55/2.73 tff(9346,plain,
% 2.55/2.73 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[374, 9345])).
% 2.55/2.73 tff(9347,plain,
% 2.55/2.73 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[7452, 9346, 423, 153])).
% 2.55/2.73 tff(9348,plain,
% 2.55/2.73 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[6516, 9344, 423, 153, 2])).
% 2.55/2.73 tff(9349,plain,
% 2.55/2.73 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[176, 9348])).
% 2.55/2.73 tff(9350,plain,
% 2.55/2.73 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[8483, 9349, 1185, 9344])).
% 2.55/2.73 tff(9351,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[31, 9350, 9347])).
% 2.55/2.73 tff(9352,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9353,plain,
% 2.55/2.73 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9352, 9316, 55, 2, 9314])).
% 2.55/2.73 tff(9354,plain,
% 2.55/2.73 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[420, 9353])).
% 2.55/2.73 tff(9355,plain,
% 2.55/2.73 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5769, 9354, 9316, 2, 9314])).
% 2.55/2.73 tff(9356,plain,
% 2.55/2.73 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[176, 9355])).
% 2.55/2.73 tff(9357,plain,
% 2.55/2.73 (~b(z, s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5960, 9314, 9316, 2, 55])).
% 2.55/2.73 tff(9358,plain,
% 2.55/2.73 (r(z, s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[593, 9357])).
% 2.55/2.73 tff(9359,plain,
% 2.55/2.73 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[7270, 9354, 55, 9314, 2, 9358])).
% 2.55/2.73 tff(9360,plain,
% 2.55/2.73 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3613, 9359])).
% 2.55/2.73 tff(9361,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[5759, 9360, 9356, 9316, 2, 55, 9314])).
% 2.55/2.73 tff(9362,plain,(b(z, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9363,plain,
% 2.55/2.73 (b(z, s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9362, 2])).
% 2.55/2.73 tff(9364,plain,
% 2.55/2.73 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9362, 42])).
% 2.55/2.73 tff(9365,plain,
% 2.55/2.73 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[3654, 9364])).
% 2.55/2.73 tff(9366,plain,
% 2.55/2.73 (~r(s(s(z)), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[6539, 150, 55, 4935])).
% 2.55/2.73 tff(9367,plain,
% 2.55/2.73 (b(s(s(z)), s(z))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[487, 9366])).
% 2.55/2.73 tff(9368,plain,
% 2.55/2.73 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 2.55/2.73 inference(commutativity,[status(thm)],[])).
% 2.55/2.73 tff(9369,plain,
% 2.55/2.73 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 2.55/2.73 inference(symmetry,[status(thm)],[9368])).
% 2.55/2.73 tff(9370,plain,
% 2.55/2.73 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9369])).
% 2.55/2.73 tff(9371,plain,
% 2.55/2.73 (~(z = s(s(z)))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[46, 9370])).
% 2.55/2.73 tff(9372,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9373,plain,
% 2.55/2.73 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9374,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9373])).
% 2.55/2.73 tff(9375,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.73 inference(transitivity,[status(thm)],[9374, 9372])).
% 2.55/2.73 tff(9376,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.73 inference(quant_inst,[status(thm)],[])).
% 2.55/2.73 tff(9377,plain,
% 2.55/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.55/2.73 inference(modus_ponens,[status(thm)],[9376, 9375])).
% 2.55/2.73 tff(9378,plain,
% 2.55/2.73 ($false),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9377, 163, 150, 153, 3639, 152])).
% 2.55/2.73 tff(9379,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.73 tff(9380,plain,
% 2.55/2.73 (~r(z, s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9379, 150, 3639, 152])).
% 2.55/2.73 tff(9381,plain,
% 2.55/2.73 ((z = s(s(z))) | b(z, s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[52, 26, 9380])).
% 2.55/2.73 tff(9382,plain,
% 2.55/2.73 (b(z, s(s(z)))),
% 2.55/2.73 inference(unit_resolution,[status(thm)],[9381, 9371])).
% 2.55/2.73 tff(9383,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9384,plain,
% 2.55/2.73 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.73 inference(rewrite,[status(thm)],[])).
% 2.55/2.73 tff(9385,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.73 inference(monotonicity,[status(thm)],[9384])).
% 2.55/2.73 tff(9386,plain,
% 2.55/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9385, 9383])).
% 2.55/2.74 tff(9387,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9388,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9387, 9386])).
% 2.55/2.74 tff(9389,plain,
% 2.55/2.74 ($false),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9388, 163, 150, 33, 3639, 152])).
% 2.55/2.74 tff(9390,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.74 tff(9391,plain,
% 2.55/2.74 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9390, 150, 3639, 152])).
% 2.55/2.74 tff(9392,plain,
% 2.55/2.74 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[31, 9391])).
% 2.55/2.74 tff(9393,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9394,plain,
% 2.55/2.74 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9395,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9394])).
% 2.55/2.74 tff(9396,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9395, 9393])).
% 2.55/2.74 tff(9397,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9398,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9397, 9396])).
% 2.55/2.74 tff(9399,plain,
% 2.55/2.74 ($false),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9398, 163, 150, 406, 3639, 152])).
% 2.55/2.74 tff(9400,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.74 tff(9401,plain,
% 2.55/2.74 (~r(z, s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9400, 150, 3639, 152])).
% 2.55/2.74 tff(9402,plain,
% 2.55/2.74 (b(z, s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[593, 9401])).
% 2.55/2.74 tff(9403,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 2.55/2.74 tff(9404,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9405,plain,
% 2.55/2.74 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9406,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9405])).
% 2.55/2.74 tff(9407,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9406, 9404])).
% 2.55/2.74 tff(9408,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9409,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9408, 9407])).
% 2.55/2.74 tff(9410,plain,
% 2.55/2.74 ($false),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9409, 198, 595, 3615, 331, 3745, 9403])).
% 2.55/2.74 tff(9411,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.74 tff(9412,plain,
% 2.55/2.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9411, 595, 3615, 331, 9403])).
% 2.55/2.74 tff(9413,plain,
% 2.55/2.74 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[420, 9412])).
% 2.55/2.74 tff(9414,plain,
% 2.55/2.74 (~r(s(s(z)), s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[3644, 9413, 3639, 150])).
% 2.55/2.74 tff(9415,plain,
% 2.55/2.74 (b(s(s(z)), s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[487, 9414])).
% 2.55/2.74 tff(9416,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9417,plain,
% 2.55/2.74 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9418,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9417])).
% 2.55/2.74 tff(9419,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9418, 9416])).
% 2.55/2.74 tff(9420,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9421,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9420, 9419])).
% 2.55/2.74 tff(9422,plain,
% 2.55/2.74 ($false),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9421, 198, 595, 9415, 3615, 331, 9403])).
% 2.55/2.74 tff(9423,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.74 tff(9424,plain,
% 2.55/2.74 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9423, 9402, 9392, 9382, 3639, 150])).
% 2.55/2.74 tff(9425,plain,
% 2.55/2.74 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[3613, 9424])).
% 2.55/2.74 tff(9426,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9427,plain,
% 2.55/2.74 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9428,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9427])).
% 2.55/2.74 tff(9429,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9428, 9426])).
% 2.55/2.74 tff(9430,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9431,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9430, 9429])).
% 2.55/2.74 tff(9432,plain,
% 2.55/2.74 (~r(s(z), s(s(z)))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9431, 163, 151, 3272, 3639])).
% 2.55/2.74 tff(9433,plain,
% 2.55/2.74 (b(s(z), s(s(z)))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[403, 9432])).
% 2.55/2.74 tff(9434,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9435,plain,
% 2.55/2.74 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9436,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9435])).
% 2.55/2.74 tff(9437,plain,
% 2.55/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9436, 9434])).
% 2.55/2.74 tff(9438,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9439,plain,
% 2.55/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9438, 9437])).
% 2.55/2.74 tff(9440,plain,
% 2.55/2.74 (~r(s(s(z)), s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9439, 163, 151, 3272, 3639])).
% 2.55/2.74 tff(9441,plain,
% 2.55/2.74 (b(s(s(z)), s(z))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[487, 9440])).
% 2.55/2.74 tff(9442,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9443,plain,
% 2.55/2.74 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9444,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9443])).
% 2.55/2.74 tff(9445,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.55/2.74 inference(transitivity,[status(thm)],[9444, 9442])).
% 2.55/2.74 tff(9446,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.55/2.74 inference(quant_inst,[status(thm)],[])).
% 2.55/2.74 tff(9447,plain,
% 2.55/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.55/2.74 inference(modus_ponens,[status(thm)],[9446, 9445])).
% 2.55/2.74 tff(9448,plain,
% 2.55/2.74 ($false),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9447, 198, 595, 9441, 9433, 9403])).
% 2.55/2.74 tff(9449,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.74 tff(9450,plain,
% 2.55/2.74 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[9449, 9402, 9382, 9425, 3639])).
% 2.55/2.74 tff(9451,plain,
% 2.55/2.74 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.74 inference(unit_resolution,[status(thm)],[374, 9450])).
% 2.55/2.74 tff(9452,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9453,plain,
% 2.55/2.74 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.74 inference(rewrite,[status(thm)],[])).
% 2.55/2.74 tff(9454,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.74 inference(monotonicity,[status(thm)],[9453])).
% 2.55/2.74 tff(9455,plain,
% 2.55/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9454, 9452])).
% 2.55/2.75 tff(9456,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9457,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9456, 9455])).
% 2.55/2.75 tff(9458,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9457, 198, 348, 331, 3745, 9403])).
% 2.55/2.75 tff(9459,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9460,plain,
% 2.55/2.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9459, 9451, 9392, 9382])).
% 2.55/2.75 tff(9461,plain,
% 2.55/2.75 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[420, 9460])).
% 2.55/2.75 tff(9462,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9463,plain,
% 2.55/2.75 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9464,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9463])).
% 2.55/2.75 tff(9465,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9464, 9462])).
% 2.55/2.75 tff(9466,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9467,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9466, 9465])).
% 2.55/2.75 tff(9468,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9467, 198, 595, 407, 348, 331, 9403])).
% 2.55/2.75 tff(9469,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9470,plain,
% 2.55/2.75 (~b(s(z), s(s(z)))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9469, 9402, 9451, 9392, 9382])).
% 2.55/2.75 tff(9471,plain,
% 2.55/2.75 (r(s(z), s(s(z)))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[403, 9470])).
% 2.55/2.75 tff(9472,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.55/2.75 tff(9473,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9474,plain,
% 2.55/2.75 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9475,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9474])).
% 2.55/2.75 tff(9476,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9475, 9473])).
% 2.55/2.75 tff(9477,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9478,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9477, 9476])).
% 2.55/2.75 tff(9479,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9478, 163, 328, 423, 3639, 9472])).
% 2.55/2.75 tff(9480,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9481,plain,
% 2.55/2.75 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9480, 9471, 9461, 3639])).
% 2.55/2.75 tff(9482,plain,
% 2.55/2.75 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[2715, 26, 507, 9481])).
% 2.55/2.75 tff(9483,plain,
% 2.55/2.75 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.55/2.75 inference(commutativity,[status(thm)],[])).
% 2.55/2.75 tff(9484,plain,
% 2.55/2.75 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 2.55/2.75 inference(symmetry,[status(thm)],[9483])).
% 2.55/2.75 tff(9485,plain,
% 2.55/2.75 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9484])).
% 2.55/2.75 tff(9486,plain,
% 2.55/2.75 (~(z = s(s(s(s(s(z))))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[366, 9485])).
% 2.55/2.75 tff(9487,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9488,plain,
% 2.55/2.75 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9489,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9488])).
% 2.55/2.75 tff(9490,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9489, 9487])).
% 2.55/2.75 tff(9491,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9492,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9491, 9490])).
% 2.55/2.75 tff(9493,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9492, 163, 150, 3639, 152, 7912])).
% 2.55/2.75 tff(9494,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9495,plain,
% 2.55/2.75 (~r(z, s(s(s(s(s(z))))))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9494, 150, 3639, 152])).
% 2.55/2.75 tff(9496,plain,
% 2.55/2.75 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[4108, 26, 9495])).
% 2.55/2.75 tff(9497,plain,
% 2.55/2.75 (b(z, s(s(s(s(s(z))))))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9496, 9486])).
% 2.55/2.75 tff(9498,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9499,plain,
% 2.55/2.75 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9500,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9499])).
% 2.55/2.75 tff(9501,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9500, 9498])).
% 2.55/2.75 tff(9502,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9503,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9502, 9501])).
% 2.55/2.75 tff(9504,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9503, 163, 328, 332, 423, 3639])).
% 2.55/2.75 tff(9505,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9506,plain,
% 2.55/2.75 (~r(s(s(z)), z)),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9505, 9471, 9461, 3639])).
% 2.55/2.75 tff(9507,plain,
% 2.55/2.75 (b(s(s(z)), z)),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[345, 9506])).
% 2.55/2.75 tff(9508,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9509,plain,
% 2.55/2.75 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9510,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9509])).
% 2.55/2.75 tff(9511,plain,
% 2.55/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9510, 9508])).
% 2.55/2.75 tff(9512,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9513,plain,
% 2.55/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.55/2.75 inference(modus_ponens,[status(thm)],[9512, 9511])).
% 2.55/2.75 tff(9514,plain,
% 2.55/2.75 ($false),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9513, 198, 595, 559, 9403, 5428, 7896])).
% 2.55/2.75 tff(9515,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.75 tff(9516,plain,
% 2.55/2.75 (~b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[9515, 9402, 9382, 9497, 9482])).
% 2.55/2.75 tff(9517,plain,
% 2.55/2.75 (r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.75 inference(unit_resolution,[status(thm)],[469, 9516])).
% 2.55/2.75 tff(9518,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9519,plain,
% 2.55/2.75 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(rewrite,[status(thm)],[])).
% 2.55/2.75 tff(9520,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.75 inference(monotonicity,[status(thm)],[9519])).
% 2.55/2.75 tff(9521,plain,
% 2.55/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(transitivity,[status(thm)],[9520, 9518])).
% 2.55/2.75 tff(9522,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.75 inference(quant_inst,[status(thm)],[])).
% 2.55/2.75 tff(9523,plain,
% 2.55/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9522, 9521])).
% 2.55/2.76 tff(9524,plain,
% 2.55/2.76 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9523, 163, 150, 3639, 9517])).
% 2.55/2.76 tff(9525,plain,
% 2.55/2.76 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3098, 9524])).
% 2.55/2.76 tff(9526,plain,
% 2.55/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9527,plain,
% 2.55/2.76 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9528,plain,
% 2.55/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9527])).
% 2.55/2.76 tff(9529,plain,
% 2.55/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9528, 9526])).
% 2.55/2.76 tff(9530,plain,
% 2.55/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9531,plain,
% 2.55/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9530, 9529])).
% 2.55/2.76 tff(9532,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9531, 198, 9525, 9451, 9507, 9497, 9482])).
% 2.55/2.76 tff(9533,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9534,plain,
% 2.55/2.76 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9533, 150, 9365])).
% 2.55/2.76 tff(9535,plain,
% 2.55/2.76 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[176, 9534])).
% 2.55/2.76 tff(9536,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9537,plain,
% 2.55/2.76 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9538,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9537])).
% 2.55/2.76 tff(9539,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9538, 9536])).
% 2.55/2.76 tff(9540,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9541,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9540, 9539])).
% 2.55/2.76 tff(9542,plain,
% 2.55/2.76 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9541, 163, 150, 4935, 9365])).
% 2.55/2.76 tff(9543,plain,
% 2.55/2.76 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[31, 9542])).
% 2.55/2.76 tff(9544,plain,
% 2.55/2.76 (r(s(s(z)), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[345, 8234])).
% 2.55/2.76 tff(9545,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9523, 163, 150, 3066, 3639, 422])).
% 2.55/2.76 tff(9546,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9547,plain,
% 2.55/2.76 (~r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9546, 3066, 150, 9365])).
% 2.55/2.76 tff(9548,plain,
% 2.55/2.76 (b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[469, 9547])).
% 2.55/2.76 tff(9549,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9550,plain,
% 2.55/2.76 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9551,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9550])).
% 2.55/2.76 tff(9552,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9551, 9549])).
% 2.55/2.76 tff(9553,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9554,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9553, 9552])).
% 2.55/2.76 tff(9555,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9554, 163, 153, 332, 562, 7912])).
% 2.55/2.76 tff(9556,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9557,plain,
% 2.55/2.76 (~r(z, s(s(s(s(s(z))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9556, 9548, 55, 9544, 407, 9367])).
% 2.55/2.76 tff(9558,plain,
% 2.55/2.76 (s(s(elem!1)) = s(s(z))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[1644])).
% 2.55/2.76 tff(9559,plain,
% 2.55/2.76 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9558])).
% 2.55/2.76 tff(9560,plain,
% 2.55/2.76 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.55/2.76 inference(symmetry,[status(thm)],[9559])).
% 2.55/2.76 tff(9561,plain,
% 2.55/2.76 ((~b(s(s(z)), z)) <=> (~b(s(s(elem!1)), z))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9560])).
% 2.55/2.76 tff(9562,plain,
% 2.55/2.76 (~b(s(s(elem!1)), z)),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[8234, 9561])).
% 2.55/2.76 tff(9563,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[723, 9562])).
% 2.55/2.76 tff(9564,plain,((~(elem!1 = z)) | (~b(s(s(elem!1)), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9565,plain,
% 2.55/2.76 (~(elem!1 = z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9564, 723, 8234])).
% 2.55/2.76 tff(9566,plain,
% 2.55/2.76 (~(z = elem!1)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[78, 9565])).
% 2.55/2.76 tff(9567,plain,
% 2.55/2.76 (b(z, elem!1)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[102, 9566, 56])).
% 2.55/2.76 tff(9568,plain,
% 2.55/2.76 (~(s(z) = elem!1)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[4600, 9567, 4598])).
% 2.55/2.76 tff(9569,plain,
% 2.55/2.76 (~(s(elem!1) = s(z))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[814, 9566])).
% 2.55/2.76 tff(9570,plain,
% 2.55/2.76 (~(s(s(z)) = s(elem!1))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[227, 9568])).
% 2.55/2.76 tff(9571,plain,
% 2.55/2.76 (~(elem!1 = s(s(z)))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[4932, 9567, 42])).
% 2.55/2.76 tff(9572,plain,
% 2.55/2.76 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[494, 198, 9367, 407, 9548])).
% 2.55/2.76 tff(9573,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.55/2.76 tff(9574,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.55/2.76 tff(9575,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[511, 26, 508, 9574, 9573])).
% 2.55/2.76 tff(9576,plain,(b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9577,plain,
% 2.55/2.76 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9576, 9572])).
% 2.55/2.76 tff(9578,plain,
% 2.55/2.76 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[5578, 332, 423, 153])).
% 2.55/2.76 tff(9579,plain,
% 2.55/2.76 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[176, 9578])).
% 2.55/2.76 tff(9580,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 2.55/2.76 tff(9581,plain,
% 2.55/2.76 (~r(s(s(s(s(s(z))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[568, 163, 153, 332, 9580])).
% 2.55/2.76 tff(9582,plain,
% 2.55/2.76 (b(s(s(s(s(s(z))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3841, 9581])).
% 2.55/2.76 tff(9583,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9584,plain,
% 2.55/2.76 (((~r(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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9585,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9584])).
% 2.55/2.76 tff(9586,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9585, 9583])).
% 2.55/2.76 tff(9587,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9588,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9587, 9586])).
% 2.55/2.76 tff(9589,plain,
% 2.55/2.76 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9588, 163, 332, 423, 9580])).
% 2.55/2.76 tff(9590,plain,
% 2.55/2.76 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3098, 9589])).
% 2.55/2.76 tff(9591,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[4174, 9590, 9582, 9579, 331])).
% 2.55/2.76 tff(9592,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9593,plain,
% 2.55/2.76 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9592, 9577, 55, 9543, 9544])).
% 2.55/2.76 tff(9594,plain,
% 2.55/2.76 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[420, 9593])).
% 2.55/2.76 tff(9595,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9596,plain,
% 2.55/2.76 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9597,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9596])).
% 2.55/2.76 tff(9598,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9597, 9595])).
% 2.55/2.76 tff(9599,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9600,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9599, 9598])).
% 2.55/2.76 tff(9601,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9600, 163, 3066, 3272, 3639, 9580])).
% 2.55/2.76 tff(9602,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9603,plain,
% 2.55/2.76 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9602, 3066, 9365, 9577])).
% 2.55/2.76 tff(9604,plain,
% 2.55/2.76 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[374, 9603])).
% 2.55/2.76 tff(9605,plain,
% 2.55/2.76 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[8845, 9604, 407, 9594])).
% 2.55/2.76 tff(9606,plain,
% 2.55/2.76 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3613, 9605])).
% 2.55/2.76 tff(9607,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9608,plain,
% 2.55/2.76 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(rewrite,[status(thm)],[])).
% 2.55/2.76 tff(9609,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.76 inference(monotonicity,[status(thm)],[9608])).
% 2.55/2.76 tff(9610,plain,
% 2.55/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.76 inference(transitivity,[status(thm)],[9609, 9607])).
% 2.55/2.76 tff(9611,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(quant_inst,[status(thm)],[])).
% 2.55/2.76 tff(9612,plain,
% 2.55/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.76 inference(modus_ponens,[status(thm)],[9611, 9610])).
% 2.55/2.76 tff(9613,plain,
% 2.55/2.76 (~r(s(z), s(s(s(s(s(z))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9612, 163, 3066, 9606, 9365])).
% 2.55/2.76 tff(9614,plain,
% 2.55/2.76 (b(s(z), s(s(s(s(s(z))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3301, 9613])).
% 2.55/2.76 tff(9615,plain,
% 2.55/2.76 (~(s(s(z)) = elem!1)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[6634, 9571])).
% 2.55/2.76 tff(9616,plain,
% 2.55/2.76 (~r(s(s(s(s(s(z))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[568, 163, 55, 9544, 9577])).
% 2.55/2.76 tff(9617,plain,
% 2.55/2.76 (b(s(s(s(s(s(z))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[3841, 9616])).
% 2.55/2.76 tff(9618,plain,
% 2.55/2.76 (b(z, s(s(s(s(s(z))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[4110, 9557])).
% 2.55/2.76 tff(9619,plain,
% 2.55/2.76 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9533, 150, 3639])).
% 2.55/2.76 tff(9620,plain,
% 2.55/2.76 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[176, 9619])).
% 2.55/2.76 tff(9621,plain,
% 2.55/2.76 ($false),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[4678, 198, 95, 271, 831, 330])).
% 2.55/2.76 tff(9622,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.76 tff(9623,plain,
% 2.55/2.76 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9622, 271, 9620, 95])).
% 2.55/2.76 tff(9624,plain,
% 2.55/2.76 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[9541, 163, 150, 406, 3639])).
% 2.55/2.76 tff(9625,plain,
% 2.55/2.76 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.76 inference(unit_resolution,[status(thm)],[31, 9624])).
% 2.55/2.76 tff(9626,plain,
% 2.55/2.76 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[8079, 198, 723, 9625, 9620, 5428, 4167])).
% 2.55/2.77 tff(9627,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9628,plain,
% 2.55/2.77 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9629,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9628])).
% 2.55/2.77 tff(9630,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.55/2.77 inference(transitivity,[status(thm)],[9629, 9627])).
% 2.55/2.77 tff(9631,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(quant_inst,[status(thm)],[])).
% 2.55/2.77 tff(9632,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9631, 9630])).
% 2.55/2.77 tff(9633,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9632, 198, 330, 5428, 4167, 3404])).
% 2.55/2.77 tff(9634,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9635,plain,
% 2.55/2.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9634, 4167, 9620, 5428])).
% 2.55/2.77 tff(9636,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.55/2.77 tff(9637,plain,
% 2.55/2.77 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 2.55/2.77 inference(symmetry,[status(thm)],[9636])).
% 2.55/2.77 tff(9638,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[314, 9637])).
% 2.55/2.77 tff(9639,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9640,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.55/2.77 tff(9641,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.55/2.77 tff(9642,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3328, 26, 9641, 9640, 9639])).
% 2.55/2.77 tff(9643,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9644,plain,
% 2.55/2.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9643, 9635])).
% 2.55/2.77 tff(9645,plain,
% 2.55/2.77 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9265, 245])).
% 2.55/2.77 tff(9646,plain,
% 2.55/2.77 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3400, 9645, 3397])).
% 2.55/2.77 tff(9647,plain,
% 2.55/2.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[245])).
% 2.55/2.77 tff(9648,plain,
% 2.55/2.77 (r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[3368, 9647])).
% 2.55/2.77 tff(9649,plain,
% 2.55/2.77 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.77 inference(monotonicity,[status(thm)],[245])).
% 2.55/2.77 tff(9650,plain,
% 2.55/2.77 (r(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[3066, 9649])).
% 2.55/2.77 tff(9651,plain,
% 2.55/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9652,plain,
% 2.55/2.77 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), 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(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9653,plain,
% 2.55/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9652])).
% 2.55/2.77 tff(9654,plain,
% 2.55/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(transitivity,[status(thm)],[9653, 9651])).
% 2.55/2.77 tff(9655,plain,
% 2.55/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.55/2.77 inference(quant_inst,[status(thm)],[])).
% 2.55/2.77 tff(9656,plain,
% 2.55/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9655, 9654])).
% 2.55/2.77 tff(9657,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9656, 163, 1115, 9650, 9648, 9646])).
% 2.55/2.77 tff(9658,plain,((~(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(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9659,plain,
% 2.55/2.77 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9658, 6966, 9644, 3066, 9626])).
% 2.55/2.77 tff(9660,plain,
% 2.55/2.77 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[256, 9659, 9623])).
% 2.55/2.77 tff(9661,plain,
% 2.55/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9662,plain,
% 2.55/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.55/2.77 inference(quant_inst,[status(thm)],[])).
% 2.55/2.77 tff(9663,plain,
% 2.55/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9662, 9661])).
% 2.55/2.77 tff(9664,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9663, 163, 150, 259, 258, 3639])).
% 2.55/2.77 tff(9665,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9666,plain,
% 2.55/2.77 (~r(elem!1, s(z))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9665, 9660, 150, 3639])).
% 2.55/2.77 tff(9667,plain,
% 2.55/2.77 (b(elem!1, s(z))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[242, 9666, 6642])).
% 2.55/2.77 tff(9668,plain,
% 2.55/2.77 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3792, 9659])).
% 2.55/2.77 tff(9669,plain,
% 2.55/2.77 (elem!1 = s(s(s(s(s(z)))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[8043, 9668, 9620, 9625, 4167, 5428, 271, 3066, 9660])).
% 2.55/2.77 tff(9670,plain,
% 2.55/2.77 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[5376])).
% 2.55/2.77 tff(9671,plain,
% 2.55/2.77 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), elem!1)),
% 2.55/2.77 inference(symmetry,[status(thm)],[9670])).
% 2.55/2.77 tff(9672,plain,
% 2.55/2.77 (b(s(z), elem!1)),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[6262, 9671])).
% 2.55/2.77 tff(9673,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[149, 9672])).
% 2.55/2.77 tff(9674,plain,((~(elem!1 = s(s(s(s(s(z))))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9675,plain,
% 2.55/2.77 (b(s(z), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9674, 9669, 6262])).
% 2.55/2.77 tff(9676,plain,
% 2.55/2.77 (~b(s(elem!1), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[6934, 9675, 150, 406, 820, 271, 9667, 95])).
% 2.55/2.77 tff(9677,plain,
% 2.55/2.77 (r(s(elem!1), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[856, 9676, 1651])).
% 2.55/2.77 tff(9678,plain,
% 2.55/2.77 (~b(s(s(z)), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[6661, 9667, 560, 9675])).
% 2.55/2.77 tff(9679,plain,
% 2.55/2.77 (r(s(s(z)), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[2139, 9678, 2105])).
% 2.55/2.77 tff(9680,plain,
% 2.55/2.77 (~r(s(elem!1), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[6961, 9679, 406, 820, 232, 1652, 9667, 560, 150, 9677])).
% 2.55/2.77 tff(9681,plain,
% 2.55/2.77 (~b(s(elem!1), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[7034, 9679, 723, 2106, 95, 232, 271, 138, 6708, 9677])).
% 2.55/2.77 tff(9682,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1217, 9681, 9680])).
% 2.55/2.77 tff(9683,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (s(s(z)) = s(elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9684,plain,
% 2.55/2.77 (s(s(elem!1)) = elem!1),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9683, 271, 95, 232, 723, 406, 820, 560, 150, 2105, 6262, 3639, 4167, 5428, 3066])).
% 2.55/2.77 tff(9685,plain,
% 2.55/2.77 (elem!1 = s(s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[118, 9684])).
% 2.55/2.77 tff(9686,plain,
% 2.55/2.77 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[317, 9685])).
% 2.55/2.77 tff(9687,plain,
% 2.55/2.77 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[256, 9686, 9623])).
% 2.55/2.77 tff(9688,plain,
% 2.55/2.77 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3792, 9686])).
% 2.55/2.77 tff(9689,plain,
% 2.55/2.77 (elem!1 = s(s(s(s(s(z)))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[8043, 9688, 9620, 9625, 4167, 5428, 271, 3066, 9687])).
% 2.55/2.77 tff(9690,plain,
% 2.55/2.77 (s(s(s(s(s(z))))) = elem!1),
% 2.55/2.77 inference(symmetry,[status(thm)],[9689])).
% 2.55/2.77 tff(9691,plain,
% 2.55/2.77 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9690])).
% 2.55/2.77 tff(9692,plain,
% 2.55/2.77 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9691])).
% 2.55/2.77 tff(9693,plain,
% 2.55/2.77 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.55/2.77 inference(symmetry,[status(thm)],[9692])).
% 2.55/2.77 tff(9694,plain,
% 2.55/2.77 (elem!1 = s(s(elem!1))),
% 2.55/2.77 inference(symmetry,[status(thm)],[9684])).
% 2.55/2.77 tff(9695,plain,
% 2.55/2.77 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.55/2.77 inference(transitivity,[status(thm)],[9694, 9693])).
% 2.55/2.77 tff(9696,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9688, 9695])).
% 2.55/2.77 tff(9697,plain,((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (s(s(z)) = s(elem!1)) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9698,plain,
% 2.55/2.77 (~b(elem!1, z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9697, 9567, 9618, 3066, 9617, 9570, 723, 4935, 9569, 9367, 150, 9615, 9614, 9365])).
% 2.55/2.77 tff(9699,plain,
% 2.55/2.77 (~b(s(z), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[6796, 9698, 55, 4935, 9567, 9571, 9570, 150, 407, 9569, 9565])).
% 2.55/2.77 tff(9700,plain,
% 2.55/2.77 (r(elem!1, z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[187, 9698, 9565])).
% 2.55/2.77 tff(9701,plain,
% 2.55/2.77 (~r(s(z), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1026, 9700, 55, 150])).
% 2.55/2.77 tff(9702,plain,
% 2.55/2.77 ($false),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[217, 9701, 9699, 9568])).
% 2.55/2.77 tff(9703,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(z, s(z)) | b(z, s(s(z))) | r(z, elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.77 tff(9704,plain,
% 2.55/2.77 (~b(s(s(elem!1)), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9703, 56, 407, 3066, 4598, 42, 150, 8234])).
% 2.55/2.77 tff(9705,plain,
% 2.55/2.77 (r(s(s(elem!1)), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[801, 9704])).
% 2.55/2.77 tff(9706,plain,
% 2.55/2.77 (s(s(z)) = s(s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3739, 9705, 55, 407, 150, 4935, 9367])).
% 2.55/2.77 tff(9707,plain,
% 2.55/2.77 (s(elem!1) = s(z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[822, 9706])).
% 2.55/2.77 tff(9708,plain,
% 2.55/2.77 (z = elem!1),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[814, 9707])).
% 2.55/2.77 tff(9709,plain,
% 2.55/2.77 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9708])).
% 2.55/2.77 tff(9710,plain,
% 2.55/2.77 (b(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9618, 9709])).
% 2.55/2.77 tff(9711,plain,
% 2.55/2.77 (b(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[6052, 9708, 9617])).
% 2.55/2.77 tff(9712,plain,
% 2.55/2.77 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9708])).
% 2.55/2.77 tff(9713,plain,
% 2.55/2.77 (elem!1 = z),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[78, 9708])).
% 2.55/2.77 tff(9714,plain,
% 2.55/2.77 (~b(elem!1, s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[71, 9708, 42])).
% 2.55/2.77 tff(9715,plain,
% 2.55/2.77 (~b(z, s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[87, 9714, 9713])).
% 2.55/2.77 tff(9716,plain,
% 2.55/2.77 (~(elem!1 = s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[110, 9715, 56])).
% 2.55/2.77 tff(9717,plain,
% 2.55/2.77 (~(s(s(elem!1)) = elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[118, 9716])).
% 2.55/2.77 tff(9718,plain,
% 2.55/2.77 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1250, 9717])).
% 2.55/2.77 tff(9719,plain,
% 2.55/2.77 (r(z, s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[3155, 9713, 4935])).
% 2.55/2.77 tff(9720,plain,
% 2.55/2.77 (r(z, s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1096, 9715])).
% 2.55/2.77 tff(9721,plain,
% 2.55/2.77 (~r(s(elem!1), s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1530, 9720, 9719, 9705])).
% 2.55/2.77 tff(9722,plain,
% 2.55/2.77 (~(s(elem!1) = s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[140, 9717])).
% 2.55/2.77 tff(9723,plain,
% 2.55/2.77 (b(s(elem!1), s(s(elem!1)))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[901, 9722, 9721])).
% 2.55/2.77 tff(9724,plain,
% 2.55/2.77 (~r(s(s(elem!1)), s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[4766, 9708, 9366])).
% 2.55/2.77 tff(9725,plain,
% 2.55/2.77 (~(s(s(elem!1)) = s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1138, 9722])).
% 2.55/2.77 tff(9726,plain,
% 2.55/2.77 (b(s(s(elem!1)), s(elem!1))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1143, 9725, 9724])).
% 2.55/2.77 tff(9727,plain,
% 2.55/2.77 (~r(s(s(s(elem!1))), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1621, 9726, 9705, 9719, 9723, 9718])).
% 2.55/2.77 tff(9728,plain,
% 2.55/2.77 (b(s(s(s(elem!1))), z)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1295, 9727])).
% 2.55/2.77 tff(9729,plain,
% 2.55/2.77 (b(s(s(s(elem!1))), elem!1)),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9728, 9712])).
% 2.55/2.77 tff(9730,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9731,plain,
% 2.55/2.77 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9732,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9731])).
% 2.55/2.77 tff(9733,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(transitivity,[status(thm)],[9732, 9730])).
% 2.55/2.77 tff(9734,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.55/2.77 inference(quant_inst,[status(thm)],[])).
% 2.55/2.77 tff(9735,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9734, 9733])).
% 2.55/2.77 tff(9736,plain,
% 2.55/2.77 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9735, 198, 9729, 9711, 9710])).
% 2.55/2.77 tff(9737,plain,
% 2.55/2.77 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[2619, 9718])).
% 2.55/2.77 tff(9738,plain,
% 2.55/2.77 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[4899, 9737, 9708])).
% 2.55/2.77 tff(9739,plain,
% 2.55/2.77 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[4903, 26, 9738, 9736])).
% 2.55/2.77 tff(9740,plain,
% 2.55/2.77 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[1032, 9713, 9535])).
% 2.55/2.77 tff(9741,plain,
% 2.55/2.77 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9708])).
% 2.55/2.77 tff(9742,plain,
% 2.55/2.77 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9543, 9741])).
% 2.55/2.77 tff(9743,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9744,plain,
% 2.55/2.77 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~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(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9745,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.77 inference(monotonicity,[status(thm)],[9744])).
% 2.55/2.77 tff(9746,plain,
% 2.55/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.77 inference(transitivity,[status(thm)],[9745, 9743])).
% 2.55/2.77 tff(9747,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.55/2.77 inference(quant_inst,[status(thm)],[])).
% 2.55/2.77 tff(9748,plain,
% 2.55/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.77 inference(modus_ponens,[status(thm)],[9747, 9746])).
% 2.55/2.77 tff(9749,plain,
% 2.55/2.77 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9748, 198, 9729, 9742, 9740, 9711, 9710])).
% 2.55/2.77 tff(9750,plain,
% 2.55/2.77 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[4845, 9708])).
% 2.55/2.77 tff(9751,plain,
% 2.55/2.77 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[4849, 26, 9750, 9749])).
% 2.55/2.77 tff(9752,plain,
% 2.55/2.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9634, 9617, 9535, 9618])).
% 2.55/2.77 tff(9753,plain,
% 2.55/2.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.55/2.77 inference(unit_resolution,[status(thm)],[9643, 9752])).
% 2.55/2.77 tff(9754,plain,
% 2.55/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9755,plain,
% 2.55/2.77 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.77 inference(rewrite,[status(thm)],[])).
% 2.55/2.77 tff(9756,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9755])).
% 2.55/2.78 tff(9757,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.78 inference(transitivity,[status(thm)],[9756, 9754])).
% 2.55/2.78 tff(9758,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(quant_inst,[status(thm)],[])).
% 2.55/2.78 tff(9759,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9758, 9757])).
% 2.55/2.78 tff(9760,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9759, 163, 3066, 9753, 9751, 9739])).
% 2.55/2.78 tff(9761,plain,(r(z, elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | b(z, s(z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9762,plain,
% 2.55/2.78 (r(z, elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9761, 3066, 42, 407, 150, 4598, 8234])).
% 2.55/2.78 tff(9763,plain,
% 2.55/2.78 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[8030, 9762, 9557])).
% 2.55/2.78 tff(9764,plain,
% 2.55/2.78 (~r(s(s(z)), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[6539, 150, 153, 406])).
% 2.55/2.78 tff(9765,plain,
% 2.55/2.78 (b(s(s(z)), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[487, 9764])).
% 2.55/2.78 tff(9766,plain,
% 2.55/2.78 (~r(s(s(elem!1)), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3739, 7365, 153, 407, 150, 406, 9765])).
% 2.55/2.78 tff(9767,plain,
% 2.55/2.78 (b(s(s(elem!1)), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[801, 9766])).
% 2.55/2.78 tff(9768,plain,
% 2.55/2.78 (~(s(s(elem!1)) = elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[6671, 6643, 9767])).
% 2.55/2.78 tff(9769,plain,
% 2.55/2.78 (~r(s(z), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[1026, 7956, 153, 150])).
% 2.55/2.78 tff(9770,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 2.55/2.78 tff(9771,plain,
% 2.55/2.78 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3654, 9770])).
% 2.55/2.78 tff(9772,plain,
% 2.55/2.78 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9541, 163, 150, 406, 9771])).
% 2.55/2.78 tff(9773,plain,
% 2.55/2.78 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[7261, 1475, 9772])).
% 2.55/2.78 tff(9774,plain,
% 2.55/2.78 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9533, 150, 9771])).
% 2.55/2.78 tff(9775,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[176, 9774])).
% 2.55/2.78 tff(9776,plain,
% 2.55/2.78 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[31, 9772])).
% 2.55/2.78 tff(9777,plain,
% 2.55/2.78 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[2877, 198, 9767, 9776, 9775])).
% 2.55/2.78 tff(9778,plain,
% 2.55/2.78 (~r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9546, 3066, 150, 9771])).
% 2.55/2.78 tff(9779,plain,
% 2.55/2.78 (b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[469, 9778])).
% 2.55/2.78 tff(9780,plain,
% 2.55/2.78 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[494, 198, 9765, 407, 9779])).
% 2.55/2.78 tff(9781,plain,
% 2.55/2.78 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9576, 9780])).
% 2.55/2.78 tff(9782,plain,
% 2.55/2.78 (~r(s(s(s(s(s(z))))), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[568, 163, 153, 332, 9781])).
% 2.55/2.78 tff(9783,plain,
% 2.55/2.78 (b(s(s(s(s(s(z))))), z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3841, 9782])).
% 2.55/2.78 tff(9784,plain,
% 2.55/2.78 (~r(z, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9556, 9779, 153, 332, 407, 9765])).
% 2.55/2.78 tff(9785,plain,
% 2.55/2.78 (b(z, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[4110, 9784])).
% 2.55/2.78 tff(9786,plain,
% 2.55/2.78 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[8079, 198, 9767, 9776, 9775, 9785, 9783])).
% 2.55/2.78 tff(9787,plain,
% 2.55/2.78 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[1250, 9768])).
% 2.55/2.78 tff(9788,plain,
% 2.55/2.78 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[2619, 9787])).
% 2.55/2.78 tff(9789,plain,
% 2.55/2.78 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9592, 9781, 153, 9776, 332])).
% 2.55/2.78 tff(9790,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[420, 9789])).
% 2.55/2.78 tff(9791,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 2.55/2.78 tff(9792,plain,
% 2.55/2.78 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[256, 244, 3790])).
% 2.55/2.78 tff(9793,plain,
% 2.55/2.78 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[3066, 5096])).
% 2.55/2.78 tff(9794,plain,
% 2.55/2.78 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[5023])).
% 2.55/2.78 tff(9795,plain,
% 2.55/2.78 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9794])).
% 2.55/2.78 tff(9796,plain,
% 2.55/2.78 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[3397, 9795])).
% 2.55/2.78 tff(9797,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[5274, 9796, 2624])).
% 2.55/2.78 tff(9798,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[935, 7346])).
% 2.55/2.78 tff(9799,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9800,plain,
% 2.55/2.78 (((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9801,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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)))))))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9800])).
% 2.55/2.78 tff(9802,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 2.55/2.78 inference(transitivity,[status(thm)],[9801, 9799])).
% 2.55/2.78 tff(9803,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.55/2.78 inference(quant_inst,[status(thm)],[])).
% 2.55/2.78 tff(9804,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9803, 9802])).
% 2.55/2.78 tff(9805,plain,
% 2.55/2.78 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9804, 163, 258, 9798])).
% 2.55/2.78 tff(9806,plain,
% 2.55/2.78 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9805, 9797])).
% 2.55/2.78 tff(9807,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9806, 9793])).
% 2.55/2.78 tff(9808,plain,((~(s(z) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9809,plain,
% 2.55/2.78 (~(s(z) = elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9808, 9792, 3066, 2624, 3397, 709])).
% 2.55/2.78 tff(9810,plain,
% 2.55/2.78 (b(s(z), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[217, 9809, 9791])).
% 2.55/2.78 tff(9811,plain,
% 2.55/2.78 (s(s(z)) = elem!1),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[7943, 9810, 332, 406, 560, 833, 1475, 150])).
% 2.55/2.78 tff(9812,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9811])).
% 2.55/2.78 tff(9813,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.78 inference(symmetry,[status(thm)],[9812])).
% 2.55/2.78 tff(9814,plain,
% 2.55/2.78 ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9813])).
% 2.55/2.78 tff(9815,plain,
% 2.55/2.78 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[244, 9814])).
% 2.55/2.78 tff(9816,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3745, 9815])).
% 2.55/2.78 tff(9817,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | r(s(z), elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9818,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9817, 7956, 332, 406, 9765, 9790, 1475, 150, 9769, 3066, 9788, 9786, 9777, 9773])).
% 2.55/2.78 tff(9819,plain,
% 2.55/2.78 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[831, 2829])).
% 2.55/2.78 tff(9820,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9770, 9819])).
% 2.55/2.78 tff(9821,plain,((~(s(z) = elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9822,plain,
% 2.55/2.78 (~(s(z) = elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9821, 9818, 9770])).
% 2.55/2.78 tff(9823,plain,
% 2.55/2.78 (b(s(z), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[217, 9822, 9769])).
% 2.55/2.78 tff(9824,plain,
% 2.55/2.78 (s(s(z)) = elem!1),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[7943, 9823, 332, 406, 9765, 7956, 1475, 150])).
% 2.55/2.78 tff(9825,plain,
% 2.55/2.78 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9824])).
% 2.55/2.78 tff(9826,plain,
% 2.55/2.78 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9825])).
% 2.55/2.78 tff(9827,plain,
% 2.55/2.78 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[8694, 9824])).
% 2.55/2.78 tff(9828,plain,
% 2.55/2.78 ((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))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[934, 26, 9777])).
% 2.55/2.78 tff(9829,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9828, 9827])).
% 2.55/2.78 tff(9830,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9831,plain,
% 2.55/2.78 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9832,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9831])).
% 2.55/2.78 tff(9833,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.55/2.78 inference(transitivity,[status(thm)],[9832, 9830])).
% 2.55/2.78 tff(9834,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.78 inference(quant_inst,[status(thm)],[])).
% 2.55/2.78 tff(9835,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9834, 9833])).
% 2.55/2.78 tff(9836,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9835, 163, 150, 1219, 3639, 681])).
% 2.55/2.78 tff(9837,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9838,plain,
% 2.55/2.78 (~r(s(s(elem!1)), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9837, 9829, 150, 9771])).
% 2.55/2.78 tff(9839,plain,
% 2.55/2.78 (b(s(s(elem!1)), s(z))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[626, 9838])).
% 2.55/2.78 tff(9840,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 2.55/2.78 tff(9841,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[4408, 198, 722, 560, 407, 9840])).
% 2.55/2.78 tff(9842,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9843,plain,
% 2.55/2.78 (~b(s(s(elem!1)), s(s(z)))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9842, 9839, 9765, 407])).
% 2.55/2.78 tff(9844,plain,
% 2.55/2.78 (~b(s(s(elem!1)), elem!1)),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9843, 9826])).
% 2.55/2.78 tff(9845,plain,
% 2.55/2.78 (s(s(s(z))) = s(elem!1)),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9824])).
% 2.55/2.78 tff(9846,plain,
% 2.55/2.78 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9845])).
% 2.55/2.78 tff(9847,plain,
% 2.55/2.78 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9846])).
% 2.55/2.78 tff(9848,plain,
% 2.55/2.78 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.55/2.78 inference(symmetry,[status(thm)],[9847])).
% 2.55/2.78 tff(9849,plain,
% 2.55/2.78 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9848])).
% 2.55/2.78 tff(9850,plain,
% 2.55/2.78 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.55/2.78 inference(symmetry,[status(thm)],[9849])).
% 2.55/2.78 tff(9851,plain,
% 2.55/2.78 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9824])).
% 2.55/2.78 tff(9852,plain,
% 2.55/2.78 (r(s(s(s(s(s(z))))), elem!1)),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9781, 9851])).
% 2.55/2.78 tff(9853,plain,
% 2.55/2.78 (r(s(s(s(elem!1))), elem!1)),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9852, 9850])).
% 2.55/2.78 tff(9854,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9847])).
% 2.55/2.78 tff(9855,plain,
% 2.55/2.78 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[3380])).
% 2.55/2.78 tff(9856,plain,
% 2.55/2.78 (s(elem!1) = s(s(s(s(z))))),
% 2.55/2.78 inference(transitivity,[status(thm)],[135, 9855, 288])).
% 2.55/2.78 tff(9857,plain,
% 2.55/2.78 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9856])).
% 2.55/2.78 tff(9858,plain,
% 2.55/2.78 (s(s(z)) = s(s(s(z)))),
% 2.55/2.78 inference(transitivity,[status(thm)],[2082, 4242, 9857, 293])).
% 2.55/2.78 tff(9859,plain,
% 2.55/2.78 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9858])).
% 2.55/2.78 tff(9860,plain,
% 2.55/2.78 (s(z) = elem!1),
% 2.55/2.78 inference(transitivity,[status(thm)],[223, 9859, 298, 2082])).
% 2.55/2.78 tff(9861,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[225, 9860])).
% 2.55/2.78 tff(9862,plain,((~(s(s(z)) = elem!1)) | (s(z) = elem!1) | (~(s(s(elem!1)) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9863,plain,
% 2.55/2.78 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9862, 9824, 9822])).
% 2.55/2.78 tff(9864,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3400, 9863, 9786])).
% 2.55/2.78 tff(9865,plain,
% 2.55/2.78 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9864, 9854])).
% 2.55/2.78 tff(9866,plain,
% 2.55/2.78 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9848])).
% 2.55/2.78 tff(9867,plain,
% 2.55/2.78 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.55/2.78 inference(symmetry,[status(thm)],[9866])).
% 2.55/2.78 tff(9868,plain,
% 2.55/2.78 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9824])).
% 2.55/2.78 tff(9869,plain,
% 2.55/2.78 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9602, 3066, 9771, 9781])).
% 2.55/2.78 tff(9870,plain,
% 2.55/2.78 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[374, 9869])).
% 2.55/2.78 tff(9871,plain,
% 2.55/2.78 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[8845, 9870, 407, 9790])).
% 2.55/2.78 tff(9872,plain,
% 2.55/2.78 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3613, 9871])).
% 2.55/2.78 tff(9873,plain,
% 2.55/2.78 (~r(s(z), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9612, 163, 3066, 9872, 9771])).
% 2.55/2.78 tff(9874,plain,
% 2.55/2.78 (b(s(z), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3301, 9873])).
% 2.55/2.78 tff(9875,plain,
% 2.55/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9876,plain,
% 2.55/2.78 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(z), s(s(z)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9877,plain,
% 2.55/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9876])).
% 2.55/2.78 tff(9878,plain,
% 2.55/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(transitivity,[status(thm)],[9877, 9875])).
% 2.55/2.78 tff(9879,plain,
% 2.55/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.55/2.78 inference(quant_inst,[status(thm)],[])).
% 2.55/2.78 tff(9880,plain,
% 2.55/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9879, 9878])).
% 2.55/2.78 tff(9881,plain,
% 2.55/2.78 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9880, 198, 9765, 407, 9874, 9779])).
% 2.55/2.78 tff(9882,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.55/2.78 tff(9883,assumption,(~r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.55/2.78 tff(9884,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[2715, 26, 507, 9883, 9882])).
% 2.55/2.78 tff(9885,plain,(r(s(s(z)), s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9886,plain,
% 2.55/2.78 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9885, 9881])).
% 2.55/2.78 tff(9887,plain,
% 2.55/2.78 (r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9886, 9868])).
% 2.55/2.78 tff(9888,plain,
% 2.55/2.78 (r(elem!1, s(s(s(elem!1))))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9887, 9867])).
% 2.55/2.78 tff(9889,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9890,plain,
% 2.55/2.78 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.55/2.78 inference(rewrite,[status(thm)],[])).
% 2.55/2.78 tff(9891,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.55/2.78 inference(monotonicity,[status(thm)],[9890])).
% 2.55/2.78 tff(9892,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.55/2.78 inference(transitivity,[status(thm)],[9891, 9889])).
% 2.55/2.78 tff(9893,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.55/2.78 inference(quant_inst,[status(thm)],[])).
% 2.55/2.78 tff(9894,plain,
% 2.55/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.55/2.78 inference(modus_ponens,[status(thm)],[9893, 9892])).
% 2.55/2.78 tff(9895,plain,
% 2.55/2.78 (~r(s(s(elem!1)), elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9894, 163, 9888, 9865, 9853])).
% 2.55/2.78 tff(9896,plain,
% 2.55/2.78 ($false),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[602, 9895, 9844, 9768])).
% 2.55/2.78 tff(9897,plain,(b(elem!1, z) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(z, elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.78 tff(9898,plain,
% 2.55/2.78 (b(elem!1, z)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[9897, 9762, 150, 9544, 4935, 407, 9364, 3066, 55])).
% 2.55/2.78 tff(9899,plain,
% 2.55/2.78 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[8037, 198, 9898, 9543, 9535, 9618, 9617])).
% 2.55/2.78 tff(9900,plain,
% 2.55/2.78 (r(elem!1, s(s(s(s(s(z))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[4810, 9899, 9763])).
% 2.55/2.78 tff(9901,plain,
% 2.55/2.78 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[7261, 9762, 9542])).
% 2.55/2.78 tff(9902,plain,
% 2.55/2.78 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[3792, 9901])).
% 2.55/2.78 tff(9903,plain,
% 2.55/2.78 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[7989, 198, 9898, 9543, 9535])).
% 2.55/2.78 tff(9904,plain,
% 2.55/2.78 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.55/2.78 inference(unit_resolution,[status(thm)],[703, 9903, 9902])).
% 2.55/2.78 tff(9905,plain,
% 2.55/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9906,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9907,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9906, 9905])).
% 2.55/2.79 tff(9908,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9907, 163, 3066, 9904, 9365, 9900])).
% 2.55/2.79 tff(9909,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | b(z, s(z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9910,plain,
% 2.55/2.79 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9909, 8234, 407, 42, 4598, 150])).
% 2.55/2.79 tff(9911,plain,
% 2.55/2.79 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3098, 9910])).
% 2.55/2.79 tff(9912,plain,
% 2.55/2.79 (~b(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4174, 9911, 9543, 9535])).
% 2.55/2.79 tff(9913,plain,
% 2.55/2.79 (r(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3841, 9912])).
% 2.55/2.79 tff(9914,plain,
% 2.55/2.79 (~r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3836, 9913, 55, 150])).
% 2.55/2.79 tff(9915,plain,
% 2.55/2.79 (b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[469, 9914])).
% 2.55/2.79 tff(9916,plain,
% 2.55/2.79 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[6822, 9913, 55, 150, 9367])).
% 2.55/2.79 tff(9917,plain,
% 2.55/2.79 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[374, 9916])).
% 2.55/2.79 tff(9918,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9919,plain,
% 2.55/2.79 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9920,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9919])).
% 2.55/2.79 tff(9921,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9920, 9918])).
% 2.55/2.79 tff(9922,plain,
% 2.55/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9923,plain,
% 2.55/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9922, 9921])).
% 2.55/2.79 tff(9924,plain,
% 2.55/2.79 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9923, 198, 407, 9911, 9917, 9915])).
% 2.55/2.79 tff(9925,plain,
% 2.55/2.79 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9576, 9924])).
% 2.55/2.79 tff(9926,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[568, 163, 55, 9544, 9925, 9913])).
% 2.55/2.79 tff(9927,plain,(b(s(s(z)), z) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | b(z, s(s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9928,plain,
% 2.55/2.79 (b(s(s(z)), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9927, 150, 407, 42, 4598])).
% 2.55/2.79 tff(9929,plain,
% 2.55/2.79 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[356, 9928, 9543, 9535])).
% 2.55/2.79 tff(9930,plain,
% 2.55/2.79 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[374, 9929])).
% 2.55/2.79 tff(9931,plain,
% 2.55/2.79 (~r(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[6822, 9930, 55, 150, 9367])).
% 2.55/2.79 tff(9932,plain,
% 2.55/2.79 (b(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3841, 9931])).
% 2.55/2.79 tff(9933,plain,
% 2.55/2.79 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4174, 9932, 9543, 9535])).
% 2.55/2.79 tff(9934,plain,
% 2.55/2.79 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3098, 9933])).
% 2.55/2.79 tff(9935,plain,
% 2.55/2.79 (~r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9546, 9934, 150, 9365])).
% 2.55/2.79 tff(9936,plain,
% 2.55/2.79 (b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[469, 9935])).
% 2.55/2.79 tff(9937,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9938,plain,
% 2.55/2.79 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9939,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9938])).
% 2.55/2.79 tff(9940,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9939, 9937])).
% 2.55/2.79 tff(9941,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9942,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9941, 9940])).
% 2.55/2.79 tff(9943,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9942, 163, 153, 3272, 562, 7912])).
% 2.55/2.79 tff(9944,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9945,plain,
% 2.55/2.79 (~r(z, s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9944, 9936, 55, 9367, 407, 9930])).
% 2.55/2.79 tff(9946,plain,
% 2.55/2.79 (b(z, s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4110, 9945])).
% 2.55/2.79 tff(9947,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4296, 198, 347, 5428, 4167, 7896])).
% 2.55/2.79 tff(9948,plain,((~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)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9949,plain,
% 2.55/2.79 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9948, 9946, 9928, 9932])).
% 2.55/2.79 tff(9950,plain,
% 2.55/2.79 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9885, 9949])).
% 2.55/2.79 tff(9951,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9952,plain,
% 2.55/2.79 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9953,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9952])).
% 2.55/2.79 tff(9954,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9953, 9951])).
% 2.55/2.79 tff(9955,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9956,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9955, 9954])).
% 2.55/2.79 tff(9957,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9956, 163, 9934, 9930, 9365, 9950])).
% 2.55/2.79 tff(9958,plain,((~r(s(z), z)) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9959,plain,
% 2.55/2.79 (~r(s(z), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9958, 4598, 42, 407])).
% 2.55/2.79 tff(9960,plain,
% 2.55/2.79 (b(s(z), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[40, 9959])).
% 2.55/2.79 tff(9961,plain,
% 2.55/2.79 (~r(s(s(z)), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4981, 152, 423, 153])).
% 2.55/2.79 tff(9962,plain,
% 2.55/2.79 (b(s(s(z)), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[487, 9961])).
% 2.55/2.79 tff(9963,plain,
% 2.55/2.79 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[7452, 33, 153, 423])).
% 2.55/2.79 tff(9964,plain,
% 2.55/2.79 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[374, 9963])).
% 2.55/2.79 tff(9965,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9966,plain,
% 2.55/2.79 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9967,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9966])).
% 2.55/2.79 tff(9968,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9967, 9965])).
% 2.55/2.79 tff(9969,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9970,plain,
% 2.55/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9969, 9968])).
% 2.55/2.79 tff(9971,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9970, 163, 153, 423, 152, 9472])).
% 2.55/2.79 tff(9972,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9973,plain,
% 2.55/2.79 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9972, 152, 423, 153])).
% 2.55/2.79 tff(9974,plain,
% 2.55/2.79 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[2715, 26, 507, 9973])).
% 2.55/2.79 tff(9975,plain,
% 2.55/2.79 (~b(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9948, 5428, 347, 7896])).
% 2.55/2.79 tff(9976,plain,
% 2.55/2.79 (r(s(s(s(s(s(z))))), z)),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3841, 9975])).
% 2.55/2.79 tff(9977,plain,
% 2.55/2.79 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3882, 9976, 153, 152])).
% 2.55/2.79 tff(9978,plain,
% 2.55/2.79 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[3098, 9977])).
% 2.55/2.79 tff(9979,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9531, 198, 9978, 348, 347, 5428, 7896])).
% 2.55/2.79 tff(9980,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9981,plain,
% 2.55/2.79 (~b(z, s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9980, 9974, 347, 9964, 153, 152])).
% 2.55/2.79 tff(9982,plain,
% 2.55/2.79 (r(z, s(s(s(s(s(z))))))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[4110, 9981])).
% 2.55/2.79 tff(9983,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9984,plain,
% 2.55/2.79 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9985,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9984])).
% 2.55/2.79 tff(9986,plain,
% 2.55/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9985, 9983])).
% 2.55/2.79 tff(9987,plain,
% 2.55/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(quant_inst,[status(thm)],[])).
% 2.55/2.79 tff(9988,plain,
% 2.55/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.55/2.79 inference(modus_ponens,[status(thm)],[9987, 9986])).
% 2.55/2.79 tff(9989,plain,
% 2.55/2.79 ($false),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9988, 198, 1185, 560, 347, 559, 7896])).
% 2.55/2.79 tff(9990,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.79 tff(9991,plain,
% 2.55/2.79 (~b(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[9990, 9962, 1185, 347, 9974])).
% 2.55/2.79 tff(9992,plain,
% 2.55/2.79 (r(s(s(s(s(s(z))))), s(z))),
% 2.55/2.79 inference(unit_resolution,[status(thm)],[469, 9991])).
% 2.55/2.79 tff(9993,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9994,plain,
% 2.55/2.79 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(rewrite,[status(thm)],[])).
% 2.55/2.79 tff(9995,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.55/2.79 inference(monotonicity,[status(thm)],[9994])).
% 2.55/2.79 tff(9996,plain,
% 2.55/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.55/2.79 inference(transitivity,[status(thm)],[9995, 9993])).
% 2.55/2.80 tff(9997,plain,
% 2.55/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 2.55/2.80 inference(quant_inst,[status(thm)],[])).
% 2.55/2.80 tff(9998,plain,
% 2.55/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.55/2.80 inference(modus_ponens,[status(thm)],[9997, 9996])).
% 2.55/2.80 tff(9999,plain,
% 2.55/2.80 ($false),
% 2.55/2.80 inference(unit_resolution,[status(thm)],[9998, 163, 153, 422, 7912, 9472])).
% 2.55/2.80 tff(10000,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.55/2.80 tff(10001,plain,
% 2.55/2.80 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.80 inference(unit_resolution,[status(thm)],[10000, 422, 153, 7912])).
% 2.55/2.80 tff(10002,plain,
% 2.55/2.80 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.55/2.80 inference(unit_resolution,[status(thm)],[2715, 26, 507, 10001])).
% 2.55/2.80 tff(10003,plain,
% 2.55/2.80 (~r(s(z), s(s(s(s(s(z))))))),
% 2.55/2.80 inference(unit_resolution,[status(thm)],[7920, 422, 406, 7912])).
% 2.55/2.80 tff(10004,plain,
% 2.55/2.80 (b(s(z), s(s(s(s(s(z))))))),
% 2.55/2.80 inference(unit_resolution,[status(thm)],[3301, 10003])).
% 2.55/2.80 tff(10005,plain,
% 2.55/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.80 inference(rewrite,[status(thm)],[])).
% 2.55/2.80 tff(10006,plain,
% 2.55/2.80 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.55/2.80 inference(rewrite,[status(thm)],[])).
% 2.55/2.80 tff(10007,plain,
% 2.55/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.55/2.80 inference(monotonicity,[status(thm)],[10006])).
% 2.55/2.80 tff(10008,plain,
% 2.55/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10007, 10005])).
% 2.65/2.80 tff(10009,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10010,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10009, 10008])).
% 2.65/2.80 tff(10011,plain,
% 2.65/2.80 ($false),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10010, 198, 407, 3819, 6262, 3615, 7896])).
% 2.65/2.80 tff(10012,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.80 tff(10013,plain,
% 2.65/2.80 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10012, 10004, 407, 3615, 10002])).
% 2.65/2.80 tff(10014,plain,
% 2.65/2.80 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[3098, 10013])).
% 2.65/2.80 tff(10015,plain,
% 2.65/2.80 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[3882, 10014, 153, 152])).
% 2.65/2.80 tff(10016,plain,
% 2.65/2.80 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[3841, 10015])).
% 2.65/2.80 tff(10017,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10018,plain,
% 2.65/2.80 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10019,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10018])).
% 2.65/2.80 tff(10020,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10019, 10017])).
% 2.65/2.80 tff(10021,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10022,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10021, 10020])).
% 2.65/2.80 tff(10023,plain,
% 2.65/2.80 ($false),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10022, 198, 1185, 407, 10004, 10016, 10002])).
% 2.65/2.80 tff(10024,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.80 tff(10025,plain,
% 2.65/2.80 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10024, 406, 407, 153, 152, 422, 1185, 7912])).
% 2.65/2.80 tff(10026,plain,
% 2.65/2.80 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[3613, 10025])).
% 2.65/2.80 tff(10027,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10028,plain,
% 2.65/2.80 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10029,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10028])).
% 2.65/2.80 tff(10030,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10029, 10027])).
% 2.65/2.80 tff(10031,plain,
% 2.65/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10032,plain,
% 2.65/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10031, 10030])).
% 2.65/2.80 tff(10033,plain,
% 2.65/2.80 ($false),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10032, 163, 406, 10026, 33, 3639])).
% 2.65/2.80 tff(10034,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.80 tff(10035,plain,
% 2.65/2.80 (~r(z, s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10034, 152, 3639, 407, 153, 33, 9992, 1185, 9982])).
% 2.65/2.80 tff(10036,plain,
% 2.65/2.80 (b(z, s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[593, 10035])).
% 2.65/2.80 tff(10037,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10038,plain,
% 2.65/2.80 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10039,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10038])).
% 2.65/2.80 tff(10040,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10039, 10037])).
% 2.65/2.80 tff(10041,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10042,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10041, 10040])).
% 2.65/2.80 tff(10043,plain,
% 2.65/2.80 ($false),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10042, 198, 1185, 10036, 9962, 347])).
% 2.65/2.80 tff(10044,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.80 tff(10045,plain,
% 2.65/2.80 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10044, 347, 1185, 3639, 407, 153, 33, 423])).
% 2.65/2.80 tff(10046,plain,
% 2.65/2.80 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[176, 10045])).
% 2.65/2.80 tff(10047,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10048,plain,
% 2.65/2.80 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10049,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10048])).
% 2.65/2.80 tff(10050,plain,
% 2.65/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10049, 10047])).
% 2.65/2.80 tff(10051,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10052,plain,
% 2.65/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10051, 10050])).
% 2.65/2.80 tff(10053,plain,
% 2.65/2.80 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10052, 198, 1185, 407, 9964, 10046])).
% 2.65/2.80 tff(10054,plain,
% 2.65/2.80 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[3613, 10053])).
% 2.65/2.80 tff(10055,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10056,plain,
% 2.65/2.80 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10057,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10056])).
% 2.65/2.80 tff(10058,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.80 inference(transitivity,[status(thm)],[10057, 10055])).
% 2.65/2.80 tff(10059,plain,
% 2.65/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 2.65/2.80 inference(quant_inst,[status(thm)],[])).
% 2.65/2.80 tff(10060,plain,
% 2.65/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.80 inference(modus_ponens,[status(thm)],[10059, 10058])).
% 2.65/2.80 tff(10061,plain,
% 2.65/2.80 (~r(z, s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10060, 163, 10054, 33, 423])).
% 2.65/2.80 tff(10062,plain,
% 2.65/2.80 (b(z, s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[593, 10061])).
% 2.65/2.80 tff(10063,plain,
% 2.65/2.80 (~b(s(s(z)), s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[10042, 198, 1185, 10062, 347])).
% 2.65/2.80 tff(10064,plain,
% 2.65/2.80 (r(s(s(z)), s(z))),
% 2.65/2.80 inference(unit_resolution,[status(thm)],[487, 10063])).
% 2.65/2.80 tff(10065,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10066,plain,
% 2.65/2.80 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.65/2.80 inference(rewrite,[status(thm)],[])).
% 2.65/2.80 tff(10067,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.65/2.80 inference(monotonicity,[status(thm)],[10066])).
% 2.65/2.80 tff(10068,plain,
% 2.65/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10067, 10065])).
% 2.65/2.81 tff(10069,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10070,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10069, 10068])).
% 2.65/2.81 tff(10071,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10070, 163, 10064, 10054, 423, 3639])).
% 2.65/2.81 tff(10072,plain,((~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10073,plain,
% 2.65/2.81 (~b(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10072, 33, 3639, 1185, 423, 407, 153])).
% 2.65/2.81 tff(10074,plain,
% 2.65/2.81 (r(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[345, 10073])).
% 2.65/2.81 tff(10075,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[5857, 163, 153, 10074, 33, 423])).
% 2.65/2.81 tff(10076,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10077,plain,
% 2.65/2.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10076, 33, 153, 3639, 1185, 407])).
% 2.65/2.81 tff(10078,plain,
% 2.65/2.81 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[420, 10077])).
% 2.65/2.81 tff(10079,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10080,plain,
% 2.65/2.81 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10081,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[10080])).
% 2.65/2.81 tff(10082,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10081, 10079])).
% 2.65/2.81 tff(10083,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10084,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10083, 10082])).
% 2.65/2.81 tff(10085,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10084, 163, 3272, 332, 33, 3639])).
% 2.65/2.81 tff(10086,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10087,plain,
% 2.65/2.81 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10086, 33, 332, 3639])).
% 2.65/2.81 tff(10088,plain,
% 2.65/2.81 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[374, 10087])).
% 2.65/2.81 tff(10089,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8845, 10088, 407, 10078])).
% 2.65/2.81 tff(10090,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10089])).
% 2.65/2.81 tff(10091,plain,
% 2.65/2.81 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10092,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[10091])).
% 2.65/2.81 tff(10093,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10092, 10027])).
% 2.65/2.81 tff(10094,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10095,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10094, 10093])).
% 2.65/2.81 tff(10096,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10095, 163, 406, 10090, 33, 3639])).
% 2.65/2.81 tff(10097,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10098,plain,
% 2.65/2.81 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10097, 332, 3639, 407, 406, 153, 1185])).
% 2.65/2.81 tff(10099,plain,
% 2.65/2.81 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[31, 10098])).
% 2.65/2.81 tff(10100,plain,
% 2.65/2.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[5578, 152, 153, 332])).
% 2.65/2.81 tff(10101,plain,
% 2.65/2.81 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[420, 10100])).
% 2.65/2.81 tff(10102,plain,
% 2.65/2.81 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[4031, 152, 406, 332])).
% 2.65/2.81 tff(10103,plain,
% 2.65/2.81 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[374, 10102])).
% 2.65/2.81 tff(10104,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8845, 10103, 407, 10101])).
% 2.65/2.81 tff(10105,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10104])).
% 2.65/2.81 tff(10106,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10107,plain,
% 2.65/2.81 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10108,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[10107])).
% 2.65/2.81 tff(10109,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10108, 10106])).
% 2.65/2.81 tff(10110,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10111,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10110, 10109])).
% 2.65/2.81 tff(10112,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10111, 163, 406, 10105, 3639, 152])).
% 2.65/2.81 tff(10113,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10114,plain,
% 2.65/2.81 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10113, 332, 3639, 407, 406, 153])).
% 2.65/2.81 tff(10115,plain,
% 2.65/2.81 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[176, 10114])).
% 2.65/2.81 tff(10116,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8483, 10115, 1185, 10099])).
% 2.65/2.81 tff(10117,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10116])).
% 2.65/2.81 tff(10118,plain,
% 2.65/2.81 (~b(s(s(s(s(s(z))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[4174, 10115, 3819, 10099])).
% 2.65/2.81 tff(10119,plain,
% 2.65/2.81 (r(s(s(s(s(s(z))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3841, 10118])).
% 2.65/2.81 tff(10120,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10121,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10122,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10121, 10120])).
% 2.65/2.81 tff(10123,plain,
% 2.65/2.81 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10122, 163, 406, 332, 10119])).
% 2.65/2.81 tff(10124,plain,
% 2.65/2.81 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9576, 10123])).
% 2.65/2.81 tff(10125,plain,
% 2.65/2.81 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8799, 3450, 153, 406])).
% 2.65/2.81 tff(10126,plain,
% 2.65/2.81 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10125])).
% 2.65/2.81 tff(10127,plain,
% 2.65/2.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8832, 10126, 153, 1185, 3450])).
% 2.65/2.81 tff(10128,plain,
% 2.65/2.81 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[420, 10127])).
% 2.65/2.81 tff(10129,plain,
% 2.65/2.81 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8845, 10128, 407, 10126])).
% 2.65/2.81 tff(10130,plain,
% 2.65/2.81 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[374, 10129])).
% 2.65/2.81 tff(10131,plain,
% 2.65/2.81 (~b(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[6226, 10128, 407, 1185, 10126])).
% 2.65/2.81 tff(10132,plain,
% 2.65/2.81 (r(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[345, 10131])).
% 2.65/2.81 tff(10133,plain,
% 2.65/2.81 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[4031, 10132, 406, 10130])).
% 2.65/2.81 tff(10134,plain,
% 2.65/2.81 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[176, 10133])).
% 2.65/2.81 tff(10135,plain,
% 2.65/2.81 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10086, 10130, 10132, 3639])).
% 2.65/2.81 tff(10136,plain,
% 2.65/2.81 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[31, 10135])).
% 2.65/2.81 tff(10137,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[8483, 10136, 10134, 1185, 10126])).
% 2.65/2.81 tff(10138,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10139,plain,
% 2.65/2.81 (~r(s(s(z)), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10138, 1185, 3639, 406, 407, 153])).
% 2.65/2.81 tff(10140,plain,
% 2.65/2.81 (b(s(s(z)), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[487, 10139])).
% 2.65/2.81 tff(10141,plain,
% 2.65/2.81 (~b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[7909, 198, 10140, 407, 10124])).
% 2.65/2.81 tff(10142,plain,
% 2.65/2.81 (r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[469, 10141])).
% 2.65/2.81 tff(10143,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10144,plain,
% 2.65/2.81 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10145,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[10144])).
% 2.65/2.81 tff(10146,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10145, 10143])).
% 2.65/2.81 tff(10147,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10148,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10147, 10146])).
% 2.65/2.81 tff(10149,plain,
% 2.65/2.81 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10148, 163, 406, 332, 10119])).
% 2.65/2.81 tff(10150,plain,
% 2.65/2.81 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9885, 10149])).
% 2.65/2.81 tff(10151,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10150, 10124])).
% 2.65/2.81 tff(10152,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3301, 10151])).
% 2.65/2.81 tff(10153,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10154,plain,
% 2.65/2.81 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10155,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[10154])).
% 2.65/2.81 tff(10156,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(transitivity,[status(thm)],[10155, 10153])).
% 2.65/2.81 tff(10157,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.65/2.81 inference(quant_inst,[status(thm)],[])).
% 2.65/2.81 tff(10158,plain,
% 2.65/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[10157, 10156])).
% 2.65/2.81 tff(10159,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10158, 163, 406, 10152, 10142, 10119])).
% 2.65/2.81 tff(10160,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10161,plain,
% 2.65/2.81 (~r(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10160, 3819, 407, 406, 3639, 153, 1185])).
% 2.65/2.81 tff(10162,plain,
% 2.65/2.81 (b(s(s(z)), z)),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[345, 10161])).
% 2.65/2.81 tff(10163,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[6226, 10078, 407, 1185, 347])).
% 2.65/2.81 tff(10164,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10163])).
% 2.65/2.81 tff(10165,plain,
% 2.65/2.81 ($false),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10095, 163, 406, 10164, 33, 3639])).
% 2.65/2.81 tff(10166,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.81 tff(10167,plain,
% 2.65/2.81 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10166, 10162, 3639, 407, 1185, 406, 153])).
% 2.65/2.81 tff(10168,plain,
% 2.65/2.81 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[31, 10167])).
% 2.65/2.81 tff(10169,plain,
% 2.65/2.81 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3763, 423, 153, 152])).
% 2.65/2.81 tff(10170,plain,
% 2.65/2.81 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[374, 10169])).
% 2.65/2.81 tff(10171,plain,
% 2.65/2.81 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9972, 423, 153, 152])).
% 2.65/2.81 tff(10172,plain,
% 2.65/2.81 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9885, 10171])).
% 2.65/2.81 tff(10173,plain,
% 2.65/2.81 (~b(z, s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9980, 10172, 153, 347, 10170, 152])).
% 2.65/2.81 tff(10174,plain,
% 2.65/2.81 (r(z, s(s(s(s(s(z))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[4110, 10173])).
% 2.65/2.81 tff(10175,plain,
% 2.65/2.81 (~b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[9990, 10172, 1185, 560, 347])).
% 2.65/2.81 tff(10176,plain,
% 2.65/2.81 (r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[469, 10175])).
% 2.65/2.81 tff(10177,plain,
% 2.65/2.81 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[10024, 10176, 407, 153, 406, 152, 1185, 10174])).
% 2.65/2.81 tff(10178,plain,
% 2.65/2.81 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[3613, 10177])).
% 2.65/2.81 tff(10179,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10180,plain,
% 2.65/2.81 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(10181,plain,
% 2.65/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[10180])).
% 2.65/2.82 tff(10182,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10181, 10179])).
% 2.65/2.82 tff(10183,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(10184,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[10183, 10182])).
% 2.65/2.82 tff(10185,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10184, 163, 406, 10178, 10176, 10174])).
% 2.65/2.82 tff(10186,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10187,plain,
% 2.65/2.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10186, 152, 407, 153, 406, 1185, 10140, 347])).
% 2.65/2.82 tff(10188,plain,
% 2.65/2.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[420, 10187])).
% 2.65/2.82 tff(10189,plain,
% 2.65/2.82 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[6226, 10188, 407, 1185, 347])).
% 2.65/2.82 tff(10190,plain,
% 2.65/2.82 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3613, 10189])).
% 2.65/2.82 tff(10191,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10111, 163, 406, 10190, 3639, 152])).
% 2.65/2.82 tff(10192,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10193,plain,
% 2.65/2.82 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10192, 10162, 3639, 407, 1185, 406, 153])).
% 2.65/2.82 tff(10194,plain,
% 2.65/2.82 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[176, 10193])).
% 2.65/2.82 tff(10195,plain,
% 2.65/2.82 (~b(s(s(s(s(s(z))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[4174, 10194, 3819, 10168])).
% 2.65/2.82 tff(10196,plain,
% 2.65/2.82 (r(s(s(s(s(s(z))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3841, 10195])).
% 2.65/2.82 tff(10197,plain,
% 2.65/2.82 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[8483, 10194, 1185, 10168])).
% 2.65/2.82 tff(10198,plain,
% 2.65/2.82 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3613, 10197])).
% 2.65/2.82 tff(10199,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[430, 163, 406, 151, 422, 3828])).
% 2.65/2.82 tff(10200,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10201,plain,
% 2.65/2.82 (~r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10200, 10198, 406, 10196])).
% 2.65/2.82 tff(10202,plain,
% 2.65/2.82 (b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[469, 10201])).
% 2.65/2.82 tff(10203,plain,
% 2.65/2.82 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9990, 10202, 1185, 10140, 10162])).
% 2.65/2.82 tff(10204,plain,
% 2.65/2.82 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9885, 10203])).
% 2.65/2.82 tff(10205,plain,
% 2.65/2.82 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[494, 198, 10140, 407, 10202])).
% 2.65/2.82 tff(10206,plain,
% 2.65/2.82 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9576, 10205])).
% 2.65/2.82 tff(10207,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[5711, 163, 153, 10206, 10204, 10196])).
% 2.65/2.82 tff(10208,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10209,plain,
% 2.65/2.82 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10208, 1185, 407, 153, 406, 3639])).
% 2.65/2.82 tff(10210,plain,
% 2.65/2.82 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3098, 10209])).
% 2.65/2.82 tff(10211,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10212,plain,
% 2.65/2.82 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(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))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10213,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[10212])).
% 2.65/2.82 tff(10214,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10213, 10211])).
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% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
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% 2.65/2.82 inference(modus_ponens,[status(thm)],[10215, 10214])).
% 2.65/2.82 tff(10217,plain,
% 2.65/2.82 (~r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10216, 163, 10210, 10117, 3639])).
% 2.65/2.82 tff(10218,plain,
% 2.65/2.82 (b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[469, 10217])).
% 2.65/2.82 tff(10219,plain,
% 2.65/2.82 (~r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9612, 163, 10210, 10117, 3639])).
% 2.65/2.82 tff(10220,plain,
% 2.65/2.82 (b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3301, 10219])).
% 2.65/2.82 tff(10221,plain,
% 2.65/2.82 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9880, 198, 10140, 407, 10220, 10218])).
% 2.65/2.82 tff(10222,plain,
% 2.65/2.82 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9885, 10221])).
% 2.65/2.82 tff(10223,plain,
% 2.65/2.82 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[494, 198, 10140, 407, 10218])).
% 2.65/2.82 tff(10224,plain,
% 2.65/2.82 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9576, 10223])).
% 2.65/2.82 tff(10225,plain,
% 2.65/2.82 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[5711, 163, 153, 10224, 10222])).
% 2.65/2.82 tff(10226,plain,
% 2.65/2.82 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3841, 10225])).
% 2.65/2.82 tff(10227,plain,
% 2.65/2.82 (~r(z, s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9556, 10218, 153, 332, 407, 10140])).
% 2.65/2.82 tff(10228,plain,
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% 2.65/2.82 tff(10229,plain,
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% 2.65/2.82 tff(10230,plain,
% 2.65/2.82 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10231,plain,
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% 2.65/2.82 inference(monotonicity,[status(thm)],[10230])).
% 2.65/2.82 tff(10232,plain,
% 2.65/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10231, 10229])).
% 2.65/2.82 tff(10233,plain,
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% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(10234,plain,
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% 2.65/2.82 inference(modus_ponens,[status(thm)],[10233, 10232])).
% 2.65/2.82 tff(10235,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10234, 198, 1185, 10220, 10218, 10228, 10226])).
% 2.65/2.82 tff(10236,plain,((~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10237,plain,
% 2.65/2.82 (~r(s(s(z)), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10236, 9960, 55, 407, 9365, 4935])).
% 2.65/2.82 tff(10238,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[345, 10237])).
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% 2.65/2.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10166, 10238, 9365, 407, 9960, 4935, 55])).
% 2.65/2.82 tff(10240,plain,
% 2.65/2.82 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[31, 10239])).
% 2.65/2.82 tff(10241,plain,
% 2.65/2.82 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10192, 10238, 9365, 407, 9960, 4935, 55])).
% 2.65/2.82 tff(10242,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[176, 10241])).
% 2.65/2.82 tff(10243,plain,
% 2.65/2.82 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[8483, 10242, 9960, 10240])).
% 2.65/2.82 tff(10244,plain,
% 2.65/2.82 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3613, 10243])).
% 2.65/2.82 tff(10245,plain,
% 2.65/2.82 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10208, 9960, 407, 55, 4935, 9365])).
% 2.65/2.82 tff(10246,plain,
% 2.65/2.82 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3098, 10245])).
% 2.65/2.82 tff(10247,plain,
% 2.65/2.82 (~r(s(s(z)), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10138, 9960, 9365, 4935, 407, 55])).
% 2.65/2.82 tff(10248,plain,
% 2.65/2.82 (b(s(s(z)), s(z))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[487, 10247])).
% 2.65/2.82 tff(10249,plain,
% 2.65/2.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 2.65/2.82 tff(10250,plain,
% 2.65/2.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[374, 10249])).
% 2.65/2.82 tff(10251,plain,
% 2.65/2.82 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9602, 3272, 3639, 3066])).
% 2.65/2.82 tff(10252,plain,
% 2.65/2.82 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9576, 10251])).
% 2.65/2.82 tff(10253,plain,
% 2.65/2.82 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9956, 163, 3066, 3272, 3639])).
% 2.65/2.82 tff(10254,plain,
% 2.65/2.82 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[9885, 10253])).
% 2.65/2.82 tff(10255,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[7902, 198, 560, 407, 6262, 10254, 10252])).
% 2.65/2.82 tff(10256,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10257,plain,
% 2.65/2.82 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10256, 10250, 407, 10248, 10246, 9365])).
% 2.65/2.82 tff(10258,plain,
% 2.65/2.82 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3301, 10257])).
% 2.65/2.82 tff(10259,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[9612, 163, 10246, 10258, 10244, 9365])).
% 2.65/2.82 tff(10260,plain,(b(z, s(z)) | (~b(s(z), s(s(z)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10261,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[10260, 42, 407])).
% 2.65/2.82 tff(10262,plain,
% 2.65/2.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3671, 150, 153, 3450, 3615, 595])).
% 2.65/2.82 tff(10263,plain,
% 2.65/2.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[420, 10262])).
% 2.65/2.82 tff(10264,plain,
% 2.65/2.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[8845, 10263, 407, 3615])).
% 2.65/2.82 tff(10265,plain,
% 2.65/2.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[374, 10264])).
% 2.65/2.82 tff(10266,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10267,plain,
% 2.65/2.82 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10268,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[10267])).
% 2.65/2.82 tff(10269,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10268, 10266])).
% 2.65/2.82 tff(10270,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(10271,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[10270, 10269])).
% 2.65/2.82 tff(10272,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[10271, 163, 150, 3450, 10265, 3639])).
% 2.65/2.82 tff(10273,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10274,plain,
% 2.65/2.82 (~r(s(z), z)),
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% 2.65/2.82 tff(10275,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[40, 10274])).
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[8832, 10275, 153, 3450, 3615])).
% 2.65/2.82 tff(10277,plain,
% 2.65/2.82 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[420, 10276])).
% 2.65/2.82 tff(10278,plain,
% 2.65/2.82 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[8845, 10277, 407, 3615])).
% 2.65/2.82 tff(10279,plain,
% 2.65/2.82 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[374, 10278])).
% 2.65/2.82 tff(10280,plain,
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% 2.65/2.82 inference(unit_resolution,[status(thm)],[6226, 10277, 407, 3615, 10275])).
% 2.65/2.82 tff(10281,plain,
% 2.65/2.82 (r(s(s(z)), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[345, 10280])).
% 2.65/2.82 tff(10282,plain,
% 2.65/2.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10086, 10281, 10279, 3639])).
% 2.65/2.82 tff(10283,plain,
% 2.65/2.82 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[31, 10282])).
% 2.65/2.82 tff(10284,plain,
% 2.65/2.82 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[8483, 10283, 3615, 10275])).
% 2.65/2.82 tff(10285,plain,
% 2.65/2.82 (r(s(s(s(s(s(s(s(z))))))), z)),
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% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10287,plain,
% 2.65/2.82 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10288,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[10287])).
% 2.65/2.82 tff(10289,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10288, 10286])).
% 2.65/2.82 tff(10290,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(10291,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[10290, 10289])).
% 2.65/2.82 tff(10292,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10291, 163, 153, 10279, 10281, 10285])).
% 2.65/2.82 tff(10293,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10294,plain,
% 2.65/2.82 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10293, 3450, 3639, 407, 153, 595])).
% 2.65/2.82 tff(10295,plain,
% 2.65/2.82 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[3613, 10294])).
% 2.65/2.82 tff(10296,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10297,plain,
% 2.65/2.82 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(10298,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[10297])).
% 2.65/2.82 tff(10299,plain,
% 2.65/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.82 inference(transitivity,[status(thm)],[10298, 10296])).
% 2.65/2.82 tff(10300,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(10301,plain,
% 2.65/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[10300, 10299])).
% 2.65/2.82 tff(10302,plain,
% 2.65/2.82 ($false),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[10301, 163, 150, 151, 33, 3639])).
% 2.65/2.82 tff(10303,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.82 tff(10304,plain,
% 2.65/2.82 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10303, 150, 3639, 151])).
% 2.65/2.83 tff(10305,plain,
% 2.65/2.83 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[31, 10304])).
% 2.65/2.83 tff(10306,plain,
% 2.65/2.83 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10307,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10306])).
% 2.65/2.83 tff(10308,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10307, 9434])).
% 2.65/2.83 tff(10309,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10310,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10309, 10308])).
% 2.65/2.83 tff(10311,plain,
% 2.65/2.83 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10310, 163, 3450, 151, 3639])).
% 2.65/2.83 tff(10312,plain,
% 2.65/2.83 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[374, 10311])).
% 2.65/2.83 tff(10313,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10314,plain,
% 2.65/2.83 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10315,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10314])).
% 2.65/2.83 tff(10316,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10315, 10313])).
% 2.65/2.83 tff(10317,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10318,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10317, 10316])).
% 2.65/2.83 tff(10319,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10318, 163, 150, 153, 3450, 332])).
% 2.65/2.83 tff(10320,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10321,plain,
% 2.65/2.83 (~r(s(s(z)), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10320, 150, 153, 3450])).
% 2.65/2.83 tff(10322,plain,
% 2.65/2.83 (b(s(s(z)), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[345, 10321])).
% 2.65/2.83 tff(10323,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[356, 10322, 9620, 10312, 10305])).
% 2.65/2.83 tff(10324,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10325,plain,
% 2.65/2.83 (~r(s(z), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10324, 3450, 153, 3639, 10295])).
% 2.65/2.83 tff(10326,plain,
% 2.65/2.83 (b(s(z), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[40, 10325])).
% 2.65/2.83 tff(10327,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10070, 163, 3450, 151, 423, 3639])).
% 2.65/2.83 tff(10328,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10329,plain,
% 2.65/2.83 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10328, 10295, 3639, 3450])).
% 2.65/2.83 tff(10330,plain,
% 2.65/2.83 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[420, 10329])).
% 2.65/2.83 tff(10331,plain,
% 2.65/2.83 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10310, 163, 3450, 10295, 3639])).
% 2.65/2.83 tff(10332,plain,
% 2.65/2.83 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[374, 10331])).
% 2.65/2.83 tff(10333,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[9190, 152, 3450, 151, 3745, 348])).
% 2.65/2.83 tff(10334,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[469, 10333])).
% 2.65/2.83 tff(10335,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[5001, 152, 153, 3450, 348])).
% 2.65/2.83 tff(10336,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3841, 10335])).
% 2.65/2.83 tff(10337,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8803, 10336, 10334, 595, 1185])).
% 2.65/2.83 tff(10338,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10339,plain,
% 2.65/2.83 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10338, 10326, 595, 153, 3450, 10332, 10295, 10330])).
% 2.65/2.83 tff(10340,plain,
% 2.65/2.83 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[176, 10339])).
% 2.65/2.83 tff(10341,plain,
% 2.65/2.83 (~b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8803, 4167, 595, 1185])).
% 2.65/2.83 tff(10342,plain,
% 2.65/2.83 (r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[469, 10341])).
% 2.65/2.83 tff(10343,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8811, 163, 3450, 151, 10342])).
% 2.65/2.83 tff(10344,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[9576, 10343])).
% 2.65/2.83 tff(10345,plain,
% 2.65/2.83 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10346,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10345])).
% 2.65/2.83 tff(10347,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10346, 10211])).
% 2.65/2.83 tff(10348,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10349,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10348, 10347])).
% 2.65/2.83 tff(10350,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10349, 163, 151, 3639, 10342])).
% 2.65/2.83 tff(10351,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3098, 10350])).
% 2.65/2.83 tff(10352,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10353,plain,
% 2.65/2.83 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10354,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10353])).
% 2.65/2.83 tff(10355,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10354, 10352])).
% 2.65/2.83 tff(10356,plain,
% 2.65/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10357,plain,
% 2.65/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10356, 10355])).
% 2.65/2.83 tff(10358,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10357, 198, 10351, 10312, 330, 4167, 10344])).
% 2.65/2.83 tff(10359,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10360,plain,
% 2.65/2.83 (~b(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10359, 10340, 10295, 3639, 3450, 595, 10326])).
% 2.65/2.83 tff(10361,plain,
% 2.65/2.83 (r(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3841, 10360])).
% 2.65/2.83 tff(10362,plain,
% 2.65/2.83 (~r(s(z), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10324, 3450, 153, 3639, 151])).
% 2.65/2.83 tff(10363,plain,
% 2.65/2.83 (b(s(z), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[40, 10362])).
% 2.65/2.83 tff(10364,plain,
% 2.65/2.83 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10328, 151, 3639, 3450])).
% 2.65/2.83 tff(10365,plain,
% 2.65/2.83 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[420, 10364])).
% 2.65/2.83 tff(10366,plain,
% 2.65/2.83 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[9576, 5704])).
% 2.65/2.83 tff(10367,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(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(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(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(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10368,plain,
% 2.65/2.83 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10369,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(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(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10368])).
% 2.65/2.83 tff(10370,plain,
% 2.65/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10369, 10367])).
% 2.65/2.83 tff(10371,plain,
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% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10372,plain,
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% 2.65/2.83 inference(modus_ponens,[status(thm)],[10371, 10370])).
% 2.65/2.83 tff(10373,plain,
% 2.65/2.83 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10372, 198, 3819, 348, 347, 330])).
% 2.65/2.83 tff(10374,plain,
% 2.65/2.83 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[9885, 10373])).
% 2.65/2.83 tff(10375,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[5711, 163, 153, 10366, 10374])).
% 2.65/2.83 tff(10376,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3841, 10375])).
% 2.65/2.83 tff(10377,plain,
% 2.65/2.83 (~b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8803, 10376, 595, 1185])).
% 2.65/2.83 tff(10378,plain,
% 2.65/2.83 (r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[469, 10377])).
% 2.65/2.83 tff(10379,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8811, 163, 3450, 151, 10378, 10366])).
% 2.65/2.83 tff(10380,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10381,plain,
% 2.65/2.83 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10380, 330, 151, 595, 10363, 153, 10312, 10365, 347, 3450])).
% 2.65/2.83 tff(10382,plain,
% 2.65/2.83 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3098, 10381])).
% 2.65/2.83 tff(10383,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10216, 163, 10382, 151, 3639])).
% 2.65/2.83 tff(10384,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[469, 10383])).
% 2.65/2.83 tff(10385,plain,
% 2.65/2.83 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[356, 330, 10312, 347])).
% 2.65/2.83 tff(10386,plain,
% 2.65/2.83 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[31, 10385])).
% 2.65/2.83 tff(10387,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10388,plain,
% 2.65/2.83 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10389,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.83 inference(monotonicity,[status(thm)],[10388])).
% 2.65/2.83 tff(10390,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.83 inference(transitivity,[status(thm)],[10389, 10387])).
% 2.65/2.83 tff(10391,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10392,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10391, 10390])).
% 2.65/2.83 tff(10393,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10392, 163, 10382, 10386, 3639])).
% 2.65/2.83 tff(10394,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[3841, 10393])).
% 2.65/2.83 tff(10395,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[8803, 10394, 10384, 595, 10363])).
% 2.65/2.83 tff(10396,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.83 tff(10397,plain,
% 2.65/2.83 (~b(s(s(z)), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10396, 10340, 3639, 10295, 153, 595, 3450])).
% 2.65/2.83 tff(10398,plain,
% 2.65/2.83 (r(s(s(z)), z)),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[345, 10397])).
% 2.65/2.83 tff(10399,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.65/2.83 inference(quant_inst,[status(thm)],[])).
% 2.65/2.83 tff(10400,plain,
% 2.65/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.65/2.83 inference(modus_ponens,[status(thm)],[10399, 563])).
% 2.65/2.83 tff(10401,plain,
% 2.65/2.83 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[10400, 163, 153, 10398, 10361])).
% 2.65/2.83 tff(10402,plain,
% 2.65/2.83 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[9576, 10401])).
% 2.65/2.83 tff(10403,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10404,plain,
% 2.65/2.83 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.83 inference(rewrite,[status(thm)],[])).
% 2.65/2.83 tff(10405,plain,
% 2.65/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10404])).
% 2.65/2.84 tff(10406,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10405, 10403])).
% 2.65/2.84 tff(10407,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10408,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10407, 10406])).
% 2.65/2.84 tff(10409,plain,
% 2.65/2.84 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10408, 163, 153, 10398, 10361])).
% 2.65/2.84 tff(10410,plain,
% 2.65/2.84 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9885, 10409])).
% 2.65/2.84 tff(10411,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10410, 10402])).
% 2.65/2.84 tff(10412,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3301, 10411])).
% 2.65/2.84 tff(10413,plain,
% 2.65/2.84 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[5672, 198, 10332, 10330, 10402])).
% 2.65/2.84 tff(10414,plain,
% 2.65/2.84 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3098, 10413])).
% 2.65/2.84 tff(10415,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9612, 163, 10414, 10412, 10295, 3639])).
% 2.65/2.84 tff(10416,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10417,plain,
% 2.65/2.84 (~r(s(s(z)), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10416, 9365, 407, 55, 10261])).
% 2.65/2.84 tff(10418,plain,
% 2.65/2.84 (b(s(s(z)), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[487, 10417])).
% 2.65/2.84 tff(10419,plain,
% 2.65/2.84 (~r(s(z), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9533, 152, 3639])).
% 2.65/2.84 tff(10420,plain,
% 2.65/2.84 (b(s(z), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[40, 10419])).
% 2.65/2.84 tff(10421,plain,
% 2.65/2.84 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10422,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10421])).
% 2.65/2.84 tff(10423,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10422, 10037])).
% 2.65/2.84 tff(10424,plain,
% 2.65/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10425,plain,
% 2.65/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10424, 10423])).
% 2.65/2.84 tff(10426,plain,
% 2.65/2.84 (~b(s(s(z)), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10425, 198, 10420, 595, 560])).
% 2.65/2.84 tff(10427,plain,
% 2.65/2.84 (r(s(s(z)), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[345, 10426])).
% 2.65/2.84 tff(10428,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10291, 163, 153, 3272, 10427, 152])).
% 2.65/2.84 tff(10429,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10430,plain,
% 2.65/2.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10429, 3272, 55, 10261, 10418, 9365])).
% 2.65/2.84 tff(10431,plain,
% 2.65/2.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[176, 10430])).
% 2.65/2.84 tff(10432,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10433,plain,
% 2.65/2.84 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10434,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10433])).
% 2.65/2.84 tff(10435,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10434, 10432])).
% 2.65/2.84 tff(10436,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10437,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10436, 10435])).
% 2.65/2.84 tff(10438,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10437, 163, 153, 3272, 33, 3639])).
% 2.65/2.84 tff(10439,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10440,plain,
% 2.65/2.84 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10439, 3272, 55, 9365])).
% 2.65/2.84 tff(10441,plain,
% 2.65/2.84 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[31, 10440])).
% 2.65/2.84 tff(10442,plain,
% 2.65/2.84 (~r(s(s(z)), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10416, 3639, 407, 153, 595])).
% 2.65/2.84 tff(10443,plain,
% 2.65/2.84 (b(s(s(z)), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[487, 10442])).
% 2.65/2.84 tff(10444,plain,
% 2.65/2.84 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10439, 3272, 153, 3639])).
% 2.65/2.84 tff(10445,plain,
% 2.65/2.84 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[31, 10444])).
% 2.65/2.84 tff(10446,plain,
% 2.65/2.84 (~r(s(s(s(s(s(z))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[6822, 150, 153, 10443, 3272])).
% 2.65/2.84 tff(10447,plain,
% 2.65/2.84 (b(s(s(s(s(s(z))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3841, 10446])).
% 2.65/2.84 tff(10448,plain,
% 2.65/2.84 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[4174, 331, 4167, 9620])).
% 2.65/2.84 tff(10449,plain,
% 2.65/2.84 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3098, 10448])).
% 2.65/2.84 tff(10450,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10256, 10449, 407, 560, 3272, 3639])).
% 2.65/2.84 tff(10451,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3301, 10450])).
% 2.65/2.84 tff(10452,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10453,plain,
% 2.65/2.84 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10454,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10453])).
% 2.65/2.84 tff(10455,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10454, 10452])).
% 2.65/2.84 tff(10456,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10457,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10456, 10455])).
% 2.65/2.84 tff(10458,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10457, 163, 150, 3066, 6249, 7912])).
% 2.65/2.84 tff(10459,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10460,plain,
% 2.65/2.84 (~r(z, s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10459, 10451, 150, 10449])).
% 2.65/2.84 tff(10461,plain,
% 2.65/2.84 (b(z, s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[4110, 10460])).
% 2.65/2.84 tff(10462,plain,
% 2.65/2.84 (~r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9546, 10449, 150, 3639])).
% 2.65/2.84 tff(10463,plain,
% 2.65/2.84 (b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[469, 10462])).
% 2.65/2.84 tff(10464,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10465,plain,
% 2.65/2.84 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(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(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10466,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10465])).
% 2.65/2.84 tff(10467,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10466, 10464])).
% 2.65/2.84 tff(10468,plain,
% 2.65/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10469,plain,
% 2.65/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10468, 10467])).
% 2.65/2.84 tff(10470,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10469, 198, 595, 3615, 331, 10463, 10461])).
% 2.65/2.84 tff(10471,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10472,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10471, 10447, 10445, 595, 3639, 407, 10443, 3272, 150])).
% 2.65/2.84 tff(10473,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3613, 10472])).
% 2.65/2.84 tff(10474,plain,
% 2.65/2.84 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10429, 3272, 153, 595, 10443, 3639])).
% 2.65/2.84 tff(10475,plain,
% 2.65/2.84 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[176, 10474])).
% 2.65/2.84 tff(10476,plain,
% 2.65/2.84 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[4174, 10447, 10445, 10475])).
% 2.65/2.84 tff(10477,plain,
% 2.65/2.84 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3098, 10476])).
% 2.65/2.84 tff(10478,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10256, 10477, 407, 10443, 3272, 3639])).
% 2.65/2.84 tff(10479,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3301, 10478])).
% 2.65/2.84 tff(10480,plain,
% 2.65/2.84 ($false),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9612, 163, 10477, 10479, 10473, 3639])).
% 2.65/2.84 tff(10481,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.84 tff(10482,plain,
% 2.65/2.84 (~r(s(z), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10481, 3272, 407, 9365, 10261, 55])).
% 2.65/2.84 tff(10483,plain,
% 2.65/2.84 (b(s(z), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[40, 10482])).
% 2.65/2.84 tff(10484,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[8483, 10483, 10441, 10431])).
% 2.65/2.84 tff(10485,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3613, 10484])).
% 2.65/2.84 tff(10486,plain,
% 2.65/2.84 (~b(s(s(s(s(s(z))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[4174, 3819, 10441, 10431])).
% 2.65/2.84 tff(10487,plain,
% 2.65/2.84 (r(s(s(s(s(s(z))))), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3841, 10486])).
% 2.65/2.84 tff(10488,plain,
% 2.65/2.84 (~b(s(s(z)), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10425, 198, 10483, 10261, 10418])).
% 2.65/2.84 tff(10489,plain,
% 2.65/2.84 (r(s(s(z)), z)),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[345, 10488])).
% 2.65/2.84 tff(10490,plain,
% 2.65/2.84 (~r(z, s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10236, 10489, 55, 407, 9365, 10483])).
% 2.65/2.84 tff(10491,plain,
% 2.65/2.84 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10408, 163, 55, 10489, 10487])).
% 2.65/2.84 tff(10492,plain,
% 2.65/2.84 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9885, 10491])).
% 2.65/2.84 tff(10493,plain,
% 2.65/2.84 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10400, 163, 55, 10489, 10487])).
% 2.65/2.84 tff(10494,plain,
% 2.65/2.84 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9576, 10493])).
% 2.65/2.84 tff(10495,plain,
% 2.65/2.84 (~b(s(s(s(s(s(z))))), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[7909, 198, 10418, 407, 10494])).
% 2.65/2.84 tff(10496,plain,
% 2.65/2.84 (r(s(s(s(s(s(z))))), s(z))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[469, 10495])).
% 2.65/2.84 tff(10497,plain,
% 2.65/2.84 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10492, 10494])).
% 2.65/2.84 tff(10498,plain,
% 2.65/2.84 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[3301, 10497])).
% 2.65/2.84 tff(10499,plain,
% 2.65/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10500,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.84 tff(10501,plain,
% 2.65/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.65/2.84 inference(modus_ponens,[status(thm)],[10500, 10499])).
% 2.65/2.84 tff(10502,plain,
% 2.65/2.84 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[10501, 163, 10498, 9365, 10496])).
% 2.65/2.84 tff(10503,plain,
% 2.65/2.84 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.65/2.84 inference(unit_resolution,[status(thm)],[9643, 10502])).
% 2.65/2.84 tff(10504,plain,
% 2.65/2.84 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(rewrite,[status(thm)],[])).
% 2.65/2.84 tff(10505,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.65/2.84 inference(monotonicity,[status(thm)],[10504])).
% 2.65/2.84 tff(10506,plain,
% 2.65/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(transitivity,[status(thm)],[10505, 5364])).
% 2.65/2.84 tff(10507,plain,
% 2.65/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.65/2.84 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10508,plain,
% 2.65/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10507, 10506])).
% 2.65/2.85 tff(10509,plain,
% 2.65/2.85 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10508, 198, 10492, 10503, 10494])).
% 2.65/2.85 tff(10510,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10511,plain,
% 2.65/2.85 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10512,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10511])).
% 2.65/2.85 tff(10513,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10512, 10510])).
% 2.65/2.85 tff(10514,plain,
% 2.65/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10515,plain,
% 2.65/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10514, 10513])).
% 2.65/2.85 tff(10516,plain,
% 2.65/2.85 (~b(z, s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10515, 198, 3819, 10441, 10503])).
% 2.65/2.85 tff(10517,plain,
% 2.65/2.85 (r(z, s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[4110, 10516])).
% 2.65/2.85 tff(10518,plain,
% 2.65/2.85 (s(s(z)) = s(s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[3493, 3490])).
% 2.65/2.85 tff(10519,plain,
% 2.65/2.85 (s(elem!1) = s(z)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[822, 10518])).
% 2.65/2.85 tff(10520,plain,
% 2.65/2.85 (z = elem!1),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[814, 10519])).
% 2.65/2.85 tff(10521,plain,
% 2.65/2.85 (elem!1 = z),
% 2.65/2.85 inference(symmetry,[status(thm)],[10520])).
% 2.65/2.85 tff(10522,plain,
% 2.65/2.85 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10521])).
% 2.65/2.85 tff(10523,plain,
% 2.65/2.85 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.65/2.85 inference(symmetry,[status(thm)],[10522])).
% 2.65/2.85 tff(10524,plain,
% 2.65/2.85 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[3490])).
% 2.65/2.85 tff(10525,plain,
% 2.65/2.85 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10524])).
% 2.65/2.85 tff(10526,plain,
% 2.65/2.85 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10525, 10520])).
% 2.65/2.85 tff(10527,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 2.65/2.85 inference(symmetry,[status(thm)],[10526])).
% 2.65/2.85 tff(10528,plain,
% 2.65/2.85 (~r(z, s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[3240, 10519, 3237])).
% 2.65/2.85 tff(10529,plain,
% 2.65/2.85 (b(z, s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1791, 10528])).
% 2.65/2.85 tff(10530,plain,
% 2.65/2.85 (b(s(elem!1), z)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1209, 10520, 1185])).
% 2.65/2.85 tff(10531,plain,
% 2.65/2.85 (~r(z, elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[7300, 10520])).
% 2.65/2.85 tff(10532,plain,
% 2.65/2.85 (~(elem!1 = s(s(elem!1)))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[110, 10531, 89])).
% 2.65/2.85 tff(10533,plain,
% 2.65/2.85 (~(s(s(elem!1)) = elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[118, 10532])).
% 2.65/2.85 tff(10534,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1250, 10533])).
% 2.65/2.85 tff(10535,plain,
% 2.65/2.85 (elem!1 = z),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[78, 10520])).
% 2.65/2.85 tff(10536,plain,
% 2.65/2.85 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1032, 10535, 330])).
% 2.65/2.85 tff(10537,plain,
% 2.65/2.85 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10520])).
% 2.65/2.85 tff(10538,plain,
% 2.65/2.85 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[331, 10537])).
% 2.65/2.85 tff(10539,plain,
% 2.65/2.85 (b(z, s(z))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[593, 3237])).
% 2.65/2.85 tff(10540,plain,
% 2.65/2.85 (b(elem!1, s(z)) <=> b(z, s(z))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[80])).
% 2.65/2.85 tff(10541,plain,
% 2.65/2.85 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10540])).
% 2.65/2.85 tff(10542,plain,
% 2.65/2.85 (b(elem!1, s(z))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[595, 10541])).
% 2.65/2.85 tff(10543,plain,
% 2.65/2.85 ($false),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[238, 10542])).
% 2.65/2.85 tff(10544,plain,((~(elem!1 = z)) | b(elem!1, s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.85 tff(10545,plain,
% 2.65/2.85 (b(elem!1, s(z))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10544, 10535, 10539])).
% 2.65/2.85 tff(10546,plain,
% 2.65/2.85 (b(s(z), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[4923, 10520, 1185])).
% 2.65/2.85 tff(10547,plain,
% 2.65/2.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10525])).
% 2.65/2.85 tff(10548,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10547])).
% 2.65/2.85 tff(10549,plain,
% 2.65/2.85 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[3490])).
% 2.65/2.85 tff(10550,plain,
% 2.65/2.85 (s(elem!1) = s(z)),
% 2.65/2.85 inference(transitivity,[status(thm)],[135, 10549, 222])).
% 2.65/2.85 tff(10551,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10550])).
% 2.65/2.85 tff(10552,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10551, 10548])).
% 2.65/2.85 tff(10553,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.65/2.85 tff(10554,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[57])).
% 2.65/2.85 tff(10555,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.65/2.85 inference(symmetry,[status(thm)],[10554])).
% 2.65/2.85 tff(10556,plain,
% 2.65/2.85 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10555])).
% 2.65/2.85 tff(10557,plain,
% 2.65/2.85 (~r(s(s(s(elem!1))), z)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10553, 10556])).
% 2.65/2.85 tff(10558,plain,
% 2.65/2.85 ($false),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1352, 10557])).
% 2.65/2.85 tff(10559,plain,((~(z = elem!1)) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.65/2.85 tff(10560,plain,
% 2.65/2.85 (~r(s(s(s(elem!1))), z)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10559, 10553, 10520])).
% 2.65/2.85 tff(10561,plain,
% 2.65/2.85 (b(s(s(s(elem!1))), z)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1295, 10560])).
% 2.65/2.85 tff(10562,plain,
% 2.65/2.85 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1810, 10561, 1175, 1801])).
% 2.65/2.85 tff(10563,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), s(elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1339, 10562, 1256])).
% 2.65/2.85 tff(10564,plain,
% 2.65/2.85 (r(s(s(s(z))), s(z))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10563, 10552])).
% 2.65/2.85 tff(10565,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10566,plain,
% 2.65/2.85 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10567,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10566])).
% 2.65/2.85 tff(10568,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10567, 10565])).
% 2.65/2.85 tff(10569,plain,
% 2.65/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10570,plain,
% 2.65/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10569, 10568])).
% 2.65/2.85 tff(10571,plain,
% 2.65/2.85 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10570, 163, 10564, 6249, 3639])).
% 2.65/2.85 tff(10572,plain,
% 2.65/2.85 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10524])).
% 2.65/2.85 tff(10573,plain,
% 2.65/2.85 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10520])).
% 2.65/2.85 tff(10574,plain,
% 2.65/2.85 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10573])).
% 2.65/2.85 tff(10575,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = elem!1)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[968, 10574])).
% 2.65/2.85 tff(10576,plain,
% 2.65/2.85 (b(s(s(s(elem!1))), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1308, 10553, 10575])).
% 2.65/2.85 tff(10577,plain,
% 2.65/2.85 (b(s(s(s(z))), elem!1)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10576, 10572])).
% 2.65/2.85 tff(10578,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10579,plain,
% 2.65/2.85 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10580,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10579])).
% 2.65/2.85 tff(10581,plain,
% 2.65/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10580, 10578])).
% 2.65/2.85 tff(10582,plain,
% 2.65/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10583,plain,
% 2.65/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10582, 10581])).
% 2.65/2.85 tff(10584,plain,
% 2.65/2.85 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10583, 198, 5927, 320, 10577, 707, 831])).
% 2.65/2.85 tff(10585,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.65/2.85 tff(10586,plain,
% 2.65/2.85 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10524, 10585])).
% 2.65/2.85 tff(10587,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[4845, 10520])).
% 2.65/2.85 tff(10588,plain,
% 2.65/2.85 ($false),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10587, 10586])).
% 2.65/2.85 tff(10589,plain,((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.85 tff(10590,plain,
% 2.65/2.85 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10589, 3490])).
% 2.65/2.85 tff(10591,plain,
% 2.65/2.85 (((~![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)))))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10592,plain,
% 2.65/2.85 ((~![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)))))))))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10593,plain,
% 2.65/2.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10592, 10591])).
% 2.65/2.85 tff(10594,plain,
% 2.65/2.85 ($false),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10593, 26, 10590, 10584, 10571])).
% 2.65/2.85 tff(10595,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(s(elem!1)) = s(s(z)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.85 tff(10596,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10595, 10546, 3639, 6249, 10545, 10538, 10536, 3490, 10534, 10530, 10529])).
% 2.65/2.85 tff(10597,plain,
% 2.65/2.85 (r(s(s(s(z))), z)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10596, 10527])).
% 2.65/2.85 tff(10598,plain,
% 2.65/2.85 (r(s(s(s(z))), elem!1)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10597, 10523])).
% 2.65/2.85 tff(10599,plain,
% 2.65/2.85 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10520])).
% 2.65/2.85 tff(10600,plain,
% 2.65/2.85 (r(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[7912, 10599])).
% 2.65/2.85 tff(10601,plain,
% 2.65/2.85 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10520])).
% 2.65/2.85 tff(10602,plain,
% 2.65/2.85 (r(s(s(s(s(s(z))))), elem!1)),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[3828, 10601])).
% 2.65/2.85 tff(10603,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10604,plain,
% 2.65/2.85 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10605,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10604])).
% 2.65/2.85 tff(10606,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10605, 10603])).
% 2.65/2.85 tff(10607,plain,
% 2.65/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10608,plain,
% 2.65/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10607, 10606])).
% 2.65/2.85 tff(10609,plain,
% 2.65/2.85 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10608, 163, 10602, 10600])).
% 2.65/2.85 tff(10610,plain,
% 2.65/2.85 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10609, 10598])).
% 2.65/2.85 tff(10611,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.65/2.85 tff(10612,plain,
% 2.65/2.85 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[9558])).
% 2.65/2.85 tff(10613,plain,
% 2.65/2.85 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.65/2.85 inference(transitivity,[status(thm)],[10612, 10611])).
% 2.65/2.85 tff(10614,plain,
% 2.65/2.85 (z = elem!1),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1079, 80])).
% 2.65/2.85 tff(10615,plain,
% 2.65/2.85 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[1644])).
% 2.65/2.85 tff(10616,plain,
% 2.65/2.85 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10615])).
% 2.65/2.85 tff(10617,plain,
% 2.65/2.85 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10616])).
% 2.65/2.85 tff(10618,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[1282, 10617])).
% 2.65/2.85 tff(10619,plain,
% 2.65/2.85 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[2619, 10618])).
% 2.65/2.85 tff(10620,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[4899, 10619, 10614])).
% 2.65/2.85 tff(10621,plain,
% 2.65/2.85 ($false),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10620, 10613])).
% 2.65/2.85 tff(10622,plain,((~(s(s(s(z))) = s(s(s(s(s(z))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.85 tff(10623,plain,
% 2.65/2.85 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10622, 10535])).
% 2.65/2.85 tff(10624,plain,
% 2.65/2.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10625,plain,
% 2.65/2.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.65/2.85 inference(quant_inst,[status(thm)],[])).
% 2.65/2.85 tff(10626,plain,
% 2.65/2.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.85 inference(modus_ponens,[status(thm)],[10625, 10624])).
% 2.65/2.85 tff(10627,plain,
% 2.65/2.85 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10626, 26, 10623, 10610])).
% 2.65/2.85 tff(10628,plain,
% 2.65/2.85 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10525, 3491])).
% 2.65/2.85 tff(10629,plain,
% 2.65/2.85 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10628])).
% 2.65/2.85 tff(10630,plain,
% 2.65/2.85 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1263, 10534])).
% 2.65/2.85 tff(10631,plain,
% 2.65/2.85 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[1270, 10630])).
% 2.65/2.85 tff(10632,plain,
% 2.65/2.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10524, 3490])).
% 2.65/2.85 tff(10633,plain,
% 2.65/2.85 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.65/2.85 inference(symmetry,[status(thm)],[10632])).
% 2.65/2.85 tff(10634,plain,
% 2.65/2.85 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10633])).
% 2.65/2.85 tff(10635,plain,
% 2.65/2.85 (~(s(s(z)) = elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[7929, 10536, 7925])).
% 2.65/2.85 tff(10636,plain,
% 2.65/2.85 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[420, 7925])).
% 2.65/2.85 tff(10637,plain,
% 2.65/2.85 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[8483, 330, 1185, 331])).
% 2.65/2.85 tff(10638,plain,
% 2.65/2.85 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[3613, 10637])).
% 2.65/2.85 tff(10639,plain,
% 2.65/2.85 (~r(s(s(z)), s(z))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[10328, 10638, 10636, 3639])).
% 2.65/2.85 tff(10640,plain,
% 2.65/2.85 (b(s(s(z)), s(z))),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[487, 10639])).
% 2.65/2.85 tff(10641,plain,
% 2.65/2.85 (~b(s(s(z)), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[6661, 10545, 10546, 10640])).
% 2.65/2.85 tff(10642,plain,
% 2.65/2.85 (r(s(s(z)), elem!1)),
% 2.65/2.85 inference(unit_resolution,[status(thm)],[2139, 10641, 10635])).
% 2.65/2.85 tff(10643,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10644,plain,
% 2.65/2.85 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.85 inference(rewrite,[status(thm)],[])).
% 2.65/2.85 tff(10645,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))))),
% 2.65/2.85 inference(monotonicity,[status(thm)],[10644])).
% 2.65/2.85 tff(10646,plain,
% 2.65/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10645, 10643])).
% 2.65/2.86 tff(10647,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10648,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10647, 10646])).
% 2.65/2.86 tff(10649,plain,
% 2.65/2.86 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10648, 163, 10642, 10600])).
% 2.65/2.86 tff(10650,plain,
% 2.65/2.86 (~r(s(s(s(z))), s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10649, 10598])).
% 2.65/2.86 tff(10651,plain,
% 2.65/2.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10650, 10634])).
% 2.65/2.86 tff(10652,plain,
% 2.65/2.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[1326, 10651, 10631])).
% 2.65/2.86 tff(10653,plain,
% 2.65/2.86 (b(s(s(s(z))), s(s(z)))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10652, 10629])).
% 2.65/2.86 tff(10654,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10655,plain,
% 2.65/2.86 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(z))), s(s(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10656,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10655])).
% 2.65/2.86 tff(10657,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10656, 10654])).
% 2.65/2.86 tff(10658,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10659,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10658, 10657])).
% 2.65/2.86 tff(10660,plain,
% 2.65/2.86 ($false),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10659, 198, 7896, 4049, 10653, 10627])).
% 2.65/2.86 tff(10661,plain,((~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | b(z, s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.86 tff(10662,plain,
% 2.65/2.86 (b(z, s(s(elem!1)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10661, 3490, 4049, 9365, 6249, 3828, 7912, 331, 7925, 7896, 330, 1185, 3237])).
% 2.65/2.86 tff(10663,plain,
% 2.65/2.86 (~b(elem!1, s(s(elem!1)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[71, 10520, 42])).
% 2.65/2.86 tff(10664,plain,
% 2.65/2.86 ($false),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[87, 10663, 10535, 10662])).
% 2.65/2.86 tff(10665,plain,((~(s(s(elem!1)) = s(s(z)))) | b(z, s(s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.86 tff(10666,plain,
% 2.65/2.86 (~(s(s(elem!1)) = s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10665, 10494, 42, 10498, 10487, 10517, 10441, 10509, 10492, 10431, 10483, 10490])).
% 2.65/2.86 tff(10667,plain,
% 2.65/2.86 (s(s(s(elem!1))) = s(elem!1)),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[2064, 677])).
% 2.65/2.86 tff(10668,plain,
% 2.65/2.86 (~b(s(s(z)), z)),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10425, 198, 1185, 595, 10443])).
% 2.65/2.86 tff(10669,plain,
% 2.65/2.86 (r(s(s(z)), z)),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[345, 10668])).
% 2.65/2.86 tff(10670,plain,
% 2.65/2.86 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10400, 163, 153, 10669, 3828])).
% 2.65/2.86 tff(10671,plain,
% 2.65/2.86 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[9576, 10670])).
% 2.65/2.86 tff(10672,plain,
% 2.65/2.86 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10408, 163, 153, 10669, 3828])).
% 2.65/2.86 tff(10673,plain,
% 2.65/2.86 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[9885, 10672])).
% 2.65/2.86 tff(10674,plain,
% 2.65/2.86 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10673, 10671])).
% 2.65/2.86 tff(10675,plain,
% 2.65/2.86 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[3301, 10674])).
% 2.65/2.86 tff(10676,plain,
% 2.65/2.86 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[90])).
% 2.65/2.86 tff(10677,plain,
% 2.65/2.86 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10676])).
% 2.65/2.86 tff(10678,plain,
% 2.65/2.86 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[3792, 7862])).
% 2.65/2.86 tff(10679,plain,
% 2.65/2.86 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10678, 10677])).
% 2.65/2.86 tff(10680,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10681,plain,
% 2.65/2.86 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10682,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10681])).
% 2.65/2.86 tff(10683,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10682, 10680])).
% 2.65/2.86 tff(10684,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10685,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10684, 10683])).
% 2.65/2.86 tff(10686,plain,
% 2.65/2.86 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10685, 198, 723, 1185, 595, 331, 330])).
% 2.65/2.86 tff(10687,plain,
% 2.65/2.86 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[934, 26, 10686, 930])).
% 2.65/2.86 tff(10688,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10689,plain,
% 2.65/2.86 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10690,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10689])).
% 2.65/2.86 tff(10691,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10690, 10688])).
% 2.65/2.86 tff(10692,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10693,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10692, 10691])).
% 2.65/2.86 tff(10694,plain,
% 2.65/2.86 ($false),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10693, 163, 9275, 6249, 3639, 10687])).
% 2.65/2.86 tff(10695,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.86 tff(10696,plain,
% 2.65/2.86 (~b(s(s(elem!1)), z)),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10695, 10679, 3639, 10675, 1185, 595, 331, 330])).
% 2.65/2.86 tff(10697,plain,
% 2.65/2.86 (r(s(s(elem!1)), z)),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[801, 10696])).
% 2.65/2.86 tff(10698,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10699,plain,
% 2.65/2.86 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10700,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10699])).
% 2.65/2.86 tff(10701,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10700, 10698])).
% 2.65/2.86 tff(10702,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10703,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10702, 10701])).
% 2.65/2.86 tff(10704,plain,
% 2.65/2.86 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10703, 163, 10697, 153, 3828])).
% 2.65/2.86 tff(10705,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 2.65/2.86 tff(10706,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10707,plain,
% 2.65/2.86 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10708,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10707])).
% 2.65/2.86 tff(10709,plain,
% 2.65/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10708, 10706])).
% 2.65/2.86 tff(10710,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10711,plain,
% 2.65/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10710, 10709])).
% 2.65/2.86 tff(10712,plain,
% 2.65/2.86 (~r(s(s(elem!1)), s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10711, 163, 10697, 153, 10669])).
% 2.65/2.86 tff(10713,plain,
% 2.65/2.86 (b(s(s(elem!1)), s(s(z)))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[3497, 26, 10712, 10705])).
% 2.65/2.86 tff(10714,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10715,plain,
% 2.65/2.86 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(rewrite,[status(thm)],[])).
% 2.65/2.86 tff(10716,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10715])).
% 2.65/2.86 tff(10717,plain,
% 2.65/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.65/2.86 inference(transitivity,[status(thm)],[10716, 10714])).
% 2.65/2.86 tff(10718,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.65/2.86 inference(quant_inst,[status(thm)],[])).
% 2.65/2.86 tff(10719,plain,
% 2.65/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.65/2.86 inference(modus_ponens,[status(thm)],[10718, 10717])).
% 2.65/2.86 tff(10720,plain,
% 2.65/2.86 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[10719, 198, 10443, 407, 10673, 10671, 10713])).
% 2.65/2.86 tff(10721,plain,
% 2.65/2.86 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.65/2.86 inference(unit_resolution,[status(thm)],[3400, 10720, 10704])).
% 2.65/2.86 tff(10722,plain,
% 2.65/2.86 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.65/2.86 inference(symmetry,[status(thm)],[10721])).
% 2.65/2.86 tff(10723,plain,
% 2.65/2.86 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.65/2.86 inference(monotonicity,[status(thm)],[10722])).
% 2.65/2.86 tff(10724,plain,
% 2.65/2.86 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.65/2.86 inference(transitivity,[status(thm)],[10723, 10667])).
% 2.65/2.86 tff(10725,plain,
% 2.65/2.86 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10724])).
% 2.65/2.87 tff(10726,plain,
% 2.65/2.87 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10725])).
% 2.65/2.87 tff(10727,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10679, 10726])).
% 2.65/2.87 tff(10728,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10729,plain,
% 2.65/2.87 (~(elem!1 = s(s(elem!1)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10728, 10666, 407, 55, 10487, 9365, 10483, 10261, 10441, 10431])).
% 2.65/2.87 tff(10730,plain,
% 2.65/2.87 (~b(s(s(z)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10425, 198, 1185, 10261, 10418])).
% 2.65/2.87 tff(10731,plain,
% 2.65/2.87 (r(s(s(z)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[345, 10730])).
% 2.65/2.87 tff(10732,plain,
% 2.65/2.87 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10400, 163, 55, 10731, 3828])).
% 2.65/2.87 tff(10733,plain,
% 2.65/2.87 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[9576, 10732])).
% 2.65/2.87 tff(10734,plain,
% 2.65/2.87 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10408, 163, 55, 10731, 3828])).
% 2.65/2.87 tff(10735,plain,
% 2.65/2.87 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[9885, 10734])).
% 2.65/2.87 tff(10736,plain,
% 2.65/2.87 (~b(s(z), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10735, 10733])).
% 2.65/2.87 tff(10737,plain,
% 2.65/2.87 (r(s(z), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[3301, 10736])).
% 2.65/2.87 tff(10738,plain,
% 2.65/2.87 (b(z, elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[102, 56, 1999])).
% 2.65/2.87 tff(10739,plain,
% 2.65/2.87 (b(z, s(s(s(s(s(z)))))) <=> b(z, elem!1)),
% 2.65/2.87 inference(monotonicity,[status(thm)],[3893])).
% 2.65/2.87 tff(10740,plain,
% 2.65/2.87 (b(z, elem!1) <=> b(z, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10739])).
% 2.65/2.87 tff(10741,plain,
% 2.65/2.87 (b(z, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[95, 10740])).
% 2.65/2.87 tff(10742,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[4105, 10741])).
% 2.65/2.87 tff(10743,plain,((~(s(s(s(s(s(z))))) = elem!1)) | b(z, s(s(s(s(s(z)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10744,plain,
% 2.65/2.87 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10743, 10738, 4105])).
% 2.65/2.87 tff(10745,plain,
% 2.65/2.87 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.65/2.87 inference(transitivity,[status(thm)],[135, 4299, 275])).
% 2.65/2.87 tff(10746,plain,
% 2.65/2.87 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10745])).
% 2.65/2.87 tff(10747,plain,
% 2.65/2.87 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10746])).
% 2.65/2.87 tff(10748,plain,
% 2.65/2.87 (s(s(s(s(s(z))))) = elem!1),
% 2.65/2.87 inference(transitivity,[status(thm)],[281, 10747, 129])).
% 2.65/2.87 tff(10749,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[570, 10748])).
% 2.65/2.87 tff(10750,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10751,plain,
% 2.65/2.87 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10750, 10744])).
% 2.65/2.87 tff(10752,plain,
% 2.65/2.87 (~b(s(s(elem!1)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10695, 10751, 9365, 10737, 1185, 10261, 331, 330])).
% 2.65/2.87 tff(10753,plain,
% 2.65/2.87 (r(s(s(elem!1)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[801, 10752])).
% 2.65/2.87 tff(10754,plain,
% 2.65/2.87 (~b(s(s(z)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10425, 198, 1185, 595, 560])).
% 2.65/2.87 tff(10755,plain,
% 2.65/2.87 (r(s(s(z)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[344, 26, 46, 10754])).
% 2.65/2.87 tff(10756,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10757,plain,
% 2.65/2.87 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10758,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10757])).
% 2.65/2.87 tff(10759,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10758, 10756])).
% 2.65/2.87 tff(10760,plain,
% 2.65/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10761,plain,
% 2.65/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10760, 10759])).
% 2.65/2.87 tff(10762,plain,
% 2.65/2.87 (~b(z, s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10761, 198, 1185, 595, 560, 407])).
% 2.65/2.87 tff(10763,plain,
% 2.65/2.87 ((z = s(s(z))) | r(z, s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[52, 26, 10762])).
% 2.65/2.87 tff(10764,plain,
% 2.65/2.87 (r(z, s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10763, 9371])).
% 2.65/2.87 tff(10765,plain,
% 2.65/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10766,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10767,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 2.65/2.87 tff(10768,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10767, 163, 790, 2894, 10764, 10755])).
% 2.65/2.87 tff(10769,plain,((~b(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10770,plain,
% 2.65/2.87 (~r(s(s(z)), s(s(elem!1)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10769, 10753, 407, 1185, 10261, 10418])).
% 2.65/2.87 tff(10771,plain,
% 2.65/2.87 (b(s(s(z)), s(s(elem!1)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[2161, 26, 10770, 2154])).
% 2.65/2.87 tff(10772,plain,
% 2.65/2.87 (~(elem!1 = z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[1032, 244, 330])).
% 2.65/2.87 tff(10773,plain,
% 2.65/2.87 (~(z = elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[78, 10772])).
% 2.65/2.87 tff(10774,plain,
% 2.65/2.87 (b(z, elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[102, 10773, 56])).
% 2.65/2.87 tff(10775,plain,
% 2.65/2.87 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10743, 10774, 4105])).
% 2.65/2.87 tff(10776,plain,
% 2.65/2.87 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10750, 10775])).
% 2.65/2.87 tff(10777,plain,
% 2.65/2.87 (~b(s(s(elem!1)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10695, 10776, 9365, 10737, 1185, 10261, 331, 330])).
% 2.65/2.87 tff(10778,plain,
% 2.65/2.87 (r(s(s(elem!1)), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[801, 10777])).
% 2.65/2.87 tff(10779,plain,
% 2.65/2.87 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10703, 163, 10778, 55, 3828])).
% 2.65/2.87 tff(10780,plain,
% 2.65/2.87 (~(s(elem!1) = s(z))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[814, 10773])).
% 2.65/2.87 tff(10781,plain,
% 2.65/2.87 (~(s(s(z)) = s(s(elem!1)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[822, 10780])).
% 2.65/2.87 tff(10782,plain,
% 2.65/2.87 (~(s(s(elem!1)) = s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[3493, 10781])).
% 2.65/2.87 tff(10783,plain,
% 2.65/2.87 (~r(s(s(elem!1)), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10711, 163, 10778, 55, 10731])).
% 2.65/2.87 tff(10784,plain,
% 2.65/2.87 (b(s(s(elem!1)), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[3497, 26, 10783, 10782])).
% 2.65/2.87 tff(10785,plain,
% 2.65/2.87 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10719, 198, 10418, 407, 10735, 10733, 10784])).
% 2.65/2.87 tff(10786,plain,
% 2.65/2.87 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[3400, 10785, 10779])).
% 2.65/2.87 tff(10787,plain,
% 2.65/2.87 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[9265, 10786])).
% 2.65/2.87 tff(10788,plain,
% 2.65/2.87 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[256, 10787, 244])).
% 2.65/2.87 tff(10789,plain,
% 2.65/2.87 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[8483, 1185, 331, 330])).
% 2.65/2.87 tff(10790,plain,
% 2.65/2.87 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[3613, 10789])).
% 2.65/2.87 tff(10791,plain,
% 2.65/2.87 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10786])).
% 2.65/2.87 tff(10792,plain,
% 2.65/2.87 (s(elem!1) = s(s(s(s(z))))),
% 2.65/2.87 inference(transitivity,[status(thm)],[135, 10791, 288])).
% 2.65/2.87 tff(10793,plain,
% 2.65/2.87 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10792])).
% 2.65/2.87 tff(10794,plain,
% 2.65/2.87 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10793])).
% 2.65/2.87 tff(10795,plain,
% 2.65/2.87 (s(s(s(z))) = elem!1),
% 2.65/2.87 inference(transitivity,[status(thm)],[294, 10794, 129])).
% 2.65/2.87 tff(10796,plain,
% 2.65/2.87 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10795])).
% 2.65/2.87 tff(10797,plain,
% 2.65/2.87 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(z))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10796, 1241])).
% 2.65/2.87 tff(10798,plain,
% 2.65/2.87 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(z)))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10797])).
% 2.65/2.87 tff(10799,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 2.65/2.87 tff(10800,plain,
% 2.65/2.87 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10799])).
% 2.65/2.87 tff(10801,plain,
% 2.65/2.87 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10800])).
% 2.65/2.87 tff(10802,plain,
% 2.65/2.87 (s(s(z)) = z),
% 2.65/2.87 inference(transitivity,[status(thm)],[299, 10801, 304])).
% 2.65/2.87 tff(10803,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[46, 10802])).
% 2.65/2.87 tff(10804,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10805,plain,
% 2.65/2.87 (~(elem!1 = s(z))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10804, 10798])).
% 2.65/2.87 tff(10806,plain,
% 2.65/2.87 (elem!1 = s(s(s(z)))),
% 2.65/2.87 inference(transitivity,[status(thm)],[4242, 10793, 293])).
% 2.65/2.87 tff(10807,plain,
% 2.65/2.87 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10806])).
% 2.65/2.87 tff(10808,plain,
% 2.65/2.87 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10807])).
% 2.65/2.87 tff(10809,plain,
% 2.65/2.87 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10808])).
% 2.65/2.87 tff(10810,plain,
% 2.65/2.87 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10786])).
% 2.65/2.87 tff(10811,plain,
% 2.65/2.87 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 2.65/2.87 inference(symmetry,[status(thm)],[10810])).
% 2.65/2.87 tff(10812,plain,
% 2.65/2.87 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10811, 113])).
% 2.65/2.87 tff(10813,plain,
% 2.65/2.87 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10812])).
% 2.65/2.87 tff(10814,plain,
% 2.65/2.87 (~(elem!1 = s(s(elem!1)))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10775, 10813])).
% 2.65/2.87 tff(10815,plain,
% 2.65/2.87 (~(elem!1 = s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[4932, 10774, 42])).
% 2.65/2.87 tff(10816,plain,
% 2.65/2.87 (~(s(s(z)) = elem!1)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[6634, 10815])).
% 2.65/2.87 tff(10817,plain,
% 2.65/2.87 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.65/2.87 inference(symmetry,[status(thm)],[9857])).
% 2.65/2.87 tff(10818,plain,
% 2.65/2.87 (s(s(s(z))) = elem!1),
% 2.65/2.87 inference(transitivity,[status(thm)],[294, 10817, 129])).
% 2.65/2.87 tff(10819,plain,
% 2.65/2.87 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10818])).
% 2.65/2.87 tff(10820,plain,
% 2.65/2.87 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10819])).
% 2.65/2.87 tff(10821,plain,
% 2.65/2.87 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[3380])).
% 2.65/2.87 tff(10822,plain,
% 2.65/2.87 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[3380])).
% 2.65/2.87 tff(10823,plain,
% 2.65/2.87 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10822])).
% 2.65/2.87 tff(10824,plain,
% 2.65/2.87 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10818])).
% 2.65/2.87 tff(10825,plain,
% 2.65/2.87 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10824, 10823])).
% 2.65/2.87 tff(10826,plain,
% 2.65/2.87 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10825])).
% 2.65/2.87 tff(10827,plain,
% 2.65/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(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))))))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10828,plain,
% 2.65/2.87 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(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))))))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10829,plain,
% 2.65/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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)))))))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10828])).
% 2.65/2.87 tff(10830,plain,
% 2.65/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(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))))))))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10829, 10827])).
% 2.65/2.87 tff(10831,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10832,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(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)))))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10831, 10830])).
% 2.65/2.87 tff(10833,plain,
% 2.65/2.87 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10832, 163, 153, 2665, 3828])).
% 2.65/2.87 tff(10834,plain,
% 2.65/2.87 (~r(elem!1, s(s(elem!1)))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10833, 10826])).
% 2.65/2.87 tff(10835,plain,
% 2.65/2.87 (b(elem!1, s(s(elem!1)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[147, 10834, 116])).
% 2.65/2.87 tff(10836,plain,
% 2.65/2.87 (b(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10835, 10821])).
% 2.65/2.87 tff(10837,plain,
% 2.65/2.87 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10836, 10820])).
% 2.65/2.87 tff(10838,plain,
% 2.65/2.87 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10818])).
% 2.65/2.87 tff(10839,plain,
% 2.65/2.87 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.65/2.87 inference(transitivity,[status(thm)],[10838, 6630])).
% 2.65/2.87 tff(10840,plain,
% 2.65/2.87 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 2.65/2.87 inference(symmetry,[status(thm)],[10839])).
% 2.65/2.87 tff(10841,plain,
% 2.65/2.87 ((~(s(s(z)) = elem!1)) <=> (~(s(s(s(z))) = s(s(z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10840])).
% 2.65/2.87 tff(10842,plain,
% 2.65/2.87 (~(s(s(s(z))) = s(s(z)))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[2105, 10841])).
% 2.65/2.87 tff(10843,plain,
% 2.65/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10844,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10845,plain,
% 2.65/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10844, 10843])).
% 2.65/2.87 tff(10846,plain,
% 2.65/2.87 (~r(s(s(s(z))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10845, 163, 153, 332, 2665])).
% 2.65/2.87 tff(10847,plain,
% 2.65/2.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10848,plain,
% 2.65/2.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10849,plain,
% 2.65/2.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10848, 10847])).
% 2.65/2.87 tff(10850,plain,
% 2.65/2.87 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10849, 26, 10846])).
% 2.65/2.87 tff(10851,plain,
% 2.65/2.87 (b(s(s(s(z))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10850, 10842])).
% 2.65/2.87 tff(10852,plain,
% 2.65/2.87 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10400, 163, 153, 332, 3828])).
% 2.65/2.87 tff(10853,plain,
% 2.65/2.87 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[9576, 10852])).
% 2.65/2.87 tff(10854,plain,
% 2.65/2.87 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10408, 163, 153, 332, 3828])).
% 2.65/2.87 tff(10855,plain,
% 2.65/2.87 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[9885, 10854])).
% 2.65/2.87 tff(10856,plain,
% 2.65/2.87 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10659, 198, 10855, 10853])).
% 2.65/2.87 tff(10857,plain,
% 2.65/2.87 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10856, 10851])).
% 2.65/2.87 tff(10858,plain,
% 2.65/2.87 ($false),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10857, 10837])).
% 2.65/2.87 tff(10859,plain,((~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (s(s(z)) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.87 tff(10860,plain,
% 2.65/2.87 (~r(s(s(s(z))), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10859, 10786, 10816, 10814, 55, 3828, 10731])).
% 2.65/2.87 tff(10861,plain,
% 2.65/2.87 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10862,plain,
% 2.65/2.87 (~(s(s(s(z))) = z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10861, 13])).
% 2.65/2.87 tff(10863,plain,
% 2.65/2.87 (((~![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))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10864,plain,
% 2.65/2.87 ((~![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))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10865,plain,
% 2.65/2.87 ((~![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)),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10864, 10863])).
% 2.65/2.87 tff(10866,plain,
% 2.65/2.87 (b(s(s(s(z))), z)),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10865, 26, 10862, 10860])).
% 2.65/2.87 tff(10867,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10868,plain,
% 2.65/2.87 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10869,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10868])).
% 2.65/2.87 tff(10870,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10869, 10867])).
% 2.65/2.87 tff(10871,plain,
% 2.65/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(quant_inst,[status(thm)],[])).
% 2.65/2.87 tff(10872,plain,
% 2.65/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10871, 10870])).
% 2.65/2.87 tff(10873,plain,
% 2.65/2.87 (~b(s(s(s(z))), s(z))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[10872, 198, 1185, 10261, 10866])).
% 2.65/2.87 tff(10874,plain,
% 2.65/2.87 (~b(elem!1, s(z))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10873, 10809])).
% 2.65/2.87 tff(10875,plain,
% 2.65/2.87 (r(elem!1, s(z))),
% 2.65/2.87 inference(unit_resolution,[status(thm)],[242, 10874, 10805])).
% 2.65/2.87 tff(10876,plain,
% 2.65/2.87 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10796])).
% 2.65/2.87 tff(10877,plain,
% 2.65/2.87 (~(s(z) = elem!1)),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10804, 10876])).
% 2.65/2.87 tff(10878,plain,
% 2.65/2.87 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10806])).
% 2.65/2.87 tff(10879,plain,
% 2.65/2.87 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.65/2.87 inference(symmetry,[status(thm)],[10878])).
% 2.65/2.87 tff(10880,plain,
% 2.65/2.87 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10879])).
% 2.65/2.87 tff(10881,plain,
% 2.65/2.87 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10806])).
% 2.65/2.87 tff(10882,plain,
% 2.65/2.87 (b(z, s(s(s(z))))),
% 2.65/2.87 inference(modus_ponens,[status(thm)],[10774, 10881])).
% 2.65/2.87 tff(10883,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10884,plain,
% 2.65/2.87 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(rewrite,[status(thm)],[])).
% 2.65/2.87 tff(10885,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.65/2.87 inference(monotonicity,[status(thm)],[10884])).
% 2.65/2.87 tff(10886,plain,
% 2.65/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.65/2.87 inference(transitivity,[status(thm)],[10885, 10883])).
% 2.65/2.87 tff(10887,plain,
% 2.65/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10888,plain,
% 2.65/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10887, 10886])).
% 2.65/2.88 tff(10889,plain,
% 2.65/2.88 (~b(s(z), s(s(s(z))))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10888, 198, 1185, 10866, 10882])).
% 2.65/2.88 tff(10890,plain,
% 2.65/2.88 (~b(s(z), elem!1)),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10889, 10880])).
% 2.65/2.88 tff(10891,plain,
% 2.65/2.88 (r(s(z), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[217, 10890, 10877])).
% 2.65/2.88 tff(10892,plain,
% 2.65/2.88 ($false),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[267, 10891, 10875, 10790, 10788])).
% 2.65/2.88 tff(10893,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | b(z, s(s(s(s(s(z)))))) | b(z, s(s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.65/2.88 tff(10894,plain,
% 2.65/2.88 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10893, 56, 3828, 407, 331, 330, 4105, 42, 1185])).
% 2.65/2.88 tff(10895,plain,
% 2.65/2.88 (~b(elem!1, z)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[9622, 10738, 330, 10894])).
% 2.65/2.88 tff(10896,plain,
% 2.65/2.88 (r(elem!1, z)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[187, 10895, 76])).
% 2.65/2.88 tff(10897,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10898,plain,
% 2.65/2.88 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10899,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10898])).
% 2.65/2.88 tff(10900,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10899, 10897])).
% 2.65/2.88 tff(10901,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10902,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10901, 10900])).
% 2.65/2.88 tff(10903,plain,
% 2.65/2.88 (~r(s(s(z)), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10902, 163, 10896, 55, 10731])).
% 2.65/2.88 tff(10904,plain,
% 2.65/2.88 (b(s(s(z)), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[2139, 10903, 2105])).
% 2.65/2.88 tff(10905,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10906,plain,
% 2.65/2.88 (((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10907,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z))))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10906])).
% 2.65/2.88 tff(10908,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10907, 10905])).
% 2.65/2.88 tff(10909,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10910,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z))))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10909, 10908])).
% 2.65/2.88 tff(10911,plain,
% 2.65/2.88 (~r(elem!1, s(s(elem!1)))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10910, 163, 10896, 10753, 55])).
% 2.65/2.88 tff(10912,plain,
% 2.65/2.88 (b(elem!1, s(s(elem!1)))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[147, 10911, 116])).
% 2.65/2.88 tff(10913,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10914,plain,
% 2.65/2.88 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10915,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z))))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10914])).
% 2.65/2.88 tff(10916,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10915, 10913])).
% 2.65/2.88 tff(10917,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10918,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z))))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10917, 10916])).
% 2.65/2.88 tff(10919,plain,
% 2.65/2.88 (~r(s(s(elem!1)), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10918, 163, 10896, 10753, 55])).
% 2.65/2.88 tff(10920,plain,
% 2.65/2.88 (b(s(s(elem!1)), elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[602, 10919, 598])).
% 2.65/2.88 tff(10921,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10922,plain,
% 2.65/2.88 (((~b(s(s(elem!1)), elem!1)) | (~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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10923,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10922])).
% 2.65/2.88 tff(10924,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10923, 10921])).
% 2.65/2.88 tff(10925,plain,
% 2.65/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10926,plain,
% 2.65/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10925, 10924])).
% 2.65/2.88 tff(10927,plain,
% 2.65/2.88 ($false),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10926, 198, 10920, 10912, 10904, 10771])).
% 2.65/2.88 tff(10928,plain,(r(z, elem!1) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = elem!1) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z) | b(z, s(s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.88 tff(10929,plain,
% 2.65/2.88 (r(z, elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10928, 2106, 2105, 116, 407, 10483, 10441, 10431, 1647, 10516, 10487, 42])).
% 2.65/2.88 tff(10930,plain,
% 2.65/2.88 (r(z, elem!1) <=> r(z, s(z))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[229])).
% 2.65/2.88 tff(10931,plain,
% 2.65/2.88 (r(z, s(z)) <=> r(z, elem!1)),
% 2.65/2.88 inference(symmetry,[status(thm)],[10930])).
% 2.65/2.88 tff(10932,plain,
% 2.65/2.88 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10931])).
% 2.65/2.88 tff(10933,plain,
% 2.65/2.88 (~r(z, elem!1)),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[3237, 10932])).
% 2.65/2.88 tff(10934,plain,
% 2.65/2.88 ($false),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[1475, 10933])).
% 2.65/2.88 tff(10935,plain,((~(elem!1 = s(z))) | (~r(z, elem!1)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.88 tff(10936,plain,
% 2.65/2.88 (~(elem!1 = s(z))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10935, 10929, 10490])).
% 2.65/2.88 tff(10937,plain,
% 2.65/2.88 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[7261, 10929, 10440])).
% 2.65/2.88 tff(10938,plain,
% 2.65/2.88 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[3792, 10937])).
% 2.65/2.88 tff(10939,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10940,plain,
% 2.65/2.88 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10941,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10940])).
% 2.65/2.88 tff(10942,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10941, 10939])).
% 2.65/2.88 tff(10943,plain,
% 2.65/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10944,plain,
% 2.65/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10943, 10942])).
% 2.65/2.88 tff(10945,plain,
% 2.65/2.88 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10944, 198, 271, 1185, 595, 331, 330])).
% 2.65/2.88 tff(10946,plain,
% 2.65/2.88 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[703, 10945, 673])).
% 2.65/2.88 tff(10947,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10948,plain,
% 2.65/2.88 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10949,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10948])).
% 2.65/2.88 tff(10950,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10949, 10947])).
% 2.65/2.88 tff(10951,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10952,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10951, 10950])).
% 2.65/2.88 tff(10953,plain,
% 2.65/2.88 ($false),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10952, 163, 9216, 6249, 10946, 3639])).
% 2.65/2.88 tff(10954,plain,((~b(elem!1, z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.88 tff(10955,plain,
% 2.65/2.88 (~b(elem!1, z)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10954, 10938, 9365, 10498, 10936, 10483, 10261, 10441, 10431])).
% 2.65/2.88 tff(10956,plain,
% 2.65/2.88 (r(elem!1, z)),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[187, 10955, 1647])).
% 2.65/2.88 tff(10957,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10958,plain,
% 2.65/2.88 (((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10959,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.65/2.88 inference(monotonicity,[status(thm)],[10958])).
% 2.65/2.88 tff(10960,plain,
% 2.65/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(transitivity,[status(thm)],[10959, 10957])).
% 2.65/2.88 tff(10961,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(quant_inst,[status(thm)],[])).
% 2.65/2.88 tff(10962,plain,
% 2.65/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.65/2.88 inference(modus_ponens,[status(thm)],[10961, 10960])).
% 2.65/2.88 tff(10963,plain,
% 2.65/2.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[10962, 163, 10929, 10956, 10487])).
% 2.65/2.88 tff(10964,plain,
% 2.65/2.88 (~r(elem!1, s(s(z)))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[9240, 163, 10929, 10956, 10489])).
% 2.65/2.88 tff(10965,plain,
% 2.65/2.88 (b(elem!1, s(s(z)))),
% 2.65/2.88 inference(unit_resolution,[status(thm)],[5572, 26, 9234, 10964])).
% 2.65/2.88 tff(10966,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10967,plain,
% 2.65/2.88 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.88 inference(rewrite,[status(thm)],[])).
% 2.65/2.88 tff(10968,plain,
% 2.65/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10967])).
% 2.65/2.89 tff(10969,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[10968, 10966])).
% 2.65/2.89 tff(10970,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(10971,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[10970, 10969])).
% 2.65/2.89 tff(10972,plain,
% 2.65/2.89 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[10971, 198, 10418, 407, 10492, 10494, 10965])).
% 2.65/2.89 tff(10973,plain,
% 2.65/2.89 (elem!1 = s(s(s(s(s(z)))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[4810, 10972, 10963])).
% 2.65/2.89 tff(10974,plain,
% 2.65/2.89 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10973])).
% 2.65/2.89 tff(10975,plain,
% 2.65/2.89 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.65/2.89 inference(symmetry,[status(thm)],[10974])).
% 2.65/2.89 tff(10976,plain,
% 2.65/2.89 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10973])).
% 2.65/2.89 tff(10977,plain,
% 2.65/2.89 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.65/2.89 inference(symmetry,[status(thm)],[10976])).
% 2.65/2.89 tff(10978,plain,
% 2.65/2.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10977])).
% 2.65/2.89 tff(10979,plain,
% 2.65/2.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.65/2.89 inference(transitivity,[status(thm)],[10978, 10975])).
% 2.65/2.89 tff(10980,plain,
% 2.65/2.89 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10979])).
% 2.65/2.89 tff(10981,plain,
% 2.65/2.89 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10976])).
% 2.65/2.89 tff(10982,plain,
% 2.65/2.89 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10976, 10981])).
% 2.65/2.89 tff(10983,plain,
% 2.65/2.89 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10981])).
% 2.65/2.89 tff(10984,plain,
% 2.65/2.89 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.65/2.89 inference(symmetry,[status(thm)],[10983])).
% 2.65/2.89 tff(10985,plain,
% 2.65/2.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10977])).
% 2.65/2.89 tff(10986,plain,
% 2.65/2.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.65/2.89 inference(transitivity,[status(thm)],[10985, 10984])).
% 2.65/2.89 tff(10987,plain,
% 2.65/2.89 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10986])).
% 2.65/2.89 tff(10988,plain,
% 2.65/2.89 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[420, 10509])).
% 2.65/2.89 tff(10989,plain,
% 2.65/2.89 (~(s(z) = elem!1)),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[2914, 10936])).
% 2.65/2.89 tff(10990,plain,
% 2.65/2.89 (~(s(s(z)) = s(elem!1))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[227, 10989])).
% 2.65/2.89 tff(10991,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.65/2.89 tff(10992,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(10993,plain,
% 2.65/2.89 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(10994,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[10993])).
% 2.65/2.89 tff(10995,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[10994, 10992])).
% 2.65/2.89 tff(10996,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(10997,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[10996, 10995])).
% 2.65/2.89 tff(10998,plain,
% 2.65/2.89 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[10997, 163, 3272, 423])).
% 2.65/2.89 tff(10999,plain,
% 2.65/2.89 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[10998, 10991])).
% 2.65/2.89 tff(11000,plain,
% 2.65/2.89 (~r(s(s(z)), s(elem!1))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[10999, 5426])).
% 2.65/2.89 tff(11001,plain,
% 2.65/2.89 (b(s(s(z)), s(elem!1))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[2378, 11000, 232])).
% 2.65/2.89 tff(11002,plain,
% 2.65/2.89 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11001, 5424])).
% 2.65/2.89 tff(11003,plain,
% 2.65/2.89 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), s(elem!1))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[5378])).
% 2.65/2.89 tff(11004,plain,
% 2.65/2.89 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(symmetry,[status(thm)],[11003])).
% 2.65/2.89 tff(11005,plain,
% 2.65/2.89 (r(s(z), s(s(s(s(s(s(z))))))) <=> r(s(z), s(elem!1))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[5378])).
% 2.65/2.89 tff(11006,plain,
% 2.65/2.89 ((~r(s(z), s(s(s(s(s(s(z)))))))) <=> (~r(s(z), s(elem!1)))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11005])).
% 2.65/2.89 tff(11007,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11008,plain,
% 2.65/2.89 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11009,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11008])).
% 2.65/2.89 tff(11010,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[11009, 11007])).
% 2.65/2.89 tff(11011,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(11012,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11011, 11010])).
% 2.65/2.89 tff(11013,plain,
% 2.65/2.89 ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11012, 163, 151, 423])).
% 2.65/2.89 tff(11014,plain,
% 2.65/2.89 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11013, 10991])).
% 2.65/2.89 tff(11015,plain,
% 2.65/2.89 (~r(s(z), s(elem!1))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11014, 11006])).
% 2.65/2.89 tff(11016,plain,
% 2.65/2.89 (b(s(z), s(elem!1))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[1164, 11015, 1157])).
% 2.65/2.89 tff(11017,plain,
% 2.65/2.89 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11016, 11004])).
% 2.65/2.89 tff(11018,plain,
% 2.65/2.89 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[5378])).
% 2.65/2.89 tff(11019,plain,
% 2.65/2.89 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.65/2.89 inference(symmetry,[status(thm)],[11018])).
% 2.65/2.89 tff(11020,plain,
% 2.65/2.89 ((~(s(elem!1) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11019])).
% 2.65/2.89 tff(11021,plain,
% 2.65/2.89 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[820, 11020])).
% 2.65/2.89 tff(11022,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11023,plain,
% 2.65/2.89 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11024,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11023])).
% 2.65/2.89 tff(11025,plain,
% 2.65/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[11024, 11022])).
% 2.65/2.89 tff(11026,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(11027,plain,
% 2.65/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11026, 11025])).
% 2.65/2.89 tff(11028,plain,
% 2.65/2.89 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11027, 163, 151, 423])).
% 2.65/2.89 tff(11029,plain,
% 2.65/2.89 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11028, 10991])).
% 2.65/2.89 tff(11030,plain,
% 2.65/2.89 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[4344, 26, 11029])).
% 2.65/2.89 tff(11031,plain,
% 2.65/2.89 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11030, 11021])).
% 2.65/2.89 tff(11032,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11033,plain,
% 2.65/2.89 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11034,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11033])).
% 2.65/2.89 tff(11035,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[11034, 11032])).
% 2.65/2.89 tff(11036,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(11037,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11036, 11035])).
% 2.65/2.89 tff(11038,plain,
% 2.65/2.89 ($false),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11037, 198, 1185, 595, 560, 11031, 11017, 11002])).
% 2.65/2.89 tff(11039,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (s(elem!1) = s(z)) | (s(s(z)) = s(elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.65/2.89 tff(11040,plain,
% 2.65/2.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[11039, 10973, 10261, 10418, 10483, 820, 10990, 3272, 10988, 10485])).
% 2.65/2.89 tff(11041,plain,
% 2.65/2.89 (~r(s(elem!1), s(s(elem!1)))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11040, 10987])).
% 2.65/2.89 tff(11042,plain,
% 2.65/2.89 (b(s(elem!1), s(s(elem!1)))),
% 2.65/2.89 inference(unit_resolution,[status(thm)],[901, 11041, 1134])).
% 2.65/2.89 tff(11043,plain,
% 2.65/2.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.65/2.89 inference(modus_ponens,[status(thm)],[11042, 10982])).
% 2.65/2.89 tff(11044,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11045,plain,
% 2.65/2.89 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(rewrite,[status(thm)],[])).
% 2.65/2.89 tff(11046,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.65/2.89 inference(monotonicity,[status(thm)],[11045])).
% 2.65/2.89 tff(11047,plain,
% 2.65/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(transitivity,[status(thm)],[11046, 11044])).
% 2.65/2.89 tff(11048,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.65/2.89 inference(quant_inst,[status(thm)],[])).
% 2.65/2.89 tff(11049,plain,
% 2.65/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11048, 11047])).
% 2.75/2.90 tff(11050,plain,
% 2.75/2.90 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11049, 198, 3819, 10503, 11043])).
% 2.75/2.90 tff(11051,plain,
% 2.75/2.90 (~b(s(elem!1), elem!1)),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11050, 10980])).
% 2.75/2.90 tff(11052,plain,
% 2.75/2.90 (r(s(elem!1), elem!1)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[856, 11051, 1396])).
% 2.75/2.90 tff(11053,plain,
% 2.75/2.90 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(elem!1), z)),
% 2.75/2.90 inference(monotonicity,[status(thm)],[10977])).
% 2.75/2.90 tff(11054,plain,
% 2.75/2.90 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(elem!1), z))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11053])).
% 2.75/2.90 tff(11055,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11056,plain,
% 2.75/2.90 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11057,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11056])).
% 2.75/2.90 tff(11058,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.75/2.90 inference(transitivity,[status(thm)],[11057, 11055])).
% 2.75/2.90 tff(11059,plain,
% 2.75/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(quant_inst,[status(thm)],[])).
% 2.75/2.90 tff(11060,plain,
% 2.75/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11059, 11058])).
% 2.75/2.90 tff(11061,plain,
% 2.75/2.90 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11060, 198, 3819, 10441, 10431, 10503, 11043])).
% 2.75/2.90 tff(11062,plain,
% 2.75/2.90 (~b(s(elem!1), z)),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11061, 11054])).
% 2.75/2.90 tff(11063,plain,
% 2.75/2.90 (r(s(elem!1), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1217, 11062])).
% 2.75/2.90 tff(11064,plain,
% 2.75/2.90 ($false),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[2020, 11063, 11052, 10956, 10929])).
% 2.75/2.90 tff(11065,plain,((s(elem!1) = s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.90 tff(11066,plain,
% 2.75/2.90 (s(elem!1) = s(z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11065, 116, 3272, 407, 2105, 3819, 42])).
% 2.75/2.90 tff(11067,plain,
% 2.75/2.90 (z = elem!1),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[814, 11066])).
% 2.75/2.90 tff(11068,plain,
% 2.75/2.90 (s(z) = s(elem!1)),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11067])).
% 2.75/2.90 tff(11069,plain,
% 2.75/2.90 (s(s(z)) = s(s(elem!1))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11068])).
% 2.75/2.90 tff(11070,plain,
% 2.75/2.90 (s(s(elem!1)) = s(s(z))),
% 2.75/2.90 inference(symmetry,[status(thm)],[11069])).
% 2.75/2.90 tff(11071,plain,
% 2.75/2.90 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11070])).
% 2.75/2.90 tff(11072,plain,
% 2.75/2.90 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.75/2.90 inference(symmetry,[status(thm)],[11071])).
% 2.75/2.90 tff(11073,plain,
% 2.75/2.90 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[10494, 11072])).
% 2.75/2.90 tff(11074,plain,
% 2.75/2.90 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11067])).
% 2.75/2.90 tff(11075,plain,
% 2.75/2.90 (r(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[10487, 11074])).
% 2.75/2.90 tff(11076,plain,
% 2.75/2.90 (~b(elem!1, s(s(elem!1)))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[71, 11067, 42])).
% 2.75/2.90 tff(11077,plain,
% 2.75/2.90 (r(elem!1, s(s(elem!1)))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[147, 11076, 116])).
% 2.75/2.90 tff(11078,plain,
% 2.75/2.90 (~r(z, s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[3240, 11066, 10490])).
% 2.75/2.90 tff(11079,plain,
% 2.75/2.90 (b(z, s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1791, 11078])).
% 2.75/2.90 tff(11080,plain,
% 2.75/2.90 (b(s(elem!1), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1209, 11067, 10483])).
% 2.75/2.90 tff(11081,plain,
% 2.75/2.90 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11068])).
% 2.75/2.90 tff(11082,plain,
% 2.75/2.90 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[9365, 11081])).
% 2.75/2.90 tff(11083,plain,
% 2.75/2.90 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[2942, 11067, 10485])).
% 2.75/2.90 tff(11084,plain,
% 2.75/2.90 (elem!1 = z),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[78, 11067])).
% 2.75/2.90 tff(11085,plain,
% 2.75/2.90 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1032, 11084, 10431])).
% 2.75/2.90 tff(11086,plain,
% 2.75/2.90 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11067])).
% 2.75/2.90 tff(11087,plain,
% 2.75/2.90 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[10441, 11086])).
% 2.75/2.90 tff(11088,plain,
% 2.75/2.90 (b(elem!1, s(elem!1))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[1801, 3130])).
% 2.75/2.90 tff(11089,plain,
% 2.75/2.90 (b(s(elem!1), elem!1)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1770, 1175, 57])).
% 2.75/2.90 tff(11090,plain,
% 2.75/2.90 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.75/2.90 inference(monotonicity,[status(thm)],[57])).
% 2.75/2.90 tff(11091,plain,
% 2.75/2.90 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11090])).
% 2.75/2.90 tff(11092,plain,
% 2.75/2.90 (~(s(s(s(elem!1))) = elem!1)),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[968, 11091])).
% 2.75/2.90 tff(11093,plain,
% 2.75/2.90 (b(s(s(s(elem!1))), elem!1)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1308, 10553, 11092])).
% 2.75/2.90 tff(11094,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11095,plain,
% 2.75/2.90 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11096,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11095])).
% 2.75/2.90 tff(11097,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(transitivity,[status(thm)],[11096, 11094])).
% 2.75/2.90 tff(11098,plain,
% 2.75/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.75/2.90 inference(quant_inst,[status(thm)],[])).
% 2.75/2.90 tff(11099,plain,
% 2.75/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11098, 11097])).
% 2.75/2.90 tff(11100,plain,
% 2.75/2.90 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11099, 198, 11093, 11089, 11088, 707, 831])).
% 2.75/2.90 tff(11101,assumption,(r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 2.75/2.90 tff(11102,plain,
% 2.75/2.90 (~r(s(s(s(elem!1))), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[10559, 10553, 57])).
% 2.75/2.90 tff(11103,plain,
% 2.75/2.90 (b(s(s(s(elem!1))), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1295, 11102])).
% 2.75/2.90 tff(11104,plain,
% 2.75/2.90 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1810, 11103, 1175, 1801])).
% 2.75/2.90 tff(11105,plain,
% 2.75/2.90 (r(s(s(s(elem!1))), s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1339, 11104, 1256])).
% 2.75/2.90 tff(11106,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11107,plain,
% 2.75/2.90 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11108,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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)))))))))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11107])).
% 2.75/2.90 tff(11109,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(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))))))))))),
% 2.75/2.90 inference(transitivity,[status(thm)],[11108, 11106])).
% 2.75/2.90 tff(11110,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.90 inference(quant_inst,[status(thm)],[])).
% 2.75/2.90 tff(11111,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11110, 11109])).
% 2.75/2.90 tff(11112,plain,
% 2.75/2.90 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11111, 163, 11105, 3065, 11101])).
% 2.75/2.90 tff(11113,plain,
% 2.75/2.90 ($false),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[4849, 26, 4846, 11112, 11100])).
% 2.75/2.90 tff(11114,plain,(r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.90 tff(11115,plain,
% 2.75/2.90 (r(s(s(s(elem!1))), elem!1)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11114, 11087, 11085, 11083, 11082, 1251, 11080, 11079, 11067])).
% 2.75/2.90 tff(11116,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11117,plain,
% 2.75/2.90 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11118,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11117])).
% 2.75/2.90 tff(11119,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(transitivity,[status(thm)],[11118, 11116])).
% 2.75/2.90 tff(11120,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(quant_inst,[status(thm)],[])).
% 2.75/2.90 tff(11121,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11120, 11119])).
% 2.75/2.90 tff(11122,plain,
% 2.75/2.90 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11121, 163, 11115, 11077, 11075])).
% 2.75/2.90 tff(11123,plain,
% 2.75/2.90 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[4899, 11067, 2620])).
% 2.75/2.90 tff(11124,plain,
% 2.75/2.90 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[4903, 26, 11123, 11122])).
% 2.75/2.90 tff(11125,plain,
% 2.75/2.90 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11069])).
% 2.75/2.90 tff(11126,plain,
% 2.75/2.90 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[10492, 11125])).
% 2.75/2.90 tff(11127,plain,
% 2.75/2.90 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11067])).
% 2.75/2.90 tff(11128,plain,
% 2.75/2.90 (~b(s(s(elem!1)), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[9564, 11084, 10488])).
% 2.75/2.90 tff(11129,plain,
% 2.75/2.90 (r(s(s(elem!1)), z)),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[801, 11128])).
% 2.75/2.90 tff(11130,plain,
% 2.75/2.90 (r(s(s(elem!1)), elem!1)),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11129, 11127])).
% 2.75/2.90 tff(11131,plain,
% 2.75/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11132,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.75/2.90 inference(quant_inst,[status(thm)],[])).
% 2.75/2.90 tff(11133,plain,
% 2.75/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[11132, 11131])).
% 2.75/2.90 tff(11134,plain,
% 2.75/2.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[11133, 163, 11130, 11115, 11077])).
% 2.75/2.90 tff(11135,plain,
% 2.75/2.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1326, 11134, 2793])).
% 2.75/2.90 tff(11136,plain,
% 2.75/2.90 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.75/2.90 inference(monotonicity,[status(thm)],[11068, 11069])).
% 2.75/2.90 tff(11137,plain,
% 2.75/2.90 (b(s(elem!1), s(s(elem!1)))),
% 2.75/2.90 inference(modus_ponens,[status(thm)],[407, 11136])).
% 2.75/2.90 tff(11138,plain,
% 2.75/2.90 (~r(s(s(elem!1)), s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[4766, 11067, 10417])).
% 2.75/2.90 tff(11139,plain,
% 2.75/2.90 (b(s(s(elem!1)), s(elem!1))),
% 2.75/2.90 inference(unit_resolution,[status(thm)],[1143, 11138, 1139])).
% 2.75/2.90 tff(11140,plain,
% 2.75/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.90 tff(11141,plain,
% 2.75/2.90 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.90 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11142,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11141])).
% 2.75/2.91 tff(11143,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(transitivity,[status(thm)],[11142, 11140])).
% 2.75/2.91 tff(11144,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11145,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11144, 11143])).
% 2.75/2.91 tff(11146,plain,
% 2.75/2.91 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11145, 198, 11139, 11137, 11135, 11126, 11124])).
% 2.75/2.91 tff(11147,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11146, 11073])).
% 2.75/2.91 tff(11148,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11149,plain,
% 2.75/2.91 (s(s(z)) = elem!1),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11148, 10729, 42, 3272, 407, 3819])).
% 2.75/2.91 tff(11150,plain,
% 2.75/2.91 (s(s(s(z))) = s(elem!1)),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11149])).
% 2.75/2.91 tff(11151,plain,
% 2.75/2.91 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11150])).
% 2.75/2.91 tff(11152,plain,
% 2.75/2.91 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11151])).
% 2.75/2.91 tff(11153,plain,
% 2.75/2.91 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.75/2.91 inference(symmetry,[status(thm)],[11152])).
% 2.75/2.91 tff(11154,plain,
% 2.75/2.91 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11153])).
% 2.75/2.91 tff(11155,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.75/2.91 inference(symmetry,[status(thm)],[11154])).
% 2.75/2.91 tff(11156,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11149])).
% 2.75/2.91 tff(11157,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[10494, 11156])).
% 2.75/2.91 tff(11158,plain,
% 2.75/2.91 (b(s(s(s(elem!1))), elem!1)),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11157, 11155])).
% 2.75/2.91 tff(11159,plain,
% 2.75/2.91 (~b(elem!1, z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[8236, 11149, 10488])).
% 2.75/2.91 tff(11160,plain,
% 2.75/2.91 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[7929, 11149, 10509])).
% 2.75/2.91 tff(11161,plain,
% 2.75/2.91 (~(elem!1 = z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1032, 11160, 10431])).
% 2.75/2.91 tff(11162,plain,
% 2.75/2.91 (r(elem!1, z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[187, 11161, 11159])).
% 2.75/2.91 tff(11163,plain,
% 2.75/2.91 (r(z, elem!1)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[10893, 11160, 10487, 407, 10441, 10431, 10516, 42, 10483])).
% 2.75/2.91 tff(11164,plain,
% 2.75/2.91 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[8694, 11149])).
% 2.75/2.91 tff(11165,plain,
% 2.75/2.91 (~b(s(s(elem!1)), z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[10695, 11164, 9365, 10498, 10483, 10261, 10441, 10431])).
% 2.75/2.91 tff(11166,plain,
% 2.75/2.91 (r(s(s(elem!1)), z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[801, 11165])).
% 2.75/2.91 tff(11167,plain,
% 2.75/2.91 (~r(elem!1, s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1823, 11166, 11163, 11162])).
% 2.75/2.91 tff(11168,plain,
% 2.75/2.91 (b(elem!1, s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[147, 11167, 10729])).
% 2.75/2.91 tff(11169,plain,
% 2.75/2.91 (~(s(s(elem!1)) = elem!1)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[118, 10729])).
% 2.75/2.91 tff(11170,plain,
% 2.75/2.91 (~r(s(s(elem!1)), elem!1)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[8716, 163, 11163, 11162, 11166])).
% 2.75/2.91 tff(11171,plain,
% 2.75/2.91 (b(s(s(elem!1)), elem!1)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[602, 11170, 11169])).
% 2.75/2.91 tff(11172,plain,
% 2.75/2.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1250, 11169])).
% 2.75/2.91 tff(11173,plain,
% 2.75/2.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1263, 11172])).
% 2.75/2.91 tff(11174,plain,
% 2.75/2.91 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1270, 11173])).
% 2.75/2.91 tff(11175,plain,
% 2.75/2.91 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11152])).
% 2.75/2.91 tff(11176,plain,
% 2.75/2.91 (r(s(s(s(elem!1))), z)),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[10487, 11175])).
% 2.75/2.91 tff(11177,plain,
% 2.75/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11178,plain,
% 2.75/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11179,plain,
% 2.75/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11178, 11177])).
% 2.75/2.91 tff(11180,plain,
% 2.75/2.91 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11179, 163, 11163, 11166, 11176])).
% 2.75/2.91 tff(11181,plain,
% 2.75/2.91 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1326, 11180, 11174])).
% 2.75/2.91 tff(11182,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[1874, 11181, 11171, 11168, 11158])).
% 2.75/2.91 tff(11183,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11184,plain,
% 2.75/2.91 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11183, 3272, 42, 407])).
% 2.75/2.91 tff(11185,plain,
% 2.75/2.91 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[3098, 11184])).
% 2.75/2.91 tff(11186,plain,
% 2.75/2.91 (~b(s(z), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[10256, 11185, 407, 10418, 3272, 9365])).
% 2.75/2.91 tff(11187,plain,
% 2.75/2.91 (r(s(z), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[3301, 11186])).
% 2.75/2.91 tff(11188,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9612, 163, 11185, 11187, 10485, 9365])).
% 2.75/2.91 tff(11189,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11190,plain,
% 2.75/2.91 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11189, 42, 407])).
% 2.75/2.91 tff(11191,plain,
% 2.75/2.91 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[374, 11190])).
% 2.75/2.91 tff(11192,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11193,plain,
% 2.75/2.91 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11194,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11193])).
% 2.75/2.91 tff(11195,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.91 inference(transitivity,[status(thm)],[11194, 11192])).
% 2.75/2.91 tff(11196,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11197,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11196, 11195])).
% 2.75/2.91 tff(11198,plain,
% 2.75/2.91 (~b(s(s(z)), z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11197, 198, 595, 10443, 348, 9620])).
% 2.75/2.91 tff(11199,plain,
% 2.75/2.91 (r(s(s(z)), z)),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[345, 11198])).
% 2.75/2.91 tff(11200,plain,
% 2.75/2.91 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[10303, 33, 3639, 150])).
% 2.75/2.91 tff(11201,plain,
% 2.75/2.91 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[3613, 11200])).
% 2.75/2.91 tff(11202,plain,
% 2.75/2.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[8845, 11201, 407, 348])).
% 2.75/2.91 tff(11203,plain,
% 2.75/2.91 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[420, 11202])).
% 2.75/2.91 tff(11204,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[5857, 163, 153, 332, 33, 11203])).
% 2.75/2.91 tff(11205,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11206,plain,
% 2.75/2.91 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11205, 11199, 153, 407, 348, 3639, 150])).
% 2.75/2.91 tff(11207,plain,
% 2.75/2.91 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[31, 11206])).
% 2.75/2.91 tff(11208,plain,
% 2.75/2.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[8845, 3615, 407, 348])).
% 2.75/2.91 tff(11209,plain,
% 2.75/2.91 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[420, 11208])).
% 2.75/2.91 tff(11210,plain,
% 2.75/2.91 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9592, 11209, 153, 11199, 11207])).
% 2.75/2.91 tff(11211,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9576, 11210])).
% 2.75/2.91 tff(11212,plain,
% 2.75/2.91 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9546, 3066, 150, 3639])).
% 2.75/2.91 tff(11213,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[469, 11212])).
% 2.75/2.91 tff(11214,plain,
% 2.75/2.91 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9556, 11213, 153, 10443, 407, 11199])).
% 2.75/2.91 tff(11215,plain,
% 2.75/2.91 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[4110, 11214])).
% 2.75/2.91 tff(11216,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11217,plain,
% 2.75/2.91 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11218,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11217])).
% 2.75/2.91 tff(11219,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(transitivity,[status(thm)],[11218, 11216])).
% 2.75/2.91 tff(11220,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11221,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11220, 11219])).
% 2.75/2.91 tff(11222,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11221, 198, 595, 331, 559, 5428, 3404])).
% 2.75/2.91 tff(11223,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11224,plain,
% 2.75/2.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11223, 11215, 595, 11207, 11213])).
% 2.75/2.91 tff(11225,plain,
% 2.75/2.91 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9643, 11224])).
% 2.75/2.91 tff(11226,plain,
% 2.75/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11227,plain,
% 2.75/2.91 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(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))))))), s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11228,plain,
% 2.75/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z)))))))))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11227])).
% 2.75/2.91 tff(11229,plain,
% 2.75/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(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(s(s(s(z))))))))),
% 2.75/2.91 inference(transitivity,[status(thm)],[11228, 11226])).
% 2.75/2.91 tff(11230,plain,
% 2.75/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11231,plain,
% 2.75/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11230, 11229])).
% 2.75/2.91 tff(11232,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11231, 163, 3066, 423, 3368, 9472])).
% 2.75/2.91 tff(11233,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11234,plain,
% 2.75/2.91 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11233, 11225, 11209, 3066])).
% 2.75/2.91 tff(11235,plain,
% 2.75/2.91 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[9885, 11234])).
% 2.75/2.91 tff(11236,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11237,plain,
% 2.75/2.91 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(rewrite,[status(thm)],[])).
% 2.75/2.91 tff(11238,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.91 inference(monotonicity,[status(thm)],[11237])).
% 2.75/2.91 tff(11239,plain,
% 2.75/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.91 inference(transitivity,[status(thm)],[11238, 11236])).
% 2.75/2.91 tff(11240,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(quant_inst,[status(thm)],[])).
% 2.75/2.91 tff(11241,plain,
% 2.75/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.91 inference(modus_ponens,[status(thm)],[11240, 11239])).
% 2.75/2.91 tff(11242,plain,
% 2.75/2.91 ($false),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11241, 198, 10443, 3615, 348, 11213, 11235])).
% 2.75/2.91 tff(11243,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.91 tff(11244,plain,
% 2.75/2.91 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.91 inference(unit_resolution,[status(thm)],[11243, 3615, 348, 595, 153, 407, 150, 3639])).
% 2.75/2.91 tff(11245,plain,
% 2.75/2.91 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3098, 11244])).
% 2.75/2.92 tff(11246,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[4174, 11245, 11207, 9620])).
% 2.75/2.92 tff(11247,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3841, 11246])).
% 2.75/2.92 tff(11248,plain,
% 2.75/2.92 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3836, 11247, 153, 150])).
% 2.75/2.92 tff(11249,plain,
% 2.75/2.92 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[469, 11248])).
% 2.75/2.92 tff(11250,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11251,plain,
% 2.75/2.92 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11252,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.92 inference(monotonicity,[status(thm)],[11251])).
% 2.75/2.92 tff(11253,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.92 inference(transitivity,[status(thm)],[11252, 11250])).
% 2.75/2.92 tff(11254,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/2.92 inference(quant_inst,[status(thm)],[])).
% 2.75/2.92 tff(11255,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.92 inference(modus_ponens,[status(thm)],[11254, 11253])).
% 2.75/2.92 tff(11256,plain,
% 2.75/2.92 ($false),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11255, 198, 10443, 11245, 3615, 11249, 11211])).
% 2.75/2.92 tff(11257,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.92 tff(11258,plain,
% 2.75/2.92 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11257, 150, 153, 348, 595, 407, 3639])).
% 2.75/2.92 tff(11259,plain,
% 2.75/2.92 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3613, 11258])).
% 2.75/2.92 tff(11260,plain,
% 2.75/2.92 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9556, 11213, 153, 10443, 407, 332])).
% 2.75/2.92 tff(11261,plain,
% 2.75/2.92 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[4110, 11260])).
% 2.75/2.92 tff(11262,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11263,plain,
% 2.75/2.92 (((~b(s(s(s(s(s(z))))), s(z))) | (~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(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(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))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11264,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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)))))))))),
% 2.75/2.92 inference(monotonicity,[status(thm)],[11263])).
% 2.75/2.92 tff(11265,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))))),
% 2.75/2.92 inference(transitivity,[status(thm)],[11264, 11262])).
% 2.75/2.92 tff(11266,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 2.75/2.92 inference(quant_inst,[status(thm)],[])).
% 2.75/2.92 tff(11267,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.75/2.92 inference(modus_ponens,[status(thm)],[11266, 11265])).
% 2.75/2.92 tff(11268,plain,
% 2.75/2.92 ($false),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11267, 198, 595, 6262, 559, 5428])).
% 2.75/2.92 tff(11269,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,[]))).
% 2.75/2.92 tff(11270,plain,
% 2.75/2.92 (~b(s(z), s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11269, 11261, 595, 11213])).
% 2.75/2.92 tff(11271,plain,
% 2.75/2.92 (r(s(z), s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3301, 11270])).
% 2.75/2.92 tff(11272,plain,
% 2.75/2.92 ($false),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9612, 163, 3066, 11271, 151, 3639])).
% 2.75/2.92 tff(11273,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.92 tff(11274,plain,
% 2.75/2.92 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11273, 11259, 3639, 595, 153, 407, 11199, 150])).
% 2.75/2.92 tff(11275,plain,
% 2.75/2.92 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3098, 11274])).
% 2.75/2.92 tff(11276,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[4174, 11275, 11207, 9620])).
% 2.75/2.92 tff(11277,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3841, 11276])).
% 2.75/2.92 tff(11278,plain,
% 2.75/2.92 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3836, 11277, 153, 150])).
% 2.75/2.92 tff(11279,plain,
% 2.75/2.92 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[469, 11278])).
% 2.75/2.92 tff(11280,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9923, 198, 407, 11275, 348, 11279])).
% 2.75/2.92 tff(11281,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9576, 11280])).
% 2.75/2.92 tff(11282,plain,
% 2.75/2.92 ($false),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[568, 163, 153, 11199, 11281, 11277])).
% 2.75/2.92 tff(11283,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.92 tff(11284,plain,
% 2.75/2.92 (~r(s(z), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11283, 55, 407, 11191, 9365, 10261])).
% 2.75/2.92 tff(11285,plain,
% 2.75/2.92 (b(s(z), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[40, 11284])).
% 2.75/2.92 tff(11286,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[8803, 559, 595, 1185])).
% 2.75/2.92 tff(11287,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3841, 11286])).
% 2.75/2.92 tff(11288,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11289,plain,
% 2.75/2.92 (((~b(s(s(z)), s(z))) | (~b(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(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11290,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.75/2.92 inference(monotonicity,[status(thm)],[11289])).
% 2.75/2.92 tff(11291,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.92 inference(transitivity,[status(thm)],[11290, 11288])).
% 2.75/2.92 tff(11292,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.92 inference(quant_inst,[status(thm)],[])).
% 2.75/2.92 tff(11293,plain,
% 2.75/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.75/2.92 inference(modus_ponens,[status(thm)],[11292, 11291])).
% 2.75/2.92 tff(11294,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11293, 198, 1185, 595, 560, 407, 559])).
% 2.75/2.92 tff(11295,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9576, 11294])).
% 2.75/2.92 tff(11296,plain,
% 2.75/2.92 (r(s(s(z)), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[345, 10754])).
% 2.75/2.92 tff(11297,plain,
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% 2.75/2.92 inference(unit_resolution,[status(thm)],[10400, 163, 153, 11296, 11295, 11287])).
% 2.75/2.92 tff(11298,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.92 tff(11299,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11298, 55, 11285, 10261, 10418, 407])).
% 2.75/2.92 tff(11300,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[469, 11299])).
% 2.75/2.92 tff(11301,plain,
% 2.75/2.92 (~b(s(s(z)), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[10425, 198, 11285, 10261, 10418])).
% 2.75/2.92 tff(11302,plain,
% 2.75/2.92 (r(s(s(z)), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[345, 11301])).
% 2.75/2.92 tff(11303,plain,
% 2.75/2.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[10076, 33, 55, 9365, 11285, 407])).
% 2.75/2.92 tff(11304,plain,
% 2.75/2.92 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[420, 11303])).
% 2.75/2.92 tff(11305,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[5672, 198, 348, 3745, 10853])).
% 2.75/2.92 tff(11306,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3098, 11305])).
% 2.75/2.92 tff(11307,plain,
% 2.75/2.92 ($false),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[10392, 163, 11306, 33, 3639, 3828])).
% 2.75/2.92 tff(11308,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.92 tff(11309,plain,
% 2.75/2.92 (~r(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11308, 11304, 9365, 11191, 33, 55, 11302])).
% 2.75/2.92 tff(11310,plain,
% 2.75/2.92 (b(s(s(s(s(s(z))))), z)),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3841, 11309])).
% 2.75/2.92 tff(11311,plain,
% 2.75/2.92 (~b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[8803, 4167, 10261, 11285])).
% 2.75/2.92 tff(11312,plain,
% 2.75/2.92 (r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[469, 11311])).
% 2.75/2.92 tff(11313,plain,
% 2.75/2.92 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[8845, 3745, 407, 11191])).
% 2.75/2.92 tff(11314,plain,
% 2.75/2.92 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3613, 11313])).
% 2.75/2.92 tff(11315,plain,
% 2.75/2.92 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[10349, 163, 11314, 9365, 11312])).
% 2.75/2.92 tff(11316,plain,
% 2.75/2.92 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[3098, 11315])).
% 2.75/2.92 tff(11317,plain,
% 2.75/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11318,plain,
% 2.75/2.92 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11319,plain,
% 2.75/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.75/2.92 inference(monotonicity,[status(thm)],[11318])).
% 2.75/2.92 tff(11320,plain,
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% 2.75/2.92 inference(transitivity,[status(thm)],[11319, 11317])).
% 2.75/2.92 tff(11321,plain,
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% 2.75/2.92 inference(quant_inst,[status(thm)],[])).
% 2.75/2.92 tff(11322,plain,
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% 2.75/2.92 inference(modus_ponens,[status(thm)],[11321, 11320])).
% 2.75/2.92 tff(11323,plain,
% 2.75/2.92 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[11322, 163, 11314, 9365, 11312])).
% 2.75/2.92 tff(11324,plain,
% 2.75/2.92 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.92 inference(unit_resolution,[status(thm)],[9643, 11323])).
% 2.75/2.92 tff(11325,plain,
% 2.75/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11326,plain,
% 2.75/2.92 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.92 inference(rewrite,[status(thm)],[])).
% 2.75/2.92 tff(11327,plain,
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% 2.75/2.92 inference(monotonicity,[status(thm)],[11326])).
% 2.75/2.92 tff(11328,plain,
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% 2.75/2.92 tff(11332,plain,
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% 2.75/2.92 tff(11333,plain,
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% 2.75/2.92 tff(11334,plain,
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% 2.75/2.92 tff(11335,plain,
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% 2.75/2.92 tff(11336,plain,
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% 2.75/2.92 tff(11337,plain,
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% 2.75/2.92 tff(11338,plain,
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% 2.75/2.92 tff(11339,plain,
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% 2.75/2.92 tff(11340,plain,
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% 2.75/2.92 tff(11341,plain,
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% 2.75/2.92 tff(11342,plain,
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% 2.75/2.92 tff(11343,plain,
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% 2.75/2.92 tff(11344,plain,
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% 2.75/2.92 tff(11345,plain,
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% 2.75/2.92 tff(11350,plain,
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% 2.75/2.92 tff(11351,plain,
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% 2.75/2.93 tff(11353,plain,
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% 2.75/2.93 tff(11357,plain,
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% 2.75/2.93 tff(11358,plain,
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% 2.75/2.93 tff(11359,plain,
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% 2.75/2.93 tff(11360,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(z)) = elem!1) | (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.93 tff(11361,plain,
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% 2.75/2.93 tff(11369,plain,
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% 2.75/2.93 inference(monotonicity,[status(thm)],[11373])).
% 2.75/2.93 tff(11375,assumption,(s(s(z)) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.75/2.93 tff(11376,plain,
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% 2.75/2.93 tff(11377,plain,
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% 2.75/2.93 tff(11378,plain,
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% 2.75/2.93 tff(11379,plain,(~(s(s(z)) = s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.93 tff(11380,plain,
% 2.75/2.93 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11379, 11374])).
% 2.75/2.93 tff(11381,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), elem!1)), introduced(assumption)).
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% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
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% 2.75/2.93 inference(modus_ponens,[status(thm)],[11388, 11387])).
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% 2.75/2.93 inference(unit_resolution,[status(thm)],[11389, 26, 11386])).
% 2.75/2.93 tff(11391,plain,
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% 2.75/2.93 inference(monotonicity,[status(thm)],[11393])).
% 2.75/2.93 tff(11395,plain,
% 2.75/2.93 (~(s(s(s(s(s(s(s(s(z)))))))) = s(z))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[1282, 11394])).
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% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
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% 2.75/2.93 inference(unit_resolution,[status(thm)],[11403, 26, 11400])).
% 2.75/2.93 tff(11405,plain,
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% 2.75/2.93 tff(11407,plain,
% 2.75/2.93 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11408,plain,
% 2.75/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11407])).
% 2.75/2.93 tff(11409,plain,
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% 2.75/2.93 inference(transitivity,[status(thm)],[11408, 11406])).
% 2.75/2.93 tff(11410,plain,
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% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
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% 2.75/2.93 inference(modus_ponens,[status(thm)],[11410, 11409])).
% 2.75/2.93 tff(11412,plain,
% 2.75/2.93 ($false),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11411, 198, 1185, 595, 560, 407, 11405, 11391])).
% 2.75/2.93 tff(11413,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.93 tff(11414,plain,
% 2.75/2.93 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11413, 2840, 595, 560, 407, 1185, 11371, 11369, 11367])).
% 2.75/2.93 tff(11415,plain,
% 2.75/2.93 (~r(s(s(s(elem!1))), elem!1)),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11414, 11363])).
% 2.75/2.93 tff(11416,plain,
% 2.75/2.93 (b(s(s(s(elem!1))), elem!1)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1308, 11415, 11361])).
% 2.75/2.93 tff(11417,plain,
% 2.75/2.93 (~b(s(s(s(elem!1))), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1319, 11416, 11347, 11343])).
% 2.75/2.93 tff(11418,plain,
% 2.75/2.93 (r(s(s(s(elem!1))), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1295, 11417])).
% 2.75/2.93 tff(11419,plain,
% 2.75/2.93 (r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11418, 11340])).
% 2.75/2.93 tff(11420,plain,
% 2.75/2.93 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11338, 2841])).
% 2.75/2.93 tff(11421,plain,
% 2.75/2.93 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(symmetry,[status(thm)],[11420])).
% 2.75/2.93 tff(11422,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 2.75/2.93 tff(11423,plain,
% 2.75/2.93 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.93 inference(monotonicity,[status(thm)],[2840])).
% 2.75/2.93 tff(11424,plain,
% 2.75/2.93 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.75/2.93 inference(symmetry,[status(thm)],[11423])).
% 2.75/2.93 tff(11425,plain,
% 2.75/2.93 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11341])).
% 2.75/2.93 tff(11426,plain,
% 2.75/2.93 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), elem!1)),
% 2.75/2.93 inference(transitivity,[status(thm)],[11425, 11424])).
% 2.75/2.93 tff(11427,plain,
% 2.75/2.93 (b(s(s(elem!1)), elem!1)),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[3404, 11426])).
% 2.75/2.93 tff(11428,plain,
% 2.75/2.93 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[2840])).
% 2.75/2.93 tff(11429,plain,
% 2.75/2.93 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 2.75/2.93 inference(symmetry,[status(thm)],[11428])).
% 2.75/2.93 tff(11430,plain,
% 2.75/2.93 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11341])).
% 2.75/2.93 tff(11431,plain,
% 2.75/2.93 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 2.75/2.93 inference(transitivity,[status(thm)],[11430, 11429])).
% 2.75/2.93 tff(11432,plain,
% 2.75/2.93 (b(elem!1, s(s(elem!1)))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[3819, 11431])).
% 2.75/2.93 tff(11433,plain,
% 2.75/2.93 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1874, 11416, 11432, 11427])).
% 2.75/2.93 tff(11434,plain,
% 2.75/2.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1326, 11433, 11422])).
% 2.75/2.93 tff(11435,plain,
% 2.75/2.93 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11434, 11421])).
% 2.75/2.93 tff(11436,plain,
% 2.75/2.93 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[9634, 11346, 3404, 4167])).
% 2.75/2.93 tff(11437,plain,
% 2.75/2.93 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[176, 11436])).
% 2.75/2.93 tff(11438,plain,
% 2.75/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11439,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
% 2.75/2.93 tff(11440,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11439, 11438])).
% 2.75/2.93 tff(11441,plain,
% 2.75/2.93 ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11440, 163, 153, 11437])).
% 2.75/2.93 tff(11442,plain,
% 2.75/2.93 ($false),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11441, 11435, 11419])).
% 2.75/2.93 tff(11443,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (s(s(z)) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.93 tff(11444,plain,
% 2.75/2.93 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11443, 2105, 2793, 595, 560, 407, 1185, 153, 3404, 11332, 4167, 3819])).
% 2.75/2.93 tff(11445,plain,
% 2.75/2.93 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[3249, 11444])).
% 2.75/2.93 tff(11446,plain,
% 2.75/2.93 (~r(s(s(elem!1)), s(s(z)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[10711, 163, 790, 153, 11296])).
% 2.75/2.93 tff(11447,plain,
% 2.75/2.93 (b(s(s(elem!1)), s(s(z)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[3497, 26, 11446, 3494])).
% 2.75/2.93 tff(11448,plain,
% 2.75/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11449,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
% 2.75/2.93 tff(11450,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11449, 11448])).
% 2.75/2.93 tff(11451,plain,
% 2.75/2.93 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11450, 163, 790, 153, 152])).
% 2.75/2.93 tff(11452,plain,
% 2.75/2.93 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[4221, 11451, 4219])).
% 2.75/2.93 tff(11453,plain,
% 2.75/2.93 (~r(s(s(z)), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[10769, 790, 407, 1185, 595, 560])).
% 2.75/2.93 tff(11454,plain,
% 2.75/2.93 (b(s(s(z)), s(s(elem!1)))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[2161, 26, 11453, 2154])).
% 2.75/2.93 tff(11455,plain,
% 2.75/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11456,plain,
% 2.75/2.93 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11457,plain,
% 2.75/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11456])).
% 2.75/2.93 tff(11458,plain,
% 2.75/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(transitivity,[status(thm)],[11457, 11455])).
% 2.75/2.93 tff(11459,plain,
% 2.75/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
% 2.75/2.93 tff(11460,plain,
% 2.75/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11459, 11458])).
% 2.75/2.93 tff(11461,plain,
% 2.75/2.93 ($false),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11460, 198, 3745, 11454, 11452, 11447])).
% 2.75/2.93 tff(11462,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.93 tff(11463,plain,
% 2.75/2.93 (~r(s(s(elem!1)), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11462, 11445, 2154, 3745, 153, 11336, 407, 1185, 595, 560])).
% 2.75/2.93 tff(11464,plain,
% 2.75/2.93 (b(s(s(elem!1)), z)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[801, 11463])).
% 2.75/2.93 tff(11465,plain,
% 2.75/2.93 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[9272, 198, 11464, 1185, 595, 11334, 4167])).
% 2.75/2.93 tff(11466,plain,
% 2.75/2.93 (~b(s(z), s(s(s(s(s(z))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[8743, 198, 1185, 11334, 4167])).
% 2.75/2.93 tff(11467,plain,
% 2.75/2.93 (r(s(z), s(s(s(s(s(z))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[3301, 11466])).
% 2.75/2.93 tff(11468,plain,
% 2.75/2.93 (~b(s(s(elem!1)), s(z))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[1191, 198, 11464, 1185, 595])).
% 2.75/2.93 tff(11469,plain,
% 2.75/2.93 (r(s(s(elem!1)), s(z))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[626, 11468])).
% 2.75/2.93 tff(11470,plain,
% 2.75/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11471,plain,
% 2.75/2.93 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(rewrite,[status(thm)],[])).
% 2.75/2.93 tff(11472,plain,
% 2.75/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11471])).
% 2.75/2.93 tff(11473,plain,
% 2.75/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(transitivity,[status(thm)],[11472, 11470])).
% 2.75/2.93 tff(11474,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.75/2.93 inference(quant_inst,[status(thm)],[])).
% 2.75/2.93 tff(11475,plain,
% 2.75/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.75/2.93 inference(modus_ponens,[status(thm)],[11474, 11473])).
% 2.75/2.93 tff(11476,plain,
% 2.75/2.93 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[11475, 163, 11469, 11467, 10342])).
% 2.75/2.93 tff(11477,plain,
% 2.75/2.93 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[3400, 11476, 11465])).
% 2.75/2.93 tff(11478,plain,
% 2.75/2.93 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.75/2.93 inference(unit_resolution,[status(thm)],[9265, 11477])).
% 2.75/2.93 tff(11479,plain,
% 2.75/2.93 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 2.75/2.93 inference(monotonicity,[status(thm)],[11477])).
% 2.75/2.93 tff(11480,plain,
% 2.75/2.93 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 2.75/2.93 inference(symmetry,[status(thm)],[11479])).
% 2.75/2.93 tff(11481,plain,
% 2.75/2.94 (b(z, s(s(elem!1)))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11334, 11480])).
% 2.75/2.94 tff(11482,plain,
% 2.75/2.94 (elem!1 = s(s(s(z)))),
% 2.75/2.94 inference(transitivity,[status(thm)],[4242, 9857, 293])).
% 2.75/2.94 tff(11483,plain,
% 2.75/2.94 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11482])).
% 2.75/2.94 tff(11484,plain,
% 2.75/2.94 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[10818])).
% 2.75/2.94 tff(11485,plain,
% 2.75/2.94 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(z))),
% 2.75/2.94 inference(transitivity,[status(thm)],[11484, 1241])).
% 2.75/2.94 tff(11486,plain,
% 2.75/2.94 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(z)))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11485])).
% 2.75/2.94 tff(11487,plain,
% 2.75/2.94 (~(elem!1 = s(z))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[10804, 11486])).
% 2.75/2.94 tff(11488,plain,
% 2.75/2.94 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11482])).
% 2.75/2.94 tff(11489,plain,
% 2.75/2.94 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.75/2.94 inference(symmetry,[status(thm)],[11488])).
% 2.75/2.94 tff(11490,plain,
% 2.75/2.94 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11489])).
% 2.75/2.94 tff(11491,plain,
% 2.75/2.94 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11482])).
% 2.75/2.94 tff(11492,plain,
% 2.75/2.94 (b(s(s(s(z))), z)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[271, 11491])).
% 2.75/2.94 tff(11493,plain,
% 2.75/2.94 (~b(s(s(s(z))), s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[10872, 198, 1185, 595, 11492])).
% 2.75/2.94 tff(11494,plain,
% 2.75/2.94 (~b(elem!1, s(z))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11493, 11490])).
% 2.75/2.94 tff(11495,plain,
% 2.75/2.94 (r(elem!1, s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[242, 11494, 11487])).
% 2.75/2.94 tff(11496,plain,
% 2.75/2.94 (r(s(s(s(z))), s(z))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11495, 11483])).
% 2.75/2.94 tff(11497,plain,
% 2.75/2.94 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(symmetry,[status(thm)],[10824])).
% 2.75/2.94 tff(11498,plain,
% 2.75/2.94 (~b(elem!1, s(s(elem!1)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1071, 271, 83, 723])).
% 2.75/2.94 tff(11499,plain,
% 2.75/2.94 (r(elem!1, s(s(elem!1)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[147, 11498, 116])).
% 2.75/2.94 tff(11500,plain,
% 2.75/2.94 (r(elem!1, s(s(s(s(s(z))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11499, 10822])).
% 2.75/2.94 tff(11501,plain,
% 2.75/2.94 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11500, 11497])).
% 2.75/2.94 tff(11502,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11503,plain,
% 2.75/2.94 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11504,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11503])).
% 2.75/2.94 tff(11505,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[11504, 11502])).
% 2.75/2.94 tff(11506,plain,
% 2.75/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(11507,plain,
% 2.75/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11506, 11505])).
% 2.75/2.94 tff(11508,plain,
% 2.75/2.94 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11507, 163, 6249, 422])).
% 2.75/2.94 tff(11509,plain,
% 2.75/2.94 (~r(s(s(s(z))), s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11508, 11501])).
% 2.75/2.94 tff(11510,plain,
% 2.75/2.94 ($false),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11509, 11496])).
% 2.75/2.94 tff(11511,plain,((~b(elem!1, z)) | (~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.94 tff(11512,plain,
% 2.75/2.94 (~b(elem!1, z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11511, 11477, 11467, 10342, 1185, 595, 116, 11481, 11464])).
% 2.75/2.94 tff(11513,plain,
% 2.75/2.94 (r(elem!1, z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[187, 11512, 76])).
% 2.75/2.94 tff(11514,plain,
% 2.75/2.94 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[5560, 11513, 153, 11336])).
% 2.75/2.94 tff(11515,plain,
% 2.75/2.94 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[3792, 11478])).
% 2.75/2.94 tff(11516,plain,
% 2.75/2.94 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[5596, 11513, 11296, 11336, 11515, 153, 9234, 348])).
% 2.75/2.94 tff(11517,plain,
% 2.75/2.94 ($false),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[256, 11516, 11514, 11478])).
% 2.75/2.94 tff(11518,plain,((s(s(z)) = elem!1) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = z) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.94 tff(11519,plain,
% 2.75/2.94 (s(s(z)) = elem!1),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11518, 3617, 348, 153, 1185, 595, 116, 4167, 5276, 3745, 407, 560, 3404, 3819])).
% 2.75/2.94 tff(11520,plain,
% 2.75/2.94 (s(s(s(z))) = s(elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11519])).
% 2.75/2.94 tff(11521,plain,
% 2.75/2.94 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11520])).
% 2.75/2.94 tff(11522,plain,
% 2.75/2.94 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11521])).
% 2.75/2.94 tff(11523,plain,
% 2.75/2.94 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11522])).
% 2.75/2.94 tff(11524,plain,
% 2.75/2.94 (b(z, s(s(s(elem!1))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11334, 11523])).
% 2.75/2.94 tff(11525,plain,
% 2.75/2.94 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11522])).
% 2.75/2.94 tff(11526,plain,
% 2.75/2.94 (b(s(s(s(elem!1))), z)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[4167, 11525])).
% 2.75/2.94 tff(11527,plain,
% 2.75/2.94 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[8694, 11519])).
% 2.75/2.94 tff(11528,plain,
% 2.75/2.94 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[3249, 11527])).
% 2.75/2.94 tff(11529,plain,
% 2.75/2.94 (~r(s(s(elem!1)), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11462, 11528, 5276, 3745, 153, 11336, 407, 1185, 595, 560])).
% 2.75/2.94 tff(11530,plain,
% 2.75/2.94 (b(s(s(elem!1)), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[801, 11529])).
% 2.75/2.94 tff(11531,plain,
% 2.75/2.94 (~b(s(s(elem!1)), s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[8734, 198, 11530, 11526, 11524, 1185, 595])).
% 2.75/2.94 tff(11532,plain,
% 2.75/2.94 (r(s(s(elem!1)), s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[626, 11531])).
% 2.75/2.94 tff(11533,plain,
% 2.75/2.94 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11522])).
% 2.75/2.94 tff(11534,plain,
% 2.75/2.94 (r(s(z), s(s(s(elem!1))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11467, 11533])).
% 2.75/2.94 tff(11535,plain,
% 2.75/2.94 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.75/2.94 inference(symmetry,[status(thm)],[11522])).
% 2.75/2.94 tff(11536,plain,
% 2.75/2.94 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11535])).
% 2.75/2.94 tff(11537,plain,
% 2.75/2.94 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.75/2.94 inference(symmetry,[status(thm)],[11536])).
% 2.75/2.94 tff(11538,plain,
% 2.75/2.94 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11519])).
% 2.75/2.94 tff(11539,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11540,plain,
% 2.75/2.94 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11541,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11540])).
% 2.75/2.94 tff(11542,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[11541, 11539])).
% 2.75/2.94 tff(11543,plain,
% 2.75/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(11544,plain,
% 2.75/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11543, 11542])).
% 2.75/2.94 tff(11545,plain,
% 2.75/2.94 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11544, 198, 3819, 348, 3745, 3404])).
% 2.75/2.94 tff(11546,plain,
% 2.75/2.94 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[9576, 11545])).
% 2.75/2.94 tff(11547,plain,
% 2.75/2.94 (r(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11546, 11538])).
% 2.75/2.94 tff(11548,plain,
% 2.75/2.94 (r(s(s(s(elem!1))), elem!1)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11547, 11537])).
% 2.75/2.94 tff(11549,plain,
% 2.75/2.94 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[8754, 198, 11530, 11526, 11524])).
% 2.75/2.94 tff(11550,plain,
% 2.75/2.94 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1377, 11549, 2731])).
% 2.75/2.94 tff(11551,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11552,plain,
% 2.75/2.94 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11553,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11552])).
% 2.75/2.94 tff(11554,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.75/2.94 inference(transitivity,[status(thm)],[11553, 11551])).
% 2.75/2.94 tff(11555,plain,
% 2.75/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(11556,plain,
% 2.75/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11555, 11554])).
% 2.75/2.94 tff(11557,plain,
% 2.75/2.94 ($false),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11556, 163, 11550, 11548, 11534, 11532])).
% 2.75/2.94 tff(11558,plain,((z = elem!1) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.94 tff(11559,plain,
% 2.75/2.94 (z = elem!1),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11558, 116, 10261, 4167, 3745, 55, 407, 10418, 11191, 11285, 11324, 11316])).
% 2.75/2.94 tff(11560,plain,
% 2.75/2.94 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11561,plain,
% 2.75/2.94 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11330, 198, 11316, 11191, 11324])).
% 2.75/2.94 tff(11562,plain,
% 2.75/2.94 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[9885, 11561])).
% 2.75/2.94 tff(11563,plain,
% 2.75/2.94 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[10000, 11562, 55, 11312])).
% 2.75/2.94 tff(11564,plain,
% 2.75/2.94 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[4110, 11563])).
% 2.75/2.94 tff(11565,plain,
% 2.75/2.94 (b(elem!1, s(s(s(s(s(z))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11564, 11560])).
% 2.75/2.94 tff(11566,plain,
% 2.75/2.94 (b(s(s(s(s(s(z))))), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6052, 11559, 4167])).
% 2.75/2.94 tff(11567,plain,
% 2.75/2.94 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11568,plain,
% 2.75/2.94 (~r(z, s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[10236, 11302, 55, 407, 9365, 11285])).
% 2.75/2.94 tff(11569,plain,
% 2.75/2.94 (elem!1 = z),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[78, 11559])).
% 2.75/2.94 tff(11570,plain,
% 2.75/2.94 (s(elem!1) = s(z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1646, 11569])).
% 2.75/2.94 tff(11571,plain,
% 2.75/2.94 (~r(z, s(elem!1))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[3240, 11570, 11568])).
% 2.75/2.94 tff(11572,plain,
% 2.75/2.94 (b(z, s(elem!1))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1791, 11571])).
% 2.75/2.94 tff(11573,plain,
% 2.75/2.94 (b(elem!1, s(elem!1))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11572, 11567])).
% 2.75/2.94 tff(11574,plain,
% 2.75/2.94 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11575,plain,
% 2.75/2.94 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11574])).
% 2.75/2.94 tff(11576,plain,
% 2.75/2.94 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[5159, 11575])).
% 2.75/2.94 tff(11577,plain,
% 2.75/2.94 (s(z) = s(elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11578,plain,
% 2.75/2.94 (s(s(z)) = s(s(elem!1))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11577])).
% 2.75/2.94 tff(11579,plain,
% 2.75/2.94 (b(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11578])).
% 2.75/2.94 tff(11580,plain,
% 2.75/2.94 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11191, 11579])).
% 2.75/2.94 tff(11581,plain,
% 2.75/2.94 (~b(elem!1, s(s(elem!1)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[71, 11559, 42])).
% 2.75/2.94 tff(11582,plain,
% 2.75/2.94 (r(elem!1, s(s(elem!1)))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[147, 11581, 116])).
% 2.75/2.94 tff(11583,plain,
% 2.75/2.94 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11584,plain,
% 2.75/2.94 (~b(s(s(elem!1)), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[9564, 11569, 11301])).
% 2.75/2.94 tff(11585,plain,
% 2.75/2.94 (r(s(s(elem!1)), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[801, 11584])).
% 2.75/2.94 tff(11586,plain,
% 2.75/2.94 (r(s(s(elem!1)), elem!1)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11585, 11583])).
% 2.75/2.94 tff(11587,plain,
% 2.75/2.94 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11559])).
% 2.75/2.94 tff(11588,plain,
% 2.75/2.94 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[9634, 11564, 11324, 4167])).
% 2.75/2.94 tff(11589,plain,
% 2.75/2.94 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[176, 11588])).
% 2.75/2.94 tff(11590,plain,
% 2.75/2.94 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11589, 11587])).
% 2.75/2.94 tff(11591,plain,
% 2.75/2.94 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[3384, 11559])).
% 2.75/2.94 tff(11592,plain,
% 2.75/2.94 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6386, 11591])).
% 2.75/2.94 tff(11593,plain,
% 2.75/2.94 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11578])).
% 2.75/2.94 tff(11594,plain,
% 2.75/2.94 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[3745, 11593])).
% 2.75/2.94 tff(11595,plain,
% 2.75/2.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6421, 11594, 11592, 11590, 2620, 11586, 11582, 11580])).
% 2.75/2.94 tff(11596,plain,
% 2.75/2.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[5065, 11595, 11576])).
% 2.75/2.94 tff(11597,plain,
% 2.75/2.94 (b(s(elem!1), z)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1209, 11559, 11285])).
% 2.75/2.94 tff(11598,plain,
% 2.75/2.94 (b(s(elem!1), elem!1)),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[1770, 11597, 11559])).
% 2.75/2.94 tff(11599,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11600,plain,
% 2.75/2.94 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11601,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11600])).
% 2.75/2.94 tff(11602,plain,
% 2.75/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(transitivity,[status(thm)],[11601, 11599])).
% 2.75/2.94 tff(11603,plain,
% 2.75/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(11604,plain,
% 2.75/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11603, 11602])).
% 2.75/2.94 tff(11605,plain,
% 2.75/2.94 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11604, 198, 11598, 11596, 11573, 11566, 11565])).
% 2.75/2.94 tff(11606,plain,
% 2.75/2.94 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6454, 11559, 2737])).
% 2.75/2.94 tff(11607,plain,
% 2.75/2.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), 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(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.75/2.94 inference(rewrite,[status(thm)],[])).
% 2.75/2.94 tff(11608,plain,
% 2.75/2.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.75/2.94 inference(quant_inst,[status(thm)],[])).
% 2.75/2.94 tff(11609,plain,
% 2.75/2.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11608, 11607])).
% 2.75/2.94 tff(11610,plain,
% 2.75/2.94 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[11609, 26, 11606, 11605])).
% 2.75/2.94 tff(11611,plain,
% 2.75/2.94 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[2942, 11559, 11314])).
% 2.75/2.94 tff(11612,plain,
% 2.75/2.94 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[3205, 11559, 11312])).
% 2.75/2.94 tff(11613,plain,
% 2.75/2.94 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11577])).
% 2.75/2.94 tff(11614,plain,
% 2.75/2.94 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.75/2.94 inference(symmetry,[status(thm)],[11613])).
% 2.75/2.94 tff(11615,plain,
% 2.75/2.94 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.75/2.94 inference(monotonicity,[status(thm)],[11614])).
% 2.75/2.94 tff(11616,plain,
% 2.75/2.94 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6429, 198, 11598, 11596, 11573])).
% 2.75/2.94 tff(11617,plain,
% 2.75/2.94 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.75/2.94 inference(modus_ponens,[status(thm)],[11616, 11615])).
% 2.75/2.94 tff(11618,plain,
% 2.75/2.94 (r(s(s(s(s(elem!1)))), s(z))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6436, 11617])).
% 2.75/2.94 tff(11619,plain,
% 2.75/2.94 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.75/2.94 inference(unit_resolution,[status(thm)],[6444, 11618, 11559])).
% 2.75/2.94 tff(11620,plain,
% 2.75/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11621,plain,
% 2.75/2.95 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11622,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[11621])).
% 2.75/2.95 tff(11623,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(transitivity,[status(thm)],[11622, 11620])).
% 2.75/2.95 tff(11624,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(11625,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[11624, 11623])).
% 2.75/2.95 tff(11626,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11625, 163, 11619, 11612, 11611, 11610])).
% 2.75/2.95 tff(11627,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | b(z, s(s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11628,plain,
% 2.75/2.95 (elem!1 = s(s(elem!1))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11627, 11304, 11310, 42, 407])).
% 2.75/2.95 tff(11629,plain,
% 2.75/2.95 (s(s(elem!1)) = elem!1),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[676, 11628])).
% 2.75/2.95 tff(11630,plain,
% 2.75/2.95 (s(s(s(elem!1))) = s(elem!1)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[2064, 11629])).
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% 2.75/2.95 inference(modus_ponens,[status(thm)],[11649, 11647])).
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[11475, 163, 11661, 11659, 11632])).
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[3400, 11662, 11657])).
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% 2.75/2.95 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[11664])).
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% 2.75/2.95 inference(transitivity,[status(thm)],[11665, 11630])).
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% 2.75/2.95 inference(monotonicity,[status(thm)],[11666])).
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% 2.75/2.95 inference(symmetry,[status(thm)],[11667])).
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% 2.75/2.95 inference(monotonicity,[status(thm)],[11645])).
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% 2.75/2.95 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[11670, 11668])).
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% 2.75/2.95 tff(11673,plain,
% 2.75/2.95 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11672, 42, 407])).
% 2.75/2.95 tff(11674,plain,
% 2.75/2.95 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[31, 11673])).
% 2.75/2.95 tff(11675,plain,
% 2.75/2.95 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[8483, 3615, 1185, 331])).
% 2.75/2.95 tff(11676,plain,
% 2.75/2.95 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[176, 11675])).
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% 2.75/2.95 tff(11678,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11679,plain,
% 2.75/2.95 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11678, 55, 11302, 11285, 11674, 407, 11191])).
% 2.75/2.95 tff(11680,plain,
% 2.75/2.95 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3613, 11679])).
% 2.75/2.95 tff(11681,plain,
% 2.75/2.95 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11322, 163, 11680, 9365, 11300])).
% 2.75/2.95 tff(11682,plain,
% 2.75/2.95 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[9643, 11681])).
% 2.75/2.95 tff(11683,plain,
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[10216, 163, 3066, 151, 3639, 422])).
% 2.75/2.95 tff(11684,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11685,plain,
% 2.75/2.95 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11684, 11680, 9365, 11300])).
% 2.75/2.95 tff(11686,plain,
% 2.75/2.95 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3098, 11685])).
% 2.75/2.95 tff(11687,plain,
% 2.75/2.95 (~b(z, s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[10515, 198, 11686, 11674, 11682])).
% 2.75/2.95 tff(11688,plain,
% 2.75/2.95 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3882, 3066, 153, 3828])).
% 2.75/2.95 tff(11689,plain,
% 2.75/2.95 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[176, 11688])).
% 2.75/2.95 tff(11690,plain,
% 2.75/2.95 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[8483, 11689, 1185, 331])).
% 2.75/2.95 tff(11691,plain,
% 2.75/2.95 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3613, 11690])).
% 2.75/2.95 tff(11692,plain,
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[10216, 163, 3066, 11691, 3639, 422])).
% 2.75/2.95 tff(11693,plain,((~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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11694,plain,
% 2.75/2.95 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11693, 3828, 422, 1185, 331, 153, 3639])).
% 2.75/2.95 tff(11695,plain,
% 2.75/2.95 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3098, 11694])).
% 2.75/2.95 tff(11696,plain,
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% 2.75/2.95 inference(unit_resolution,[status(thm)],[9885, 11331, 10854])).
% 2.75/2.95 tff(11697,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11698,plain,
% 2.75/2.95 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11697, 11695, 348, 153, 332, 3828])).
% 2.75/2.95 tff(11699,plain,
% 2.75/2.95 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[9643, 11698])).
% 2.75/2.95 tff(11700,plain,
% 2.75/2.95 (~b(s(z), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[6842, 198, 407, 10855, 10853])).
% 2.75/2.95 tff(11701,plain,
% 2.75/2.95 (r(s(z), s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3301, 11700])).
% 2.75/2.95 tff(11702,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11703,plain,
% 2.75/2.95 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11704,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[11703])).
% 2.75/2.95 tff(11705,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(transitivity,[status(thm)],[11704, 11702])).
% 2.75/2.95 tff(11706,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(11707,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[11706, 11705])).
% 2.75/2.95 tff(11708,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11707, 163, 11701, 3639, 422, 11699])).
% 2.75/2.95 tff(11709,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11710,plain,
% 2.75/2.95 (~r(s(s(s(s(s(z))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11709, 9365, 11300, 407, 55, 11302, 11191, 11285, 11674])).
% 2.75/2.95 tff(11711,plain,
% 2.75/2.95 (b(s(s(s(s(s(z))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[3841, 11710])).
% 2.75/2.95 tff(11712,plain,
% 2.75/2.95 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[4174, 11686, 11674, 11711])).
% 2.75/2.95 tff(11713,plain,
% 2.75/2.95 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[176, 11712])).
% 2.75/2.95 tff(11714,plain,
% 2.75/2.95 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[5578, 11713, 55, 11302])).
% 2.75/2.95 tff(11715,plain,
% 2.75/2.95 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[420, 11714])).
% 2.75/2.95 tff(11716,plain,
% 2.75/2.95 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[4991, 198, 11686, 11191, 11715])).
% 2.75/2.95 tff(11717,plain,
% 2.75/2.95 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[9576, 11716])).
% 2.75/2.95 tff(11718,plain,
% 2.75/2.95 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[9554, 163, 55, 11302, 11717])).
% 2.75/2.95 tff(11719,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[4110, 11718, 11687])).
% 2.75/2.95 tff(11720,plain,(b(z, s(s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11721,plain,
% 2.75/2.95 (b(z, s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11720, 407])).
% 2.75/2.95 tff(11722,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11723,plain,
% 2.75/2.95 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11724,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[11723])).
% 2.75/2.95 tff(11725,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.75/2.95 inference(transitivity,[status(thm)],[11724, 11722])).
% 2.75/2.95 tff(11726,plain,
% 2.75/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(11727,plain,
% 2.75/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[11726, 11725])).
% 2.75/2.95 tff(11728,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11727, 198, 1185, 407, 347, 11721])).
% 2.75/2.95 tff(11729,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11730,plain,
% 2.75/2.95 (~b(s(s(z)), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11729, 1185, 407])).
% 2.75/2.95 tff(11731,plain,
% 2.75/2.95 (r(s(s(z)), z)),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[345, 11730])).
% 2.75/2.95 tff(11732,plain,
% 2.75/2.95 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[4031, 406, 332, 152])).
% 2.75/2.95 tff(11733,plain,
% 2.75/2.95 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[374, 11732])).
% 2.75/2.95 tff(11734,plain,
% 2.75/2.95 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[9459, 11733, 9403, 331])).
% 2.75/2.95 tff(11735,plain,
% 2.75/2.95 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[420, 11734])).
% 2.75/2.95 tff(11736,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11737,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(11738,plain,
% 2.75/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[11737, 11736])).
% 2.75/2.95 tff(11739,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11738, 163, 406, 332, 11735, 152])).
% 2.75/2.95 tff(11740,plain,((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11741,plain,
% 2.75/2.95 (~r(z, s(z))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11740, 331, 11721, 152, 332])).
% 2.75/2.95 tff(11742,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11743,plain,
% 2.75/2.95 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.95 inference(rewrite,[status(thm)],[])).
% 2.75/2.95 tff(11744,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.95 inference(monotonicity,[status(thm)],[11743])).
% 2.75/2.95 tff(11745,plain,
% 2.75/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.95 inference(transitivity,[status(thm)],[11744, 11742])).
% 2.75/2.95 tff(11746,plain,
% 2.75/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.95 inference(quant_inst,[status(thm)],[])).
% 2.75/2.95 tff(11747,plain,
% 2.75/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.95 inference(modus_ponens,[status(thm)],[11746, 11745])).
% 2.75/2.95 tff(11748,plain,
% 2.75/2.95 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11747, 198, 407, 2, 11721])).
% 2.75/2.95 tff(11749,plain,
% 2.75/2.95 (~b(z, s(z))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11748, 331])).
% 2.75/2.95 tff(11750,plain,
% 2.75/2.95 ($false),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[593, 11749, 11741])).
% 2.75/2.95 tff(11751,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.95 tff(11752,plain,
% 2.75/2.95 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[11751, 152, 2, 407, 11731])).
% 2.75/2.95 tff(11753,plain,
% 2.75/2.95 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.95 inference(unit_resolution,[status(thm)],[31, 11752])).
% 2.75/2.95 tff(11754,plain,
% 2.75/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
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% 2.75/2.96 tff(11761,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[374, 11760])).
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% 2.75/2.96 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
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% 2.75/2.96 inference(monotonicity,[status(thm)],[11763])).
% 2.75/2.96 tff(11765,plain,
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% 2.75/2.96 inference(transitivity,[status(thm)],[11764, 11762])).
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% 2.75/2.96 inference(modus_ponens,[status(thm)],[11766, 11765])).
% 2.75/2.96 tff(11768,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[11767, 163, 332, 33, 423, 152])).
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% 2.75/2.96 tff(11770,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[11769, 11753, 11731, 152])).
% 2.75/2.96 tff(11771,plain,
% 2.75/2.96 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[420, 11770])).
% 2.75/2.96 tff(11772,plain,
% 2.75/2.96 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[8845, 11761, 407, 11771])).
% 2.75/2.96 tff(11773,plain,
% 2.75/2.96 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[3613, 11772])).
% 2.75/2.96 tff(11774,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[3753, 3745, 407, 2])).
% 2.75/2.96 tff(11775,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[487, 11774])).
% 2.75/2.96 tff(11776,plain,
% 2.75/2.96 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 2.75/2.96 tff(11779,plain,
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% 2.75/2.96 tff(11780,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[374, 11779, 11776])).
% 2.75/2.96 tff(11781,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.96 tff(11782,plain,
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% 2.75/2.96 tff(11783,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[469, 11782])).
% 2.75/2.96 tff(11784,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[3753, 11771, 407, 2])).
% 2.75/2.96 tff(11785,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[487, 11784])).
% 2.75/2.96 tff(11786,plain,
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% 2.75/2.96 tff(11787,plain,
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% 2.75/2.96 tff(11788,plain,
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% 2.75/2.96 tff(11789,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[3841, 11788])).
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% 2.75/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
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% 2.75/2.96 tff(11791,plain,
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% 2.75/2.96 inference(monotonicity,[status(thm)],[11791])).
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% 2.75/2.96 inference(transitivity,[status(thm)],[11792, 11790])).
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% 2.75/2.96 inference(modus_ponens,[status(thm)],[11794, 11793])).
% 2.75/2.96 tff(11796,plain,
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% 2.75/2.96 tff(11797,plain,
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% 2.75/2.96 inference(unit_resolution,[status(thm)],[9643, 11796])).
% 2.75/2.96 tff(11798,plain,
% 2.75/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11799,plain,
% 2.75/2.96 (((~r(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(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11800,plain,
% 2.75/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.96 inference(monotonicity,[status(thm)],[11799])).
% 2.75/2.96 tff(11801,plain,
% 2.75/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.96 inference(transitivity,[status(thm)],[11800, 11798])).
% 2.75/2.96 tff(11802,plain,
% 2.75/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))))))),
% 2.75/2.96 inference(quant_inst,[status(thm)],[])).
% 2.75/2.96 tff(11803,plain,
% 2.75/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.96 inference(modus_ponens,[status(thm)],[11802, 11801])).
% 2.75/2.96 tff(11804,plain,
% 2.75/2.96 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[11803, 163, 33, 152, 3828])).
% 2.75/2.96 tff(11805,plain,
% 2.75/2.96 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[3098, 11804])).
% 2.75/2.96 tff(11806,plain,
% 2.75/2.96 ($false),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[11544, 198, 11805, 348, 3745, 11797, 4049])).
% 2.75/2.96 tff(11807,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.96 tff(11808,plain,
% 2.75/2.96 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[11807, 11789, 152, 11771, 11753, 11761])).
% 2.75/2.96 tff(11809,plain,
% 2.75/2.96 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[9576, 11808])).
% 2.75/2.96 tff(11810,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11811,plain,
% 2.75/2.96 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11812,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.75/2.96 inference(monotonicity,[status(thm)],[11811])).
% 2.75/2.96 tff(11813,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/2.96 inference(transitivity,[status(thm)],[11812, 11810])).
% 2.75/2.96 tff(11814,plain,
% 2.75/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(quant_inst,[status(thm)],[])).
% 2.75/2.96 tff(11815,plain,
% 2.75/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.75/2.96 inference(modus_ponens,[status(thm)],[11814, 11813])).
% 2.75/2.96 tff(11816,plain,
% 2.75/2.96 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[11815, 198, 407, 11771, 2, 11783])).
% 2.75/2.96 tff(11817,plain,
% 2.75/2.96 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[9643, 11816])).
% 2.75/2.96 tff(11818,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11819,plain,
% 2.75/2.96 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(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(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11820,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.75/2.96 inference(monotonicity,[status(thm)],[11819])).
% 2.75/2.96 tff(11821,plain,
% 2.75/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.75/2.96 inference(transitivity,[status(thm)],[11820, 11818])).
% 2.75/2.96 tff(11822,plain,
% 2.75/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.75/2.96 inference(quant_inst,[status(thm)],[])).
% 2.75/2.96 tff(11823,plain,
% 2.75/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.75/2.96 inference(modus_ponens,[status(thm)],[11822, 11821])).
% 2.75/2.96 tff(11824,plain,
% 2.75/2.96 (~b(z, s(s(s(s(s(z))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[11823, 198, 11787, 407, 11783, 11721])).
% 2.75/2.96 tff(11825,plain,
% 2.75/2.96 (r(z, s(s(s(s(s(z))))))),
% 2.75/2.96 inference(unit_resolution,[status(thm)],[4110, 11824])).
% 2.75/2.96 tff(11826,plain,
% 2.75/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.96 inference(rewrite,[status(thm)],[])).
% 2.75/2.96 tff(11827,plain,
% 2.75/2.96 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11828,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11827])).
% 2.75/2.97 tff(11829,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11828, 11826])).
% 2.75/2.97 tff(11830,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11831,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11830, 11829])).
% 2.75/2.97 tff(11832,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11831, 163, 33, 9580, 3368, 7912])).
% 2.75/2.97 tff(11833,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11834,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11833, 11825, 11817, 11753, 11809])).
% 2.75/2.97 tff(11835,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11836,plain,
% 2.75/2.97 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11835, 2, 407, 1185])).
% 2.75/2.97 tff(11837,plain,
% 2.75/2.97 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[176, 11836])).
% 2.75/2.97 tff(11838,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11839,plain,
% 2.75/2.97 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11840,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11839])).
% 2.75/2.97 tff(11841,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11840, 11838])).
% 2.75/2.97 tff(11842,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11843,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11842, 11841])).
% 2.75/2.97 tff(11844,plain,
% 2.75/2.97 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11843, 198, 1185, 407, 2, 11837, 11721])).
% 2.75/2.97 tff(11845,plain,
% 2.75/2.97 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3613, 11844])).
% 2.75/2.97 tff(11846,plain,
% 2.75/2.97 (~b(s(s(z)), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[5769, 2, 1185, 330, 3745])).
% 2.75/2.97 tff(11847,plain,
% 2.75/2.97 (r(s(s(z)), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[487, 11846])).
% 2.75/2.97 tff(11848,plain,
% 2.75/2.97 (~b(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[4953, 2, 1185, 330])).
% 2.75/2.97 tff(11849,plain,
% 2.75/2.97 (r(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[593, 11848])).
% 2.75/2.97 tff(11850,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[7140, 11849, 11847, 332, 151])).
% 2.75/2.97 tff(11851,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11852,plain,
% 2.75/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11851, 11845, 1185, 11731, 2, 11837])).
% 2.75/2.97 tff(11853,plain,
% 2.75/2.97 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[420, 11852])).
% 2.75/2.97 tff(11854,plain,
% 2.75/2.97 (~b(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[4953, 11837, 1185, 2])).
% 2.75/2.97 tff(11855,plain,
% 2.75/2.97 (r(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[593, 11854])).
% 2.75/2.97 tff(11856,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10060, 163, 406, 151, 33, 423])).
% 2.75/2.97 tff(11857,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11858,plain,
% 2.75/2.97 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11857, 11855, 11845, 11853])).
% 2.75/2.97 tff(11859,plain,
% 2.75/2.97 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[31, 11858])).
% 2.75/2.97 tff(11860,plain,
% 2.75/2.97 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[456, 11859, 11837, 11855, 11845, 11853])).
% 2.75/2.97 tff(11861,plain,
% 2.75/2.97 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[469, 11860])).
% 2.75/2.97 tff(11862,plain,
% 2.75/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[5805, 198, 1185, 2, 11837, 11861])).
% 2.75/2.97 tff(11863,plain,
% 2.75/2.97 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9643, 11862])).
% 2.75/2.97 tff(11864,plain,
% 2.75/2.97 (~r(s(s(z)), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[7140, 11845, 11855, 11731])).
% 2.75/2.97 tff(11865,plain,
% 2.75/2.97 (b(s(s(z)), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[487, 11864])).
% 2.75/2.97 tff(11866,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[7909, 198, 560, 407, 559, 4049])).
% 2.75/2.97 tff(11867,plain,((~b(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(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11868,plain,
% 2.75/2.97 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11867, 11861, 407, 11865])).
% 2.75/2.97 tff(11869,plain,
% 2.75/2.97 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9576, 11868])).
% 2.75/2.97 tff(11870,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9337, 163, 11731, 11853, 11869, 11863])).
% 2.75/2.97 tff(11871,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11872,plain,
% 2.75/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11871, 1185, 407])).
% 2.75/2.97 tff(11873,plain,
% 2.75/2.97 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3654, 11872])).
% 2.75/2.97 tff(11874,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11875,plain,
% 2.75/2.97 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11876,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11875])).
% 2.75/2.97 tff(11877,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11876, 11874])).
% 2.75/2.97 tff(11878,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11879,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11878, 11877])).
% 2.75/2.97 tff(11880,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11879, 198, 1185, 407, 3615, 348, 11721])).
% 2.75/2.97 tff(11881,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11882,plain,
% 2.75/2.97 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11881, 3615, 407, 1185])).
% 2.75/2.97 tff(11883,plain,
% 2.75/2.97 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[374, 11882])).
% 2.75/2.97 tff(11884,plain,
% 2.75/2.97 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10086, 11883, 11731, 11873])).
% 2.75/2.97 tff(11885,plain,
% 2.75/2.97 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[31, 11884])).
% 2.75/2.97 tff(11886,plain,
% 2.75/2.97 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[8483, 11885, 1185, 3615])).
% 2.75/2.97 tff(11887,plain,
% 2.75/2.97 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[176, 11886])).
% 2.75/2.97 tff(11888,plain,
% 2.75/2.97 (~r(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11740, 11887, 11721, 11885, 11731])).
% 2.75/2.97 tff(11889,plain,
% 2.75/2.97 (b(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[593, 11888])).
% 2.75/2.97 tff(11890,plain,
% 2.75/2.97 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9411, 11889, 11721, 3615, 11885])).
% 2.75/2.97 tff(11891,plain,
% 2.75/2.97 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[420, 11890])).
% 2.75/2.97 tff(11892,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11893,plain,
% 2.75/2.97 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11894,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11893])).
% 2.75/2.97 tff(11895,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11894, 11892])).
% 2.75/2.97 tff(11896,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11897,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11896, 11895])).
% 2.75/2.97 tff(11898,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11897, 163, 332, 423, 152, 7912])).
% 2.75/2.97 tff(11899,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11900,plain,
% 2.75/2.97 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11899, 11891, 11731, 11887])).
% 2.75/2.97 tff(11901,plain,
% 2.75/2.97 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[4110, 11900])).
% 2.75/2.97 tff(11902,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11823, 198, 595, 407, 559, 11721, 5428])).
% 2.75/2.97 tff(11903,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11904,plain,
% 2.75/2.97 (~b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11903, 11889, 407, 11901])).
% 2.75/2.97 tff(11905,plain,
% 2.75/2.97 (r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[469, 11904])).
% 2.75/2.97 tff(11906,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[5798, 163, 3272, 423, 9580, 3368])).
% 2.75/2.97 tff(11907,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11908,plain,
% 2.75/2.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11907, 9580, 3272, 423])).
% 2.75/2.97 tff(11909,plain,
% 2.75/2.97 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9643, 11908])).
% 2.75/2.97 tff(11910,plain,
% 2.75/2.97 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9602, 9580, 3639, 3272])).
% 2.75/2.97 tff(11911,plain,
% 2.75/2.97 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3098, 11910])).
% 2.75/2.97 tff(11912,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10515, 198, 11911, 331, 5428, 11909])).
% 2.75/2.97 tff(11913,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11914,plain,
% 2.75/2.97 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11913, 11885, 11901, 11883, 11891, 11873])).
% 2.75/2.97 tff(11915,plain,
% 2.75/2.97 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9576, 11914])).
% 2.75/2.97 tff(11916,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11917,plain,
% 2.75/2.97 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11918,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11917])).
% 2.75/2.97 tff(11919,plain,
% 2.75/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11918, 11916])).
% 2.75/2.97 tff(11920,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11921,plain,
% 2.75/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11920, 11919])).
% 2.75/2.97 tff(11922,plain,
% 2.75/2.97 (~b(s(z), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11921, 198, 1185, 407, 11901, 11915])).
% 2.75/2.97 tff(11923,plain,
% 2.75/2.97 (r(s(z), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3301, 11922])).
% 2.75/2.97 tff(11924,plain,
% 2.75/2.97 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10501, 163, 11923, 11873, 11905])).
% 2.75/2.97 tff(11925,plain,
% 2.75/2.97 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[9643, 11924])).
% 2.75/2.97 tff(11926,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11927,plain,
% 2.75/2.97 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11928,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.97 inference(monotonicity,[status(thm)],[11927])).
% 2.75/2.97 tff(11929,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(transitivity,[status(thm)],[11928, 11926])).
% 2.75/2.97 tff(11930,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(quant_inst,[status(thm)],[])).
% 2.75/2.97 tff(11931,plain,
% 2.75/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.97 inference(modus_ponens,[status(thm)],[11930, 11929])).
% 2.75/2.97 tff(11932,plain,
% 2.75/2.97 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11931, 163, 11923, 11873, 11905])).
% 2.75/2.97 tff(11933,plain,
% 2.75/2.97 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3098, 11932])).
% 2.75/2.97 tff(11934,plain,
% 2.75/2.97 ($false),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10515, 198, 11933, 11885, 11901, 11925])).
% 2.75/2.97 tff(11935,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.97 tff(11936,plain,
% 2.75/2.97 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[11935, 1185, 407])).
% 2.75/2.97 tff(11937,plain,
% 2.75/2.97 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3613, 11936])).
% 2.75/2.97 tff(11938,plain,
% 2.75/2.97 (~r(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[10095, 163, 151, 33, 3639])).
% 2.75/2.97 tff(11939,plain,
% 2.75/2.97 (b(z, s(z))),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[593, 11938])).
% 2.75/2.97 tff(11940,plain,
% 2.75/2.97 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[8803, 11939, 1185, 559])).
% 2.75/2.97 tff(11941,plain,
% 2.75/2.97 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.97 inference(unit_resolution,[status(thm)],[3841, 11940])).
% 2.75/2.97 tff(11942,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11943,plain,
% 2.75/2.97 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(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))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.97 inference(rewrite,[status(thm)],[])).
% 2.75/2.97 tff(11944,plain,
% 2.75/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.98 inference(monotonicity,[status(thm)],[11943])).
% 2.75/2.98 tff(11945,plain,
% 2.75/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.98 inference(transitivity,[status(thm)],[11944, 11942])).
% 2.75/2.98 tff(11946,plain,
% 2.75/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/2.98 inference(quant_inst,[status(thm)],[])).
% 2.75/2.98 tff(11947,plain,
% 2.75/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.98 inference(modus_ponens,[status(thm)],[11946, 11945])).
% 2.75/2.98 tff(11948,plain,
% 2.75/2.98 ($false),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11947, 163, 332, 33, 9580, 11941])).
% 2.75/2.98 tff(11949,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.98 tff(11950,plain,
% 2.75/2.98 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11949, 9580, 332, 1185, 559, 151, 3639])).
% 2.75/2.98 tff(11951,plain,
% 2.75/2.98 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[31, 11950])).
% 2.75/2.98 tff(11952,plain,
% 2.75/2.98 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9602, 3066, 3639, 9580])).
% 2.75/2.98 tff(11953,plain,
% 2.75/2.98 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[374, 11952])).
% 2.75/2.98 tff(11954,plain,
% 2.75/2.98 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9459, 11953, 9403, 331])).
% 2.75/2.98 tff(11955,plain,
% 2.75/2.98 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[420, 11954])).
% 2.75/2.98 tff(11956,plain,
% 2.75/2.98 ($false),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9588, 163, 3066, 332, 11955, 9580])).
% 2.75/2.98 tff(11957,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.98 tff(11958,plain,
% 2.75/2.98 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11957, 11951, 332, 9403, 3639, 9580])).
% 2.75/2.98 tff(11959,plain,
% 2.75/2.98 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[3098, 11958])).
% 2.75/2.98 tff(11960,plain,
% 2.75/2.98 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9459, 11951, 9403, 3745])).
% 2.75/2.98 tff(11961,plain,
% 2.75/2.98 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[374, 11960])).
% 2.75/2.98 tff(11962,plain,
% 2.75/2.98 (~b(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9449, 11961, 9403, 151, 3639])).
% 2.75/2.98 tff(11963,plain,
% 2.75/2.98 (r(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[593, 11962])).
% 2.75/2.98 tff(11964,plain,
% 2.75/2.98 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[4031, 11963, 332, 11961])).
% 2.75/2.98 tff(11965,plain,
% 2.75/2.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[176, 11964])).
% 2.75/2.98 tff(11966,plain,
% 2.75/2.98 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[4174, 11965, 11959, 11951])).
% 2.75/2.98 tff(11967,plain,
% 2.75/2.98 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[3841, 11966])).
% 2.75/2.98 tff(11968,plain,
% 2.75/2.98 ($false),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[10122, 163, 11963, 332, 9580, 11967])).
% 2.75/2.98 tff(11969,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.98 tff(11970,plain,
% 2.75/2.98 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11969, 3745, 11721, 11937, 11873, 11731, 1185, 559])).
% 2.75/2.98 tff(11971,plain,
% 2.75/2.98 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9576, 11970])).
% 2.75/2.98 tff(11972,plain,
% 2.75/2.98 (~b(s(s(z)), s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11867, 11971, 407, 559])).
% 2.75/2.98 tff(11973,plain,
% 2.75/2.98 (r(s(s(z)), s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[487, 11972])).
% 2.75/2.98 tff(11974,plain,
% 2.75/2.98 (~r(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[7140, 11973, 11937, 11731])).
% 2.75/2.98 tff(11975,plain,
% 2.75/2.98 (b(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[593, 11974])).
% 2.75/2.98 tff(11976,plain,
% 2.75/2.98 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9449, 11975, 11721, 11937, 11873])).
% 2.75/2.98 tff(11977,plain,
% 2.75/2.98 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[374, 11976])).
% 2.75/2.98 tff(11978,plain,
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% 2.75/2.98 tff(11979,plain,
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% 2.75/2.98 inference(monotonicity,[status(thm)],[11981])).
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% 2.75/2.98 inference(modus_ponens,[status(thm)],[11984, 11983])).
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% 2.75/2.98 tff(11988,plain,
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% 2.75/2.98 tff(11989,plain,
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% 2.75/2.98 inference(unit_resolution,[status(thm)],[3098, 11988])).
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% 2.75/2.98 tff(11991,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.98 tff(11992,plain,
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% 2.75/2.98 tff(11993,plain,
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% 2.75/2.98 inference(unit_resolution,[status(thm)],[420, 11992])).
% 2.75/2.98 tff(11994,plain,
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% 2.75/2.98 tff(11995,plain,
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% 2.75/2.98 tff(11996,plain,
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% 2.75/2.98 tff(11997,plain,
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% 2.75/2.98 inference(unit_resolution,[status(thm)],[9576, 11996])).
% 2.75/2.98 tff(11998,plain,
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% 2.75/2.98 tff(11999,plain,
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% 2.75/2.98 tff(12000,plain,
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% 2.75/2.98 tff(12001,plain,
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% 2.75/2.98 tff(12002,plain,
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% 2.75/2.98 tff(12003,plain,
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% 2.75/2.98 tff(12004,plain,
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% 2.75/2.98 tff(12014,plain,
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% 2.75/2.98 tff(12015,plain,
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% 2.75/2.98 tff(12026,plain,
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% 2.75/2.98 tff(12027,plain,
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% 2.75/2.98 inference(unit_resolution,[status(thm)],[9885, 12026])).
% 2.75/2.98 tff(12028,plain,
% 2.75/2.98 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11684, 12015, 11873, 11937])).
% 2.75/2.98 tff(12029,plain,
% 2.75/2.98 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[3098, 12028])).
% 2.75/2.98 tff(12030,plain,
% 2.75/2.98 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(rewrite,[status(thm)],[])).
% 2.75/2.98 tff(12031,plain,
% 2.75/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.75/2.98 inference(monotonicity,[status(thm)],[12030])).
% 2.75/2.98 tff(12032,plain,
% 2.75/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(transitivity,[status(thm)],[12031, 11325])).
% 2.75/2.98 tff(12033,plain,
% 2.75/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(quant_inst,[status(thm)],[])).
% 2.75/2.98 tff(12034,plain,
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% 2.75/2.98 inference(modus_ponens,[status(thm)],[12033, 12032])).
% 2.75/2.98 tff(12035,plain,
% 2.75/2.98 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[12034, 198, 12029, 12027, 12017])).
% 2.75/2.98 tff(12036,plain,
% 2.75/2.98 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[374, 12035])).
% 2.75/2.98 tff(12037,plain,
% 2.75/2.98 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[10086, 12036, 11731, 11873])).
% 2.75/2.98 tff(12038,plain,
% 2.75/2.98 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[31, 12037])).
% 2.75/2.98 tff(12039,plain,
% 2.75/2.98 (~b(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9449, 12036, 11721, 11937, 11873])).
% 2.75/2.98 tff(12040,plain,
% 2.75/2.98 (r(z, s(z))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[593, 12039])).
% 2.75/2.98 tff(12041,plain,
% 2.75/2.98 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[4031, 12040, 11731, 12036])).
% 2.75/2.98 tff(12042,plain,
% 2.75/2.98 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[176, 12041])).
% 2.75/2.98 tff(12043,plain,
% 2.75/2.98 (~r(s(s(s(s(s(z))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[10200, 12040, 12015, 11937])).
% 2.75/2.98 tff(12044,plain,
% 2.75/2.98 (b(s(s(s(s(s(z))))), z)),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[3841, 12043])).
% 2.75/2.98 tff(12045,plain,
% 2.75/2.98 ($false),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[4174, 12044, 12042, 12029, 12038])).
% 2.75/2.98 tff(12046,plain,((~r(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.98 tff(12047,plain,
% 2.75/2.98 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[12046, 1185, 407])).
% 2.75/2.98 tff(12048,plain,
% 2.75/2.98 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[4110, 12047])).
% 2.75/2.98 tff(12049,plain,
% 2.75/2.98 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11322, 163, 151, 3639, 422])).
% 2.75/2.98 tff(12050,plain,
% 2.75/2.98 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[9643, 12049])).
% 2.75/2.98 tff(12051,plain,
% 2.75/2.98 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[11684, 422, 3639, 151])).
% 2.75/2.98 tff(12052,plain,
% 2.75/2.98 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.98 inference(unit_resolution,[status(thm)],[3098, 12051])).
% 2.75/2.98 tff(12053,plain,
% 2.75/2.98 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.98 inference(rewrite,[status(thm)],[])).
% 2.75/2.98 tff(12054,plain,
% 2.75/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.98 inference(monotonicity,[status(thm)],[12053])).
% 2.75/2.98 tff(12055,plain,
% 2.75/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12054, 10510])).
% 2.75/2.99 tff(12056,plain,
% 2.75/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12057,plain,
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% 2.75/2.99 inference(modus_ponens,[status(thm)],[12056, 12055])).
% 2.75/2.99 tff(12058,plain,
% 2.75/2.99 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12057, 198, 12052, 5428, 12050])).
% 2.75/2.99 tff(12059,plain,
% 2.75/2.99 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[31, 12058])).
% 2.75/2.99 tff(12060,plain,
% 2.75/2.99 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[10086, 12059, 332, 3639])).
% 2.75/2.99 tff(12061,plain,
% 2.75/2.99 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[374, 12060])).
% 2.75/2.99 tff(12062,plain,
% 2.75/2.99 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11330, 198, 12052, 12061, 12050])).
% 2.75/2.99 tff(12063,plain,
% 2.75/2.99 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[9885, 12062])).
% 2.75/2.99 tff(12064,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12065,plain,
% 2.75/2.99 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12066,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12065])).
% 2.75/2.99 tff(12067,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12066, 12064])).
% 2.75/2.99 tff(12068,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12069,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12068, 12067])).
% 2.75/2.99 tff(12070,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12069, 163, 332, 33, 9472, 3828])).
% 2.75/2.99 tff(12071,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.99 tff(12072,plain,
% 2.75/2.99 (~r(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12071, 12059, 332, 12063])).
% 2.75/2.99 tff(12073,plain,
% 2.75/2.99 (b(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[3841, 12072])).
% 2.75/2.99 tff(12074,plain,
% 2.75/2.99 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[9634, 12073, 5428, 12050])).
% 2.75/2.99 tff(12075,plain,
% 2.75/2.99 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[176, 12074])).
% 2.75/2.99 tff(12076,plain,
% 2.75/2.99 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11769, 12075, 332, 12059])).
% 2.75/2.99 tff(12077,plain,
% 2.75/2.99 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[420, 12076])).
% 2.75/2.99 tff(12078,plain,
% 2.75/2.99 (~r(s(s(z)), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[9190, 12077, 151, 422, 12061, 12075])).
% 2.75/2.99 tff(12079,plain,
% 2.75/2.99 (b(s(s(z)), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[487, 12078])).
% 2.75/2.99 tff(12080,plain,
% 2.75/2.99 (~r(z, s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[10095, 163, 151, 12059, 3639])).
% 2.75/2.99 tff(12081,plain,
% 2.75/2.99 (b(z, s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[593, 12080])).
% 2.75/2.99 tff(12082,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[9447, 198, 12081, 12079, 407, 11721])).
% 2.75/2.99 tff(12083,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.99 tff(12084,plain,
% 2.75/2.99 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12083, 11937, 407, 11731, 12048, 11873])).
% 2.75/2.99 tff(12085,plain,
% 2.75/2.99 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[469, 12084])).
% 2.75/2.99 tff(12086,plain,
% 2.75/2.99 (~b(z, s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11903, 12085, 407, 12048])).
% 2.75/2.99 tff(12087,plain,
% 2.75/2.99 (r(z, s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[593, 12086])).
% 2.75/2.99 tff(12088,plain,
% 2.75/2.99 (~r(s(s(z)), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[7140, 12087, 11937, 11731])).
% 2.75/2.99 tff(12089,plain,
% 2.75/2.99 (b(s(s(z)), s(z))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[487, 12088])).
% 2.75/2.99 tff(12090,plain,
% 2.75/2.99 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11867, 12089, 407, 12085])).
% 2.75/2.99 tff(12091,plain,
% 2.75/2.99 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[9576, 12090])).
% 2.75/2.99 tff(12092,plain,
% 2.75/2.99 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11949, 12091, 11731, 1185, 12085, 11937, 11873])).
% 2.75/2.99 tff(12093,plain,
% 2.75/2.99 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[31, 12092])).
% 2.75/2.99 tff(12094,plain,
% 2.75/2.99 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11957, 12093, 11731, 11721, 11873, 12091])).
% 2.75/2.99 tff(12095,plain,
% 2.75/2.99 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[3098, 12094])).
% 2.75/2.99 tff(12096,plain,
% 2.75/2.99 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[11740, 12093, 11721, 12087, 11731])).
% 2.75/2.99 tff(12097,plain,
% 2.75/2.99 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[176, 12096])).
% 2.75/2.99 tff(12098,plain,
% 2.75/2.99 (~b(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[4174, 12097, 12095, 12093])).
% 2.75/2.99 tff(12099,plain,
% 2.75/2.99 (r(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[3841, 12098])).
% 2.75/2.99 tff(12100,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[10122, 163, 12087, 11731, 12091, 12099])).
% 2.75/2.99 tff(12101,plain,((~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.99 tff(12102,plain,
% 2.75/2.99 (~b(s(z), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12101, 407])).
% 2.75/2.99 tff(12103,plain,
% 2.75/2.99 (r(s(z), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[40, 12102])).
% 2.75/2.99 tff(12104,plain,
% 2.75/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12105,plain,
% 2.75/2.99 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12106,plain,
% 2.75/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12105])).
% 2.75/2.99 tff(12107,plain,
% 2.75/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12106, 12104])).
% 2.75/2.99 tff(12108,plain,
% 2.75/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12109,plain,
% 2.75/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12108, 12107])).
% 2.75/2.99 tff(12110,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12109, 198, 3933, 3745, 330, 9403])).
% 2.75/2.99 tff(12111,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.99 tff(12112,plain,
% 2.75/2.99 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12111, 4935, 9363, 150, 330, 3450])).
% 2.75/2.99 tff(12113,plain,
% 2.75/2.99 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[420, 12112])).
% 2.75/2.99 tff(12114,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12115,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12116,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12115, 12114])).
% 2.75/2.99 tff(12117,plain,
% 2.75/2.99 (~r(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12116, 163, 150, 406, 3827])).
% 2.75/2.99 tff(12118,plain,
% 2.75/2.99 (b(s(s(s(s(s(z))))), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[3841, 12117])).
% 2.75/2.99 tff(12119,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12120,plain,
% 2.75/2.99 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12121,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12120])).
% 2.75/2.99 tff(12122,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12121, 12119])).
% 2.75/2.99 tff(12123,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12124,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12123, 12122])).
% 2.75/2.99 tff(12125,plain,
% 2.75/2.99 (~r(z, s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12124, 163, 150, 406, 3827])).
% 2.75/2.99 tff(12126,plain,
% 2.75/2.99 (b(z, s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[4110, 12125])).
% 2.75/2.99 tff(12127,plain,
% 2.75/2.99 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[4174, 12118, 330, 3819])).
% 2.75/2.99 tff(12128,plain,
% 2.75/2.99 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[31, 12127])).
% 2.75/2.99 tff(12129,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12130,plain,
% 2.75/2.99 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12131,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12130])).
% 2.75/2.99 tff(12132,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12131, 12129])).
% 2.75/2.99 tff(12133,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12134,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12133, 12132])).
% 2.75/2.99 tff(12135,plain,
% 2.75/2.99 (~r(s(s(z)), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12134, 163, 3272, 12128, 423])).
% 2.75/2.99 tff(12136,plain,
% 2.75/2.99 (b(s(s(z)), z)),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[345, 12135])).
% 2.75/2.99 tff(12137,plain,
% 2.75/2.99 (((~b(s(s(s(s(s(z))))), z)) | (~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(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))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12138,plain,
% 2.75/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12137])).
% 2.75/2.99 tff(12139,plain,
% 2.75/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12138, 4291])).
% 2.75/2.99 tff(12140,plain,
% 2.75/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~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(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12141,plain,
% 2.75/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12140, 12139])).
% 2.75/2.99 tff(12142,plain,
% 2.75/2.99 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12141, 198, 12136, 12126, 12118])).
% 2.75/2.99 tff(12143,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12144,plain,
% 2.75/2.99 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(rewrite,[status(thm)],[])).
% 2.75/2.99 tff(12145,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.75/2.99 inference(monotonicity,[status(thm)],[12144])).
% 2.75/2.99 tff(12146,plain,
% 2.75/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(transitivity,[status(thm)],[12145, 12143])).
% 2.75/2.99 tff(12147,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/2.99 inference(quant_inst,[status(thm)],[])).
% 2.75/2.99 tff(12148,plain,
% 2.75/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.75/2.99 inference(modus_ponens,[status(thm)],[12147, 12146])).
% 2.75/2.99 tff(12149,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12148, 163, 150, 3450, 422, 9472])).
% 2.75/2.99 tff(12150,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/2.99 tff(12151,plain,
% 2.75/2.99 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[12150, 3827, 150, 3450])).
% 2.75/2.99 tff(12152,plain,
% 2.75/2.99 ($false),
% 2.75/2.99 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12151, 12142])).
% 2.75/2.99 tff(12153,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.00 tff(12154,plain,
% 2.75/3.00 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12153, 423, 3272, 330, 150, 4935, 3450, 3615, 2])).
% 2.75/3.00 tff(12155,plain,
% 2.75/3.00 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[3098, 12154])).
% 2.75/3.00 tff(12156,plain,
% 2.75/3.00 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[4502, 163, 12155, 3272, 423])).
% 2.75/3.00 tff(12157,plain,
% 2.75/3.00 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[511, 26, 508, 12156])).
% 2.75/3.00 tff(12158,plain,
% 2.75/3.00 (~r(s(s(z)), z)),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[3931, 163, 150, 4935, 3450])).
% 2.75/3.00 tff(12159,plain,
% 2.75/3.00 (b(s(s(z)), z)),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[345, 12158])).
% 2.75/3.00 tff(12160,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12161,plain,
% 2.75/3.00 (((~b(z, s(s(z)))) | (~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(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12162,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12161])).
% 2.75/3.00 tff(12163,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12162, 12160])).
% 2.75/3.00 tff(12164,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12165,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12164, 12163])).
% 2.75/3.00 tff(12166,plain,
% 2.75/3.00 (~b(s(s(s(s(s(z))))), z)),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12165, 198, 12159, 9363, 12157])).
% 2.75/3.00 tff(12167,plain,
% 2.75/3.00 (r(s(s(s(s(s(z))))), z)),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[3841, 12166])).
% 2.75/3.00 tff(12168,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12169,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12170,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12169, 12168])).
% 2.75/3.00 tff(12171,plain,
% 2.75/3.00 (~r(s(s(s(s(s(z))))), s(z))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12170, 163, 150, 4935, 12167])).
% 2.75/3.00 tff(12172,plain,
% 2.75/3.00 (b(s(s(s(s(s(z))))), s(z))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[469, 12171])).
% 2.75/3.00 tff(12173,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12174,plain,
% 2.75/3.00 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12175,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12174])).
% 2.75/3.00 tff(12176,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12175, 12173])).
% 2.75/3.00 tff(12177,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12178,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12177, 12176])).
% 2.75/3.00 tff(12179,plain,
% 2.75/3.00 (~r(s(z), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12178, 163, 150, 4935, 12167])).
% 2.75/3.00 tff(12180,plain,
% 2.75/3.00 (b(s(z), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[3301, 12179])).
% 2.75/3.00 tff(12181,plain,
% 2.75/3.00 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[6834, 163, 12155, 3272, 423])).
% 2.75/3.00 tff(12182,plain,
% 2.75/3.00 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12181])).
% 2.75/3.00 tff(12183,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12184,plain,
% 2.75/3.00 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12185,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12184])).
% 2.75/3.00 tff(12186,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12185, 12183])).
% 2.75/3.00 tff(12187,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12188,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12187, 12186])).
% 2.75/3.00 tff(12189,plain,
% 2.75/3.00 (~b(z, s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12188, 198, 9363, 12182, 12157])).
% 2.75/3.00 tff(12190,plain,
% 2.75/3.00 (r(z, s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[4110, 12189])).
% 2.75/3.00 tff(12191,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12192,plain,
% 2.75/3.00 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12193,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12192])).
% 2.75/3.00 tff(12194,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12193, 12191])).
% 2.75/3.00 tff(12195,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12196,plain,
% 2.75/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12195, 12194])).
% 2.75/3.00 tff(12197,plain,
% 2.75/3.00 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12196, 198, 12180, 2, 12172])).
% 2.75/3.00 tff(12198,plain,
% 2.75/3.00 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[3328, 26, 12197])).
% 2.75/3.00 tff(12199,plain,
% 2.75/3.00 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12198, 2935])).
% 2.75/3.00 tff(12200,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12201,plain,
% 2.75/3.00 (((~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12202,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12201])).
% 2.75/3.00 tff(12203,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12202, 12200])).
% 2.75/3.00 tff(12204,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12205,plain,
% 2.75/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.75/3.00 inference(modus_ponens,[status(thm)],[12204, 12203])).
% 2.75/3.00 tff(12206,plain,
% 2.75/3.00 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[12205, 163, 12155, 12199, 12190])).
% 2.75/3.00 tff(12207,plain,
% 2.75/3.00 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.75/3.00 inference(unit_resolution,[status(thm)],[31, 12206])).
% 2.75/3.00 tff(12208,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12209,plain,
% 2.75/3.00 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(rewrite,[status(thm)],[])).
% 2.75/3.00 tff(12210,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/3.00 inference(monotonicity,[status(thm)],[12209])).
% 2.75/3.00 tff(12211,plain,
% 2.75/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.00 inference(transitivity,[status(thm)],[12210, 12208])).
% 2.75/3.00 tff(12212,plain,
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% 2.75/3.00 inference(quant_inst,[status(thm)],[])).
% 2.75/3.00 tff(12213,plain,
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% 2.75/3.00 tff(12214,plain,
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% 2.75/3.00 tff(12215,plain,
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% 2.75/3.00 tff(12216,plain,
% 2.75/3.00 ($false),
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% 2.75/3.00 tff(12217,plain,((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.00 tff(12218,plain,
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% 2.75/3.00 tff(12219,plain,
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% 2.75/3.00 tff(12220,plain,
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% 2.75/3.00 tff(12221,plain,
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% 2.75/3.00 tff(12222,plain,
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% 2.75/3.00 tff(12223,plain,
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% 2.75/3.00 tff(12224,plain,
% 2.75/3.00 (r(z, s(s(s(s(s(z))))))),
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% 2.75/3.00 tff(12225,plain,
% 2.75/3.00 (~b(s(z), s(s(s(s(s(z))))))),
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% 2.75/3.00 tff(12226,plain,
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% 2.75/3.00 tff(12227,plain,
% 2.75/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12228,plain,
% 2.75/3.01 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12229,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12228])).
% 2.75/3.01 tff(12230,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12229, 12227])).
% 2.75/3.01 tff(12231,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12232,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12231, 12230])).
% 2.75/3.01 tff(12233,plain,
% 2.75/3.01 ($false),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12232, 163, 406, 3066, 12226, 12224])).
% 2.75/3.01 tff(12234,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.01 tff(12235,plain,
% 2.75/3.01 (~b(s(z), s(s(z)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12234, 12155, 9363, 4935, 3272, 423])).
% 2.75/3.01 tff(12236,plain,
% 2.75/3.01 (r(s(z), s(s(z)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[403, 12235])).
% 2.75/3.01 tff(12237,plain,
% 2.75/3.01 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[10612, 9558])).
% 2.75/3.01 tff(12238,plain,
% 2.75/3.01 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1263, 10618])).
% 2.75/3.01 tff(12239,plain,
% 2.75/3.01 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1270, 12238])).
% 2.75/3.01 tff(12240,plain,
% 2.75/3.01 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 2.75/3.01 inference(monotonicity,[status(thm)],[80])).
% 2.75/3.01 tff(12241,plain,
% 2.75/3.01 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.75/3.01 inference(symmetry,[status(thm)],[12240])).
% 2.75/3.01 tff(12242,plain,
% 2.75/3.01 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.75/3.01 inference(transitivity,[status(thm)],[9560, 12241])).
% 2.75/3.01 tff(12243,plain,
% 2.75/3.01 (b(s(s(elem!1)), elem!1)),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[347, 12242])).
% 2.75/3.01 tff(12244,plain,
% 2.75/3.01 (s(s(z)) = s(s(elem!1))),
% 2.75/3.01 inference(symmetry,[status(thm)],[9558])).
% 2.75/3.01 tff(12245,plain,
% 2.75/3.01 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12244])).
% 2.75/3.01 tff(12246,plain,
% 2.75/3.01 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.75/3.01 inference(symmetry,[status(thm)],[12245])).
% 2.75/3.01 tff(12247,plain,
% 2.75/3.01 (r(z, s(s(z)))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[1098, 12246])).
% 2.75/3.01 tff(12248,plain,
% 2.75/3.01 ($false),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[49, 12247])).
% 2.75/3.01 tff(12249,plain,(r(z, s(s(z))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.01 tff(12250,plain,
% 2.75/3.01 (~r(z, s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12249, 80, 49])).
% 2.75/3.01 tff(12251,plain,
% 2.75/3.01 (b(z, s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1096, 12250])).
% 2.75/3.01 tff(12252,plain,
% 2.75/3.01 (b(elem!1, s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[87, 12251, 80])).
% 2.75/3.01 tff(12253,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.75/3.01 inference(monotonicity,[status(thm)],[80])).
% 2.75/3.01 tff(12254,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.75/3.01 inference(symmetry,[status(thm)],[12253])).
% 2.75/3.01 tff(12255,plain,
% 2.75/3.01 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[1644])).
% 2.75/3.01 tff(12256,plain,
% 2.75/3.01 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.75/3.01 inference(symmetry,[status(thm)],[12255])).
% 2.75/3.01 tff(12257,plain,
% 2.75/3.01 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[9558])).
% 2.75/3.01 tff(12258,plain,
% 2.75/3.01 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 2.75/3.01 inference(symmetry,[status(thm)],[12257])).
% 2.75/3.01 tff(12259,plain,
% 2.75/3.01 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12258, 12256])).
% 2.75/3.01 tff(12260,plain,
% 2.75/3.01 (r(s(elem!1), s(s(elem!1)))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[328, 12259])).
% 2.75/3.01 tff(12261,plain,
% 2.75/3.01 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.75/3.01 inference(symmetry,[status(thm)],[10612])).
% 2.75/3.01 tff(12262,plain,
% 2.75/3.01 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12261])).
% 2.75/3.01 tff(12263,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.75/3.01 inference(symmetry,[status(thm)],[12262])).
% 2.75/3.01 tff(12264,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[1644])).
% 2.75/3.01 tff(12265,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12264, 12263])).
% 2.75/3.01 tff(12266,plain,
% 2.75/3.01 (r(z, s(elem!1))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[3155, 80, 406])).
% 2.75/3.01 tff(12267,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12268,plain,
% 2.75/3.01 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12269,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12268])).
% 2.75/3.01 tff(12270,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12269, 12267])).
% 2.75/3.01 tff(12271,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12272,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12271, 12270])).
% 2.75/3.01 tff(12273,plain,
% 2.75/3.01 ($false),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12272, 163, 1353, 791, 1352, 1220])).
% 2.75/3.01 tff(12274,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.01 tff(12275,plain,
% 2.75/3.01 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12274, 1352, 1220, 12266])).
% 2.75/3.01 tff(12276,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), s(elem!1))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1339, 12275, 10618])).
% 2.75/3.01 tff(12277,plain,
% 2.75/3.01 (b(s(s(s(z))), s(z))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12276, 12265])).
% 2.75/3.01 tff(12278,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12279,plain,
% 2.75/3.01 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12280,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12279])).
% 2.75/3.01 tff(12281,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12280, 12278])).
% 2.75/3.01 tff(12282,plain,
% 2.75/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))))),
% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12283,plain,
% 2.75/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12282, 12281])).
% 2.75/3.01 tff(12284,plain,
% 2.75/3.01 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12283, 198, 6262, 3615, 2, 559, 12277])).
% 2.75/3.01 tff(12285,plain,
% 2.75/3.01 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12261])).
% 2.75/3.01 tff(12286,plain,
% 2.75/3.01 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 2.75/3.01 inference(symmetry,[status(thm)],[12285])).
% 2.75/3.01 tff(12287,plain,
% 2.75/3.01 (r(s(s(s(z))), z)),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[1352, 12286])).
% 2.75/3.01 tff(12288,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(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))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12289,plain,
% 2.75/3.01 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(z, s(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))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12290,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))))))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12289])).
% 2.75/3.01 tff(12291,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(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))))))))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12290, 12288])).
% 2.75/3.01 tff(12292,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12293,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12292, 12291])).
% 2.75/3.01 tff(12294,plain,
% 2.75/3.01 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12293, 163, 406, 12287, 3828])).
% 2.75/3.01 tff(12295,plain,
% 2.75/3.01 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[10622, 80])).
% 2.75/3.01 tff(12296,plain,
% 2.75/3.01 ($false),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[10626, 26, 12295, 12294, 12284])).
% 2.75/3.01 tff(12297,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~(elem!1 = z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.01 tff(12298,plain,
% 2.75/3.01 (~r(s(s(s(elem!1))), z)),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12297, 80, 3615, 2, 559, 406, 3828, 6262, 12260])).
% 2.75/3.01 tff(12299,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), z)),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1295, 12298])).
% 2.75/3.01 tff(12300,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), elem!1)),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12299, 12254])).
% 2.75/3.01 tff(12301,plain,
% 2.75/3.01 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1874, 12300, 12252, 12243])).
% 2.75/3.01 tff(12302,plain,
% 2.75/3.01 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[1326, 12301, 12239])).
% 2.75/3.01 tff(12303,plain,
% 2.75/3.01 (r(s(s(s(z))), s(s(z)))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12302, 12237])).
% 2.75/3.01 tff(12304,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12305,plain,
% 2.75/3.01 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12306,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12305])).
% 2.75/3.01 tff(12307,plain,
% 2.75/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12306, 12304])).
% 2.75/3.01 tff(12308,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12309,plain,
% 2.75/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12308, 12307])).
% 2.75/3.01 tff(12310,plain,
% 2.75/3.01 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12309, 163, 12303, 3450, 423])).
% 2.75/3.01 tff(12311,plain,
% 2.75/3.01 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.75/3.01 inference(monotonicity,[status(thm)],[10612])).
% 2.75/3.01 tff(12312,plain,
% 2.75/3.01 (b(s(s(s(z))), z)),
% 2.75/3.01 inference(modus_ponens,[status(thm)],[12299, 12311])).
% 2.75/3.01 tff(12313,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12314,plain,
% 2.75/3.01 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(rewrite,[status(thm)],[])).
% 2.75/3.01 tff(12315,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.75/3.01 inference(monotonicity,[status(thm)],[12314])).
% 2.75/3.01 tff(12316,plain,
% 2.75/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.75/3.01 inference(transitivity,[status(thm)],[12315, 12313])).
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% 2.75/3.01 inference(quant_inst,[status(thm)],[])).
% 2.75/3.01 tff(12318,plain,
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% 2.75/3.01 tff(12320,plain,
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% 2.75/3.01 tff(12321,plain,
% 2.75/3.01 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[12320, 12310])).
% 2.75/3.01 tff(12322,plain,
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% 2.75/3.01 inference(transitivity,[status(thm)],[10612, 12321])).
% 2.75/3.01 tff(12323,plain,
% 2.75/3.01 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.75/3.01 inference(unit_resolution,[status(thm)],[4845, 10614])).
% 2.75/3.01 tff(12324,plain,
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% 2.75/3.01 inference(unit_resolution,[status(thm)],[12323, 12322])).
% 2.75/3.02 tff(12325,plain,((~(elem!1 = z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.02 tff(12326,plain,
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% 2.75/3.02 tff(12330,plain,
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% 2.75/3.02 tff(12331,plain,
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% 2.75/3.02 inference(monotonicity,[status(thm)],[5024])).
% 2.75/3.02 tff(12332,plain,
% 2.75/3.02 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
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% 2.75/3.02 tff(12333,plain,
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% 2.75/3.02 (((~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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
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% 2.75/3.02 inference(modus_ponens,[status(thm)],[12347, 12346])).
% 2.75/3.02 tff(12349,plain,
% 2.75/3.02 ($false),
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% 2.75/3.02 tff(12351,plain,
% 2.75/3.02 (s(s(elem!1)) = s(s(s(s(s(z)))))),
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% 2.75/3.02 tff(12352,plain,
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% 2.75/3.02 tff(12353,plain,
% 2.75/3.02 ($false),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[2619, 5092, 12352])).
% 2.75/3.02 tff(12354,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.75/3.02 tff(12355,plain,
% 2.75/3.02 (~(s(z) = elem!1)),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[12354, 12172, 12330, 12180, 3272, 423, 12155, 12218])).
% 2.75/3.02 tff(12356,plain,
% 2.75/3.02 (~(s(s(z)) = s(elem!1))),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[227, 12355])).
% 2.75/3.02 tff(12357,plain,
% 2.75/3.02 (~(elem!1 = s(z))),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[234, 12356])).
% 2.75/3.02 tff(12358,plain,
% 2.75/3.02 (~(s(z) = elem!1)),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[4600, 95, 4598])).
% 2.75/3.02 tff(12359,plain,
% 2.75/3.02 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[8614, 149, 3615])).
% 2.75/3.02 tff(12360,plain,
% 2.75/3.02 (r(s(z), elem!1)),
% 2.75/3.02 inference(unit_resolution,[status(thm)],[217, 149, 225])).
% 2.75/3.02 tff(12361,plain,
% 2.75/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.75/3.02 inference(rewrite,[status(thm)],[])).
% 2.75/3.02 tff(12362,plain,
% 2.75/3.02 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.75/3.02 inference(rewrite,[status(thm)],[])).
% 2.75/3.02 tff(12363,plain,
% 2.75/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z)))))),
% 2.75/3.02 inference(monotonicity,[status(thm)],[12362])).
% 2.75/3.02 tff(12364,plain,
% 2.75/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.75/3.02 inference(transitivity,[status(thm)],[12363, 12361])).
% 2.75/3.02 tff(12365,plain,
% 2.75/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.75/3.02 inference(quant_inst,[status(thm)],[])).
% 2.86/3.02 tff(12366,plain,
% 2.86/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z)))),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[12365, 12364])).
% 2.86/3.02 tff(12367,plain,
% 2.86/3.02 ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12366, 163])).
% 2.86/3.02 tff(12368,plain,
% 2.86/3.02 (~r(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12367, 12360, 150, 406])).
% 2.86/3.02 tff(12369,plain,
% 2.86/3.02 (b(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[187, 12368, 76])).
% 2.86/3.02 tff(12370,plain,
% 2.86/3.02 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[6808, 198, 95, 12369, 331, 330])).
% 2.86/3.02 tff(12371,plain,
% 2.86/3.02 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[703, 12370, 12359])).
% 2.86/3.02 tff(12372,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(12373,plain,
% 2.86/3.02 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(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(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(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(12374,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12373])).
% 2.86/3.02 tff(12375,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.02 inference(transitivity,[status(thm)],[12374, 12372])).
% 2.86/3.02 tff(12376,plain,
% 2.86/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(z)))))),
% 2.86/3.02 inference(quant_inst,[status(thm)],[])).
% 2.86/3.02 tff(12377,plain,
% 2.86/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[12376, 12375])).
% 2.86/3.02 tff(12378,plain,
% 2.86/3.02 (~r(elem!1, s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12377, 163, 12371, 3272, 423])).
% 2.86/3.02 tff(12379,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(12380,plain,
% 2.86/3.02 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(12381,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12380])).
% 2.86/3.02 tff(12382,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.02 inference(transitivity,[status(thm)],[12381, 12379])).
% 2.86/3.02 tff(12383,plain,
% 2.86/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.86/3.02 inference(quant_inst,[status(thm)],[])).
% 2.86/3.02 tff(12384,plain,
% 2.86/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[12383, 12382])).
% 2.86/3.02 tff(12385,plain,
% 2.86/3.02 (~b(elem!1, s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12384, 198, 95, 12369, 3933, 9403])).
% 2.86/3.02 tff(12386,plain,
% 2.86/3.02 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[5572, 26, 12385])).
% 2.86/3.02 tff(12387,plain,
% 2.86/3.02 (elem!1 = s(s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12386, 12378])).
% 2.86/3.02 tff(12388,plain,
% 2.86/3.02 (s(elem!1) = s(s(s(z)))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12387])).
% 2.86/3.02 tff(12389,plain,
% 2.86/3.02 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12388])).
% 2.86/3.02 tff(12390,plain,
% 2.86/3.02 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.86/3.02 inference(symmetry,[status(thm)],[12389])).
% 2.86/3.02 tff(12391,plain,
% 2.86/3.02 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12390])).
% 2.86/3.02 tff(12392,plain,
% 2.86/3.02 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(symmetry,[status(thm)],[12391])).
% 2.86/3.02 tff(12393,plain,
% 2.86/3.02 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[12392])).
% 2.86/3.02 tff(12394,plain,
% 2.86/3.02 (~b(s(s(z)), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2404, 198, 95, 12369, 3933])).
% 2.86/3.02 tff(12395,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12396,plain,
% 2.86/3.03 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12397,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12396])).
% 2.86/3.03 tff(12398,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12397, 12395])).
% 2.86/3.03 tff(12399,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), elem!1)))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12400,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12399, 12398])).
% 2.86/3.03 tff(12401,plain,
% 2.86/3.03 (~r(s(s(z)), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12400, 163, 12371, 3272, 423])).
% 2.86/3.03 tff(12402,plain,
% 2.86/3.03 (s(s(z)) = elem!1),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2139, 12401, 12394])).
% 2.86/3.03 tff(12403,plain,
% 2.86/3.03 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8694, 12402])).
% 2.86/3.03 tff(12404,plain,
% 2.86/3.03 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12403, 12393])).
% 2.86/3.03 tff(12405,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12390])).
% 2.86/3.03 tff(12406,plain,
% 2.86/3.03 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12405])).
% 2.86/3.03 tff(12407,plain,
% 2.86/3.03 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12387])).
% 2.86/3.03 tff(12408,plain,
% 2.86/3.03 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12407, 12406])).
% 2.86/3.03 tff(12409,plain,
% 2.86/3.03 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.86/3.03 inference(commutativity,[status(thm)],[])).
% 2.86/3.03 tff(12410,plain,
% 2.86/3.03 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12387])).
% 2.86/3.03 tff(12411,plain,
% 2.86/3.03 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12410, 12409])).
% 2.86/3.03 tff(12412,plain,
% 2.86/3.03 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.86/3.03 inference(symmetry,[status(thm)],[12411])).
% 2.86/3.03 tff(12413,plain,
% 2.86/3.03 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12412])).
% 2.86/3.03 tff(12414,plain,
% 2.86/3.03 (~(s(elem!1) = s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[814, 1999])).
% 2.86/3.03 tff(12415,plain,
% 2.86/3.03 (~(s(s(z)) = s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[822, 12414])).
% 2.86/3.03 tff(12416,plain,
% 2.86/3.03 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12415, 12413])).
% 2.86/3.03 tff(12417,plain,
% 2.86/3.03 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12389, 12387])).
% 2.86/3.03 tff(12418,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(symmetry,[status(thm)],[12417])).
% 2.86/3.03 tff(12419,plain,
% 2.86/3.03 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12418])).
% 2.86/3.03 tff(12420,plain,
% 2.86/3.03 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1250, 12416])).
% 2.86/3.03 tff(12421,plain,
% 2.86/3.03 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1263, 12420])).
% 2.86/3.03 tff(12422,plain,
% 2.86/3.03 (s(elem!1) = s(s(s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[4926])).
% 2.86/3.03 tff(12423,plain,
% 2.86/3.03 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12422])).
% 2.86/3.03 tff(12424,plain,
% 2.86/3.03 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12423])).
% 2.86/3.03 tff(12425,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12424])).
% 2.86/3.03 tff(12426,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12425])).
% 2.86/3.03 tff(12427,plain,
% 2.86/3.03 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12423])).
% 2.86/3.03 tff(12428,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12427])).
% 2.86/3.03 tff(12429,plain,
% 2.86/3.03 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12427])).
% 2.86/3.03 tff(12430,plain,
% 2.86/3.03 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12429])).
% 2.86/3.03 tff(12431,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12424])).
% 2.86/3.03 tff(12432,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12431, 12430])).
% 2.86/3.03 tff(12433,plain,
% 2.86/3.03 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12432])).
% 2.86/3.03 tff(12434,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.86/3.03 tff(12435,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12436,plain,
% 2.86/3.03 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(z, 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))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12437,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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)))))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12436])).
% 2.86/3.03 tff(12438,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12437, 12435])).
% 2.86/3.03 tff(12439,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12440,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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)))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12439, 12438])).
% 2.86/3.03 tff(12441,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12440, 163, 406, 12434, 3828])).
% 2.86/3.03 tff(12442,plain,
% 2.86/3.03 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12441, 12433])).
% 2.86/3.03 tff(12443,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1377, 12442, 1268])).
% 2.86/3.03 tff(12444,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12443, 12428])).
% 2.86/3.03 tff(12445,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12444, 12426])).
% 2.86/3.03 tff(12446,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12424])).
% 2.86/3.03 tff(12447,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12446])).
% 2.86/3.03 tff(12448,plain,
% 2.86/3.03 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12423])).
% 2.86/3.03 tff(12449,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(symmetry,[status(thm)],[12448])).
% 2.86/3.03 tff(12450,plain,
% 2.86/3.03 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12449])).
% 2.86/3.03 tff(12451,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12452,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12453,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12452, 12451])).
% 2.86/3.03 tff(12454,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12453, 163, 150, 406, 12434])).
% 2.86/3.03 tff(12455,plain,
% 2.86/3.03 (~r(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12454, 12450])).
% 2.86/3.03 tff(12456,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[626, 12455])).
% 2.86/3.03 tff(12457,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12456, 12447])).
% 2.86/3.03 tff(12458,plain,
% 2.86/3.03 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12170, 163, 150, 406, 3828])).
% 2.86/3.03 tff(12459,plain,
% 2.86/3.03 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[469, 12458])).
% 2.86/3.03 tff(12460,plain,
% 2.86/3.03 (~r(s(z), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12178, 163, 150, 406, 3828])).
% 2.86/3.03 tff(12461,plain,
% 2.86/3.03 (b(s(z), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[3301, 12460])).
% 2.86/3.03 tff(12462,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12463,plain,
% 2.86/3.03 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(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))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12464,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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)))))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12463])).
% 2.86/3.03 tff(12465,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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))))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12464, 12462])).
% 2.86/3.03 tff(12466,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12467,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12466, 12465])).
% 2.86/3.03 tff(12468,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12467, 198, 12461, 12459, 12457, 12445])).
% 2.86/3.03 tff(12469,plain,((~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(12470,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12469, 12387, 12421, 406, 3828, 150])).
% 2.86/3.03 tff(12471,plain,
% 2.86/3.03 (((~![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))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12472,plain,
% 2.86/3.03 ((~![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))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12473,plain,
% 2.86/3.03 ((~![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)),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12472, 12471])).
% 2.86/3.03 tff(12474,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12473, 26, 462, 12470])).
% 2.86/3.03 tff(12475,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12476,plain,
% 2.86/3.03 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12477,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12476])).
% 2.86/3.03 tff(12478,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12477, 12475])).
% 2.86/3.03 tff(12479,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12480,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12479, 12478])).
% 2.86/3.03 tff(12481,plain,
% 2.86/3.03 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12480, 198, 3933, 9403, 12474])).
% 2.86/3.03 tff(12482,plain,
% 2.86/3.03 (~b(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12481, 12419])).
% 2.86/3.03 tff(12483,plain,
% 2.86/3.03 (r(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[602, 12482, 12416])).
% 2.86/3.03 tff(12484,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12483, 12408])).
% 2.86/3.03 tff(12485,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12486,plain,
% 2.86/3.03 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12487,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[12486])).
% 2.86/3.03 tff(12488,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[12487, 12485])).
% 2.86/3.03 tff(12489,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(12490,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[12489, 12488])).
% 2.86/3.03 tff(12491,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12490, 163, 3450, 423, 12484])).
% 2.86/3.03 tff(12492,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12493,plain,
% 2.86/3.03 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(12494,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12493])).
% 2.86/3.04 tff(12495,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[12494, 12492])).
% 2.86/3.04 tff(12496,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12497,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12496, 12495])).
% 2.86/3.04 tff(12498,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12497, 198, 3933, 331, 330, 9403, 12474])).
% 2.86/3.04 tff(12499,plain,
% 2.86/3.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12500,plain,
% 2.86/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12501,plain,
% 2.86/3.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12500, 12499])).
% 2.86/3.04 tff(12502,plain,
% 2.86/3.04 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12501, 26, 12498])).
% 2.86/3.04 tff(12503,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12502, 12491, 12404])).
% 2.86/3.04 tff(12504,plain,(b(s(z), elem!1) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (elem!1 = z) | (s(z) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12505,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12504, 12358, 95, 423, 331, 330, 9403, 4935, 3828, 150, 3272, 3450, 76, 149, 3615])).
% 2.86/3.04 tff(12506,plain,((~b(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (elem!1 = z) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12507,plain,
% 2.86/3.04 (~b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12506, 149, 12207, 330, 9363, 12167, 150, 3272, 3450, 76, 423, 3615, 4598])).
% 2.86/3.04 tff(12508,plain,
% 2.86/3.04 (r(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[102, 12507, 1999])).
% 2.86/3.04 tff(12509,plain,
% 2.86/3.04 (~(s(s(elem!1)) = s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3493, 12415])).
% 2.86/3.04 tff(12510,plain,
% 2.86/3.04 (~(s(z) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12354, 12172, 12509, 12180, 3272, 423, 12155, 12218])).
% 2.86/3.04 tff(12511,plain,
% 2.86/3.04 (r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[217, 149, 12510])).
% 2.86/3.04 tff(12512,plain,
% 2.86/3.04 (~r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12367, 12511, 150, 4935])).
% 2.86/3.04 tff(12513,plain,
% 2.86/3.04 (b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[187, 183, 76])).
% 2.86/3.04 tff(12514,plain,
% 2.86/3.04 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[7778, 218, 150, 1475])).
% 2.86/3.04 tff(12515,plain,
% 2.86/3.04 (~r(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[7631, 218, 150, 1475])).
% 2.86/3.04 tff(12516,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[242, 12515, 235])).
% 2.86/3.04 tff(12517,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[7807, 12516, 12514, 1475, 2, 7255, 12513])).
% 2.86/3.04 tff(12518,plain,(r(elem!1, z) | (~r(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, s(s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | b(s(z), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12519,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12518, 12512, 12508, 2, 12206, 150, 149, 76])).
% 2.86/3.04 tff(12520,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12521,plain,
% 2.86/3.04 (b(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12520, 12326, 150, 2, 330, 3272, 3450, 423, 3615, 4598])).
% 2.86/3.04 tff(12522,plain,
% 2.86/3.04 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12165, 198, 347, 9403, 12220])).
% 2.86/3.04 tff(12523,plain,
% 2.86/3.04 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3841, 12522])).
% 2.86/3.04 tff(12524,plain,
% 2.86/3.04 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12170, 163, 150, 406, 12523])).
% 2.86/3.04 tff(12525,plain,
% 2.86/3.04 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[469, 12524])).
% 2.86/3.04 tff(12526,plain,
% 2.86/3.04 (~r(s(z), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12178, 163, 150, 406, 12523])).
% 2.86/3.04 tff(12527,plain,
% 2.86/3.04 (b(s(z), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3301, 12526])).
% 2.86/3.04 tff(12528,plain,
% 2.86/3.04 (~(s(z) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12354, 12525, 12509, 12527, 3272, 423, 3066, 709])).
% 2.86/3.04 tff(12529,plain,
% 2.86/3.04 (~(s(s(z)) = s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[227, 12528])).
% 2.86/3.04 tff(12530,plain,
% 2.86/3.04 (~(elem!1 = s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[234, 12529])).
% 2.86/3.04 tff(12531,plain,
% 2.86/3.04 (~b(s(z), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12234, 3066, 9403, 406, 3272, 423])).
% 2.86/3.04 tff(12532,plain,
% 2.86/3.04 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[2082])).
% 2.86/3.04 tff(12533,plain,
% 2.86/3.04 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.86/3.04 inference(symmetry,[status(thm)],[12532])).
% 2.86/3.04 tff(12534,plain,
% 2.86/3.04 (b(s(z), s(s(z)))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[5927, 12533])).
% 2.86/3.04 tff(12535,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[398, 12534])).
% 2.86/3.04 tff(12536,plain,((~(s(s(z)) = elem!1)) | b(s(z), s(s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12537,plain,
% 2.86/3.04 (~(s(s(z)) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12536, 12531, 5927])).
% 2.86/3.04 tff(12538,plain,
% 2.86/3.04 (~b(s(s(z)), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2404, 198, 95, 271, 347])).
% 2.86/3.04 tff(12539,plain,
% 2.86/3.04 (~b(elem!1, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12384, 198, 95, 271, 347, 9403])).
% 2.86/3.04 tff(12540,plain,
% 2.86/3.04 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6808, 198, 95, 271, 331, 330])).
% 2.86/3.04 tff(12541,plain,
% 2.86/3.04 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[204, 198, 95, 271, 330])).
% 2.86/3.04 tff(12542,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 2.86/3.04 tff(12543,plain,
% 2.86/3.04 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[5572, 26, 12542])).
% 2.86/3.04 tff(12544,plain,
% 2.86/3.04 (r(elem!1, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12543, 9234])).
% 2.86/3.04 tff(12545,plain,
% 2.86/3.04 (r(s(s(z)), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2139, 2105, 9056])).
% 2.86/3.04 tff(12546,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12547,plain,
% 2.86/3.04 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), elem!1)) | (~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))))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12548,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12547])).
% 2.86/3.04 tff(12549,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[12548, 12546])).
% 2.86/3.04 tff(12550,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12551,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12550, 12549])).
% 2.86/3.04 tff(12552,plain,
% 2.86/3.04 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12551, 163, 12545, 423, 12544])).
% 2.86/3.04 tff(12553,plain,
% 2.86/3.04 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[703, 12552, 6861])).
% 2.86/3.04 tff(12554,plain,
% 2.86/3.04 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12553])).
% 2.86/3.04 tff(12555,plain,
% 2.86/3.04 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 2.86/3.04 inference(symmetry,[status(thm)],[12554])).
% 2.86/3.04 tff(12556,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12557,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12558,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12557, 12556])).
% 2.86/3.04 tff(12559,plain,
% 2.86/3.04 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12558, 163, 12545, 423, 12544])).
% 2.86/3.04 tff(12560,plain,
% 2.86/3.04 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[256, 12559, 244])).
% 2.86/3.04 tff(12561,plain,
% 2.86/3.04 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9265, 12560])).
% 2.86/3.04 tff(12562,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12350, 12561, 559, 10705, 6262, 3272, 423, 3066])).
% 2.86/3.04 tff(12563,plain,
% 2.86/3.04 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[935, 12562])).
% 2.86/3.04 tff(12564,plain,
% 2.86/3.04 (s(s(elem!1)) = elem!1),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12563, 12555])).
% 2.86/3.04 tff(12565,plain,
% 2.86/3.04 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[317, 12560])).
% 2.86/3.04 tff(12566,plain,
% 2.86/3.04 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[118, 12565])).
% 2.86/3.04 tff(12567,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12566, 12564])).
% 2.86/3.04 tff(12568,plain,((s(s(z)) = elem!1) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), 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)))))))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12569,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12568, 12541, 12540, 559, 10705, 6262, 3272, 423, 3066, 709, 2105, 12539, 12538])).
% 2.86/3.04 tff(12570,plain,((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12571,plain,
% 2.86/3.04 (~b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12570, 95, 12509, 12527, 3272, 423, 3066, 709, 12537, 12525, 330, 347, 331, 9403])).
% 2.86/3.04 tff(12572,plain,
% 2.86/3.04 (r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[187, 12571, 76])).
% 2.86/3.04 tff(12573,plain,
% 2.86/3.04 (~r(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6651, 12572, 150, 406])).
% 2.86/3.04 tff(12574,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[242, 12573, 12530])).
% 2.86/3.04 tff(12575,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12576,plain,
% 2.86/3.04 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12577,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12576])).
% 2.86/3.04 tff(12578,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[12577, 12575])).
% 2.86/3.04 tff(12579,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12580,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12579, 12578])).
% 2.86/3.04 tff(12581,plain,
% 2.86/3.04 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12580, 198, 5927, 12574, 12527, 12525])).
% 2.86/3.04 tff(12582,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12583,plain,
% 2.86/3.04 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12584,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12583])).
% 2.86/3.04 tff(12585,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[12584, 12582])).
% 2.86/3.04 tff(12586,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(12587,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12586, 12585])).
% 2.86/3.04 tff(12588,plain,
% 2.86/3.04 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12587, 163, 12572, 406, 12523])).
% 2.86/3.04 tff(12589,plain,
% 2.86/3.04 (elem!1 = s(s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[4810, 12588, 12581])).
% 2.86/3.04 tff(12590,plain,
% 2.86/3.04 (b(z, elem!1) <=> b(z, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12589])).
% 2.86/3.04 tff(12591,plain,
% 2.86/3.04 (b(z, s(s(s(s(s(z)))))) <=> b(z, elem!1)),
% 2.86/3.04 inference(symmetry,[status(thm)],[12590])).
% 2.86/3.04 tff(12592,plain,
% 2.86/3.04 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, elem!1))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[12591])).
% 2.86/3.04 tff(12593,plain,
% 2.86/3.04 (~b(z, elem!1)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[12223, 12592])).
% 2.86/3.04 tff(12594,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[95, 12593])).
% 2.86/3.04 tff(12595,plain,((~b(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (elem!1 = z) | (~r(s(s(z)), s(s(s(s(s(s(s(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))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(12596,plain,
% 2.86/3.04 (~b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12595, 12521, 4935, 150, 12326, 3272, 423, 12155, 12218, 330, 12159, 12207, 9363])).
% 2.86/3.04 tff(12597,plain,
% 2.86/3.04 (r(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[102, 12596, 12327])).
% 2.86/3.04 tff(12598,plain,
% 2.86/3.04 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[7261, 12597, 12206])).
% 2.86/3.04 tff(12599,plain,
% 2.86/3.04 (~(s(s(z)) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12536, 12235, 12521])).
% 2.86/3.04 tff(12600,plain,
% 2.86/3.04 (~(elem!1 = s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8661, 12599])).
% 2.86/3.04 tff(12601,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12602,plain,
% 2.86/3.04 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(12603,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12602])).
% 2.86/3.05 tff(12604,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12603, 12601])).
% 2.86/3.05 tff(12605,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12606,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12605, 12604])).
% 2.86/3.05 tff(12607,plain,
% 2.86/3.05 (~b(elem!1, s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12606, 198, 271, 347, 9363])).
% 2.86/3.05 tff(12608,plain,
% 2.86/3.05 (r(elem!1, s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 12607])).
% 2.86/3.05 tff(12609,plain,
% 2.86/3.05 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[7951, 198, 271, 5927, 2, 330])).
% 2.86/3.05 tff(12610,plain,
% 2.86/3.05 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[256, 12609, 3790])).
% 2.86/3.05 tff(12611,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12612,plain,
% 2.86/3.05 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12613,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12612])).
% 2.86/3.05 tff(12614,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12613, 12611])).
% 2.86/3.05 tff(12615,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12616,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12615, 12614])).
% 2.86/3.05 tff(12617,plain,
% 2.86/3.05 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12616, 198, 271, 347, 331, 330, 9363])).
% 2.86/3.05 tff(12618,plain,
% 2.86/3.05 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[703, 12617, 7891])).
% 2.86/3.05 tff(12619,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6876, 163, 12618, 3272, 12610, 12608])).
% 2.86/3.05 tff(12620,plain,((~b(elem!1, z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(12621,plain,
% 2.86/3.05 (~b(elem!1, z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12620, 12600, 3272, 12598, 12521, 2, 330, 12159, 12207])).
% 2.86/3.05 tff(12622,plain,
% 2.86/3.05 (r(elem!1, z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[187, 12621, 12326])).
% 2.86/3.05 tff(12623,plain,
% 2.86/3.05 (~r(elem!1, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6651, 12622, 150, 4935])).
% 2.86/3.05 tff(12624,plain,
% 2.86/3.05 (b(elem!1, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[242, 12623, 12357])).
% 2.86/3.05 tff(12625,plain,
% 2.86/3.05 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12580, 198, 12521, 12624, 12180, 12172])).
% 2.86/3.05 tff(12626,plain,
% 2.86/3.05 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10962, 163, 12597, 12622, 12167])).
% 2.86/3.05 tff(12627,plain,
% 2.86/3.05 (elem!1 = s(s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[4810, 12626, 12625])).
% 2.86/3.05 tff(12628,plain,
% 2.86/3.05 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12627])).
% 2.86/3.05 tff(12629,plain,
% 2.86/3.05 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.86/3.05 inference(symmetry,[status(thm)],[12628])).
% 2.86/3.05 tff(12630,plain,
% 2.86/3.05 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(z)), s(elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629])).
% 2.86/3.05 tff(12631,plain,
% 2.86/3.05 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12630])).
% 2.86/3.05 tff(12632,plain,
% 2.86/3.05 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(z)), s(elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629])).
% 2.86/3.05 tff(12633,plain,
% 2.86/3.05 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12632])).
% 2.86/3.05 tff(12634,plain,
% 2.86/3.05 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629])).
% 2.86/3.05 tff(12635,plain,
% 2.86/3.05 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12634])).
% 2.86/3.05 tff(12636,plain,
% 2.86/3.05 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12628])).
% 2.86/3.05 tff(12637,plain,
% 2.86/3.05 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12636])).
% 2.86/3.05 tff(12638,plain,
% 2.86/3.05 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12627])).
% 2.86/3.05 tff(12639,plain,
% 2.86/3.05 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 2.86/3.05 inference(symmetry,[status(thm)],[12638])).
% 2.86/3.05 tff(12640,plain,
% 2.86/3.05 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12636])).
% 2.86/3.05 tff(12641,plain,
% 2.86/3.05 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12640, 2932])).
% 2.86/3.05 tff(12642,plain,
% 2.86/3.05 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12641])).
% 2.86/3.05 tff(12643,plain,
% 2.86/3.05 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 2.86/3.05 inference(transitivity,[status(thm)],[12642, 12639])).
% 2.86/3.05 tff(12644,plain,
% 2.86/3.05 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12643])).
% 2.86/3.05 tff(12645,plain,
% 2.86/3.05 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[314, 12644])).
% 2.86/3.05 tff(12646,plain,
% 2.86/3.05 (~(s(elem!1) = s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[140, 12645])).
% 2.86/3.05 tff(12647,plain,
% 2.86/3.05 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12636])).
% 2.86/3.05 tff(12648,plain,
% 2.86/3.05 (b(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12647])).
% 2.86/3.05 tff(12649,plain,
% 2.86/3.05 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629])).
% 2.86/3.05 tff(12650,plain,
% 2.86/3.05 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12649, 12648])).
% 2.86/3.05 tff(12651,plain,
% 2.86/3.05 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12650])).
% 2.86/3.05 tff(12652,plain,
% 2.86/3.05 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(elem!1), z))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[5379])).
% 2.86/3.05 tff(12653,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.86/3.05 tff(12654,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12655,plain,
% 2.86/3.05 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12656,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12655])).
% 2.86/3.05 tff(12657,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12656, 12654])).
% 2.86/3.05 tff(12658,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12659,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12658, 12657])).
% 2.86/3.05 tff(12660,plain,
% 2.86/3.05 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12659, 198, 3615, 331, 2, 330])).
% 2.86/3.05 tff(12661,plain,
% 2.86/3.05 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12660, 12653])).
% 2.86/3.05 tff(12662,plain,
% 2.86/3.05 (~b(s(elem!1), z)),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12661, 12652])).
% 2.86/3.05 tff(12663,plain,
% 2.86/3.05 (r(s(elem!1), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1217, 12662])).
% 2.86/3.05 tff(12664,plain,
% 2.86/3.05 (r(s(s(s(s(s(s(z)))))), z)),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12663, 5427])).
% 2.86/3.05 tff(12665,plain,
% 2.86/3.05 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[4339, 163, 150, 406, 12664])).
% 2.86/3.05 tff(12666,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12667,plain,
% 2.86/3.05 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12668,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12667])).
% 2.86/3.05 tff(12669,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12668, 12666])).
% 2.86/3.05 tff(12670,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12671,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12670, 12669])).
% 2.86/3.05 tff(12672,plain,
% 2.86/3.05 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12671, 198, 3615, 2])).
% 2.86/3.05 tff(12673,plain,
% 2.86/3.05 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12672, 12653])).
% 2.86/3.05 tff(12674,plain,
% 2.86/3.05 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[4344, 26, 12673])).
% 2.86/3.05 tff(12675,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12674, 12665, 11021])).
% 2.86/3.05 tff(12676,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(12677,plain,
% 2.86/3.05 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12676, 12328, 4935, 150, 12627, 3615, 12207, 2, 330])).
% 2.86/3.05 tff(12678,plain,
% 2.86/3.05 (~b(s(elem!1), s(s(elem!1)))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12677, 12651])).
% 2.86/3.05 tff(12679,plain,
% 2.86/3.05 (r(s(elem!1), s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[901, 12678, 12646])).
% 2.86/3.05 tff(12680,plain,
% 2.86/3.05 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12679, 12637])).
% 2.86/3.05 tff(12681,plain,
% 2.86/3.05 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12680, 12635])).
% 2.86/3.05 tff(12682,plain,
% 2.86/3.05 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10997, 163, 3272, 423, 12681])).
% 2.86/3.05 tff(12683,plain,
% 2.86/3.05 (~r(s(s(z)), s(elem!1))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12682, 12633])).
% 2.86/3.05 tff(12684,plain,
% 2.86/3.05 (b(s(s(z)), s(elem!1))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[2378, 12683, 12356])).
% 2.86/3.05 tff(12685,plain,
% 2.86/3.05 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12684, 12631])).
% 2.86/3.05 tff(12686,plain,
% 2.86/3.05 (s(s(s(s(s(z))))) = elem!1),
% 2.86/3.05 inference(symmetry,[status(thm)],[12627])).
% 2.86/3.05 tff(12687,plain,
% 2.86/3.05 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629, 12686])).
% 2.86/3.05 tff(12688,plain,
% 2.86/3.05 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12687])).
% 2.86/3.05 tff(12689,plain,
% 2.86/3.05 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12688])).
% 2.86/3.05 tff(12690,plain,
% 2.86/3.05 (~(s(elem!1) = elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1395, 12645])).
% 2.86/3.05 tff(12691,plain,
% 2.86/3.05 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12690, 12689])).
% 2.86/3.05 tff(12692,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12693,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12694,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12693, 12692])).
% 2.86/3.05 tff(12695,plain,
% 2.86/3.05 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12694, 163, 12155, 423, 12681])).
% 2.86/3.05 tff(12696,plain,
% 2.86/3.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12697,plain,
% 2.86/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12698,plain,
% 2.86/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12697, 12696])).
% 2.86/3.05 tff(12699,plain,
% 2.86/3.05 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12698, 26, 12695])).
% 2.86/3.05 tff(12700,plain,
% 2.86/3.05 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[12699, 12691])).
% 2.86/3.05 tff(12701,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12629])).
% 2.86/3.05 tff(12702,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12701])).
% 2.86/3.05 tff(12703,plain,
% 2.86/3.05 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12702])).
% 2.86/3.05 tff(12704,plain,
% 2.86/3.05 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12627])).
% 2.86/3.05 tff(12705,plain,
% 2.86/3.05 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12704])).
% 2.86/3.05 tff(12706,plain,
% 2.86/3.05 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12636])).
% 2.86/3.05 tff(12707,plain,
% 2.86/3.05 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12706])).
% 2.86/3.05 tff(12708,plain,
% 2.86/3.05 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12199, 12707])).
% 2.86/3.05 tff(12709,plain,
% 2.86/3.05 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12627])).
% 2.86/3.05 tff(12710,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12709])).
% 2.86/3.05 tff(12711,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12636])).
% 2.86/3.05 tff(12712,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12711])).
% 2.86/3.05 tff(12713,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(elem!1)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[12712, 12710])).
% 2.86/3.05 tff(12714,plain,
% 2.86/3.05 (r(elem!1, s(s(elem!1)))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12155, 12713])).
% 2.86/3.05 tff(12715,plain,
% 2.86/3.05 (~r(elem!1, s(elem!1))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[3394, 12679, 12714, 12708])).
% 2.86/3.05 tff(12716,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12715, 12705])).
% 2.86/3.05 tff(12717,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12716, 12703])).
% 2.86/3.05 tff(12718,plain,
% 2.86/3.05 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12686, 12629])).
% 2.86/3.05 tff(12719,plain,
% 2.86/3.05 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = elem!1)),
% 2.86/3.05 inference(transitivity,[status(thm)],[12718, 1755])).
% 2.86/3.05 tff(12720,plain,
% 2.86/3.05 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(symmetry,[status(thm)],[12719])).
% 2.86/3.05 tff(12721,plain,
% 2.86/3.05 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[12720])).
% 2.86/3.05 tff(12722,plain,
% 2.86/3.05 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[12690, 12721])).
% 2.86/3.05 tff(12723,plain,
% 2.86/3.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(12724,plain,
% 2.86/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(12725,plain,
% 2.86/3.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[12724, 12723])).
% 2.86/3.06 tff(12726,plain,
% 2.86/3.06 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12725, 26])).
% 2.86/3.06 tff(12727,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12726, 12722, 12717])).
% 2.86/3.06 tff(12728,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12729,plain,
% 2.86/3.06 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12730,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12729])).
% 2.86/3.06 tff(12731,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12730, 12728])).
% 2.86/3.06 tff(12732,plain,
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% 2.86/3.06 inference(modus_ponens,[status(thm)],[12732, 12731])).
% 2.86/3.06 tff(12734,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[12733, 198, 12182, 12727, 12700, 12685])).
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% 2.86/3.06 tff(12736,plain,
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% 2.86/3.06 tff(12737,plain,
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% 2.86/3.06 tff(12738,plain,
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% 2.86/3.06 tff(12739,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[31, 12738])).
% 2.86/3.06 tff(12740,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[12150, 422, 150, 3450])).
% 2.86/3.06 tff(12741,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12740])).
% 2.86/3.06 tff(12742,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[12116, 163, 150, 406, 422])).
% 2.86/3.06 tff(12743,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3841, 12742])).
% 2.86/3.06 tff(12744,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[12124, 163, 150, 406, 422])).
% 2.86/3.06 tff(12745,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[4110, 12744])).
% 2.86/3.06 tff(12746,plain,
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% 2.86/3.06 tff(12747,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(12748,plain,
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% 2.86/3.06 tff(12749,plain,
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% 2.86/3.06 tff(12750,plain,
% 2.86/3.06 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
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% 2.86/3.06 tff(12751,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12750])).
% 2.86/3.06 tff(12752,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12751, 3820])).
% 2.86/3.06 tff(12753,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(12754,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[12753, 12752])).
% 2.86/3.06 tff(12755,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 12749])).
% 2.86/3.06 tff(12756,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3098, 12755])).
% 2.86/3.06 tff(12757,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12758,plain,
% 2.86/3.06 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(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(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12759,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12758])).
% 2.86/3.06 tff(12760,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12759, 12757])).
% 2.86/3.06 tff(12761,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
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% 2.86/3.06 inference(modus_ponens,[status(thm)],[12761, 12760])).
% 2.86/3.06 tff(12763,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12762, 163, 12756, 12739, 12113])).
% 2.86/3.06 tff(12764,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3841, 12763])).
% 2.86/3.06 tff(12765,plain,
% 2.86/3.06 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(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(z)))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12766,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12765])).
% 2.86/3.06 tff(12767,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12766, 12160])).
% 2.86/3.06 tff(12768,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(12769,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[12768, 12767])).
% 2.86/3.06 tff(12770,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12769, 198, 12159, 9363, 12764])).
% 2.86/3.06 tff(12771,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[511, 26, 508, 12770])).
% 2.86/3.06 tff(12772,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12773,plain,
% 2.86/3.06 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12774,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(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)))))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12773])).
% 2.86/3.06 tff(12775,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(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))))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12774, 12772])).
% 2.86/3.06 tff(12776,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(12777,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[12776, 12775])).
% 2.86/3.06 tff(12778,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12777, 163, 12756, 3450, 12113, 12771])).
% 2.86/3.06 tff(12779,plain,(b(z, s(z)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(12780,plain,
% 2.86/3.06 (b(z, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12779, 3450, 3615, 2, 150, 330, 49])).
% 2.86/3.06 tff(12781,plain,
% 2.86/3.06 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[7281, 198, 12780, 3615, 2])).
% 2.86/3.06 tff(12782,plain,
% 2.86/3.06 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[31, 12781])).
% 2.86/3.06 tff(12783,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12784,plain,
% 2.86/3.06 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12785,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[12784])).
% 2.86/3.06 tff(12786,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12785, 12783])).
% 2.86/3.06 tff(12787,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(12788,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[12787, 12786])).
% 2.86/3.06 tff(12789,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12788, 163, 150, 3450, 332, 33])).
% 2.86/3.06 tff(12790,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(12791,plain,
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% 2.86/3.06 inference(unit_resolution,[status(thm)],[12790, 3450, 150, 12782])).
% 2.86/3.06 tff(12792,plain,
% 2.86/3.06 (b(s(s(z)), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[345, 12791])).
% 2.86/3.06 tff(12793,plain,
% 2.86/3.06 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3961, 198, 12780, 12792, 2, 330])).
% 2.86/3.06 tff(12794,plain,
% 2.86/3.06 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[420, 12793])).
% 2.86/3.06 tff(12795,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[4046, 163, 150, 3450, 422])).
% 2.86/3.06 tff(12796,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[511, 26, 508, 12795])).
% 2.86/3.06 tff(12797,plain,
% 2.86/3.06 (~r(s(s(z)), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12790, 3450, 150, 33])).
% 2.86/3.06 tff(12798,plain,
% 2.86/3.06 (b(s(s(z)), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[345, 12797])).
% 2.86/3.06 tff(12799,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12165, 198, 12798, 9403, 12796])).
% 2.86/3.06 tff(12800,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3841, 12799])).
% 2.86/3.06 tff(12801,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12802,plain,
% 2.86/3.06 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(12803,plain,
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% 2.86/3.06 inference(monotonicity,[status(thm)],[12802])).
% 2.86/3.06 tff(12804,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[12803, 12801])).
% 2.86/3.06 tff(12805,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(12806,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12805, 12804])).
% 2.86/3.07 tff(12807,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12806, 163, 150, 33, 422, 12800])).
% 2.86/3.07 tff(12808,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12809,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12808, 12782, 150, 9363, 3450])).
% 2.86/3.07 tff(12810,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[469, 12809])).
% 2.86/3.07 tff(12811,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 12810])).
% 2.86/3.07 tff(12812,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3098, 12811])).
% 2.86/3.07 tff(12813,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12762, 163, 12812, 12782, 12794])).
% 2.86/3.07 tff(12814,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3841, 12813])).
% 2.86/3.07 tff(12815,plain,
% 2.86/3.07 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[8132, 198, 12780, 12792, 12810])).
% 2.86/3.07 tff(12816,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12815, 12814])).
% 2.86/3.07 tff(12817,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[511, 26, 508, 12816])).
% 2.86/3.07 tff(12818,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12777, 163, 12812, 3450, 12794, 12817])).
% 2.86/3.07 tff(12819,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12820,plain,
% 2.86/3.07 (~r(s(s(z)), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12819, 330, 2, 150, 3615, 49])).
% 2.86/3.07 tff(12821,plain,
% 2.86/3.07 (b(s(s(z)), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[487, 12820])).
% 2.86/3.07 tff(12822,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12823,plain,
% 2.86/3.07 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(z)), s(z))) | (~b(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12824,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[12823])).
% 2.86/3.07 tff(12825,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[12824, 12822])).
% 2.86/3.07 tff(12826,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12827,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12826, 12825])).
% 2.86/3.07 tff(12828,plain,
% 2.86/3.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12827, 198, 12821, 2, 330, 9363])).
% 2.86/3.07 tff(12829,plain,
% 2.86/3.07 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[420, 12828])).
% 2.86/3.07 tff(12830,plain,
% 2.86/3.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12827, 198, 560, 2, 330, 9363])).
% 2.86/3.07 tff(12831,plain,
% 2.86/3.07 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[420, 12830])).
% 2.86/3.07 tff(12832,plain,
% 2.86/3.07 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[7281, 198, 595, 3615, 2])).
% 2.86/3.07 tff(12833,plain,
% 2.86/3.07 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[31, 12832])).
% 2.86/3.07 tff(12834,plain,
% 2.86/3.07 (~r(s(s(z)), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12134, 163, 7266, 12833, 12831])).
% 2.86/3.07 tff(12835,plain,
% 2.86/3.07 (b(s(s(z)), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[345, 12834])).
% 2.86/3.07 tff(12836,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12837,plain,
% 2.86/3.07 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12838,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[12837])).
% 2.86/3.07 tff(12839,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[12838, 12836])).
% 2.86/3.07 tff(12840,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12841,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12840, 12839])).
% 2.86/3.07 tff(12842,plain,
% 2.86/3.07 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12841, 198, 595, 560, 347, 4167])).
% 2.86/3.07 tff(12843,plain,
% 2.86/3.07 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12842])).
% 2.86/3.07 tff(12844,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12769, 198, 347, 9363, 4167])).
% 2.86/3.07 tff(12845,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[511, 26, 508, 12844])).
% 2.86/3.07 tff(12846,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12847,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12848,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12847, 12846])).
% 2.86/3.07 tff(12849,plain,
% 2.86/3.07 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12848, 163, 12831, 12845, 12843])).
% 2.86/3.07 tff(12850,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12851,plain,
% 2.86/3.07 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12852,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[12851])).
% 2.86/3.07 tff(12853,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[12852, 12850])).
% 2.86/3.07 tff(12854,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12855,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12854, 12853])).
% 2.86/3.07 tff(12856,plain,
% 2.86/3.07 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12855, 198, 595, 2, 330, 4167])).
% 2.86/3.07 tff(12857,plain,
% 2.86/3.07 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3328, 26, 12856])).
% 2.86/3.07 tff(12858,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12857, 12849, 2935])).
% 2.86/3.07 tff(12859,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12860,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12859, 12835, 595, 2, 330, 560])).
% 2.86/3.07 tff(12861,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3841, 12860])).
% 2.86/3.07 tff(12862,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12806, 163, 150, 12833, 12861])).
% 2.86/3.07 tff(12863,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[469, 12862])).
% 2.86/3.07 tff(12864,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 12863])).
% 2.86/3.07 tff(12865,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3098, 12864])).
% 2.86/3.07 tff(12866,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12762, 163, 12865, 12833, 12831, 12861])).
% 2.86/3.07 tff(12867,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12868,plain,
% 2.86/3.07 (~b(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12867, 330, 2, 150, 3615, 12821])).
% 2.86/3.07 tff(12869,plain,
% 2.86/3.07 (r(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[593, 12868])).
% 2.86/3.07 tff(12870,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 559])).
% 2.86/3.07 tff(12871,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3098, 12870])).
% 2.86/3.07 tff(12872,plain,
% 2.86/3.07 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6834, 163, 12871, 7266, 423])).
% 2.86/3.07 tff(12873,plain,
% 2.86/3.07 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12872])).
% 2.86/3.07 tff(12874,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12875,plain,
% 2.86/3.07 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12876,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[12875])).
% 2.86/3.07 tff(12877,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[12876, 12874])).
% 2.86/3.07 tff(12878,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12879,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12878, 12877])).
% 2.86/3.07 tff(12880,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12879, 198, 560, 12461, 559, 12873])).
% 2.86/3.07 tff(12881,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12882,plain,
% 2.86/3.07 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12881, 3828, 150, 406, 560, 423, 3615, 2])).
% 2.86/3.07 tff(12883,plain,
% 2.86/3.07 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[469, 12882])).
% 2.86/3.07 tff(12884,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12170, 163, 150, 406, 12883, 3828])).
% 2.86/3.07 tff(12885,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(12886,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12885, 12869, 150, 12821, 12829, 3615, 2])).
% 2.86/3.07 tff(12887,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3841, 12886])).
% 2.86/3.07 tff(12888,plain,
% 2.86/3.07 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3626, 12821, 2, 3615])).
% 2.86/3.07 tff(12889,plain,
% 2.86/3.07 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[374, 12888])).
% 2.86/3.07 tff(12890,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12891,plain,
% 2.86/3.07 (((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(12892,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[12891])).
% 2.86/3.07 tff(12893,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.86/3.07 inference(transitivity,[status(thm)],[12892, 12890])).
% 2.86/3.07 tff(12894,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(12895,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[12894, 12893])).
% 2.86/3.07 tff(12896,plain,
% 2.86/3.07 (~r(s(z), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12895, 163, 150, 406, 332])).
% 2.86/3.07 tff(12897,plain,
% 2.86/3.07 (b(s(z), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[403, 12896])).
% 2.86/3.07 tff(12898,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12234, 12897, 9363, 3272, 406, 423])).
% 2.86/3.08 tff(12899,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3098, 12898])).
% 2.86/3.08 tff(12900,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3825, 198, 12899, 3615, 2])).
% 2.86/3.08 tff(12901,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[469, 12900])).
% 2.86/3.08 tff(12902,plain,
% 2.86/3.08 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12116, 163, 150, 406, 12901])).
% 2.86/3.08 tff(12903,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3841, 12902])).
% 2.86/3.08 tff(12904,plain,
% 2.86/3.08 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[4174, 12903, 330, 12899])).
% 2.86/3.08 tff(12905,plain,
% 2.86/3.08 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[31, 12904])).
% 2.86/3.08 tff(12906,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12134, 163, 3272, 332, 12905, 423])).
% 2.86/3.08 tff(12907,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12908,plain,
% 2.86/3.08 (~r(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12907, 12889, 12829, 330, 150, 12869, 3615, 2])).
% 2.86/3.08 tff(12909,plain,
% 2.86/3.08 (b(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[345, 12908])).
% 2.86/3.08 tff(12910,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12769, 198, 12909, 9363, 12887])).
% 2.86/3.08 tff(12911,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[511, 26, 508, 12910])).
% 2.86/3.08 tff(12912,plain,
% 2.86/3.08 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[5798, 163, 12889, 12829, 12911])).
% 2.86/3.08 tff(12913,plain,
% 2.86/3.08 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3328, 26, 12912])).
% 2.86/3.08 tff(12914,plain,
% 2.86/3.08 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12913, 2935])).
% 2.86/3.08 tff(12915,plain,
% 2.86/3.08 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12916,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12915])).
% 2.86/3.08 tff(12917,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12916, 4497])).
% 2.86/3.08 tff(12918,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12919,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(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(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12918, 12917])).
% 2.86/3.08 tff(12920,plain,
% 2.86/3.08 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12919, 163, 12889, 12829, 12911])).
% 2.86/3.08 tff(12921,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3098, 12920])).
% 2.86/3.08 tff(12922,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12923,plain,
% 2.86/3.08 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12924,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12923])).
% 2.86/3.08 tff(12925,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12924, 12922])).
% 2.86/3.08 tff(12926,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12927,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12926, 12925])).
% 2.86/3.08 tff(12928,plain,
% 2.86/3.08 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12927, 198, 3615, 330, 12887])).
% 2.86/3.08 tff(12929,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12928, 12921])).
% 2.86/3.08 tff(12930,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[469, 12929])).
% 2.86/3.08 tff(12931,plain,
% 2.86/3.08 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12124, 163, 150, 12869, 12930])).
% 2.86/3.08 tff(12932,plain,
% 2.86/3.08 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[4110, 12931])).
% 2.86/3.08 tff(12933,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12934,plain,
% 2.86/3.08 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12935,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12934])).
% 2.86/3.08 tff(12936,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12935, 12933])).
% 2.86/3.08 tff(12937,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12938,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12937, 12936])).
% 2.86/3.08 tff(12939,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12938, 198, 12909, 330, 9363, 12932, 12887, 12914])).
% 2.86/3.08 tff(12940,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12941,plain,
% 2.86/3.08 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12940, 3615, 150, 2, 49])).
% 2.86/3.08 tff(12942,plain,
% 2.86/3.08 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[176, 12941])).
% 2.86/3.08 tff(12943,plain,
% 2.86/3.08 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9411, 595, 9363, 3615, 3745])).
% 2.86/3.08 tff(12944,plain,
% 2.86/3.08 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[31, 12943])).
% 2.86/3.08 tff(12945,plain,
% 2.86/3.08 (~r(s(s(z)), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12790, 332, 150, 33])).
% 2.86/3.08 tff(12946,plain,
% 2.86/3.08 (b(s(s(z)), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[487, 12945])).
% 2.86/3.08 tff(12947,plain,
% 2.86/3.08 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3626, 12946, 2, 3615])).
% 2.86/3.08 tff(12948,plain,
% 2.86/3.08 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[374, 12947])).
% 2.86/3.08 tff(12949,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11759, 163, 12948, 332, 33, 152])).
% 2.86/3.08 tff(12950,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12951,plain,
% 2.86/3.08 (~r(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12950, 12944, 152, 2, 3615, 150])).
% 2.86/3.08 tff(12952,plain,
% 2.86/3.08 (b(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[345, 12951])).
% 2.86/3.08 tff(12953,plain,
% 2.86/3.08 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12808, 3450, 150, 9363, 33])).
% 2.86/3.08 tff(12954,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[469, 12953])).
% 2.86/3.08 tff(12955,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 12954])).
% 2.86/3.08 tff(12956,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3098, 12955])).
% 2.86/3.08 tff(12957,plain,
% 2.86/3.08 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[5347, 163, 12956, 33, 152])).
% 2.86/3.08 tff(12958,plain,
% 2.86/3.08 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[4110, 12957])).
% 2.86/3.08 tff(12959,plain,
% 2.86/3.08 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9515, 12958, 9363, 595, 12954])).
% 2.86/3.08 tff(12960,plain,
% 2.86/3.08 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2715, 26, 507, 12959])).
% 2.86/3.08 tff(12961,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12962,plain,
% 2.86/3.08 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(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(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(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(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12963,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12962])).
% 2.86/3.08 tff(12964,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12963, 12961])).
% 2.86/3.08 tff(12965,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12966,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12965, 12964])).
% 2.86/3.08 tff(12967,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12966, 198, 595, 6262, 3615, 2, 559, 5428])).
% 2.86/3.08 tff(12968,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12969,plain,
% 2.86/3.08 (~b(s(z), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12968, 12954, 3615, 2, 595, 12958])).
% 2.86/3.08 tff(12970,plain,
% 2.86/3.08 (r(s(z), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3301, 12969])).
% 2.86/3.08 tff(12971,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12972,plain,
% 2.86/3.08 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12973,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12972])).
% 2.86/3.08 tff(12974,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12973, 12971])).
% 2.86/3.08 tff(12975,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12976,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12975, 12974])).
% 2.86/3.08 tff(12977,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12976, 163, 12956, 3450, 12970, 12960])).
% 2.86/3.08 tff(12978,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12979,plain,
% 2.86/3.08 (~r(s(s(z)), s(z))),
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% 2.86/3.08 tff(12980,plain,
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% 2.86/3.08 tff(12982,plain,
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% 2.86/3.08 inference(unit_resolution,[status(thm)],[374, 12981])).
% 2.86/3.08 tff(12983,plain,
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% 2.86/3.08 tff(12984,plain,
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% 2.86/3.08 inference(unit_resolution,[status(thm)],[403, 12983])).
% 2.86/3.08 tff(12985,plain,
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% 2.86/3.08 tff(12987,plain,
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% 2.86/3.08 inference(unit_resolution,[status(thm)],[12986, 422, 33, 150])).
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% 2.86/3.08 inference(unit_resolution,[status(thm)],[3841, 12987])).
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% 2.86/3.08 tff(12990,plain,
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% 2.86/3.09 tff(12999,plain,
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% 2.86/3.09 inference(unit_resolution,[status(thm)],[469, 12999])).
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% 2.86/3.09 tff(13003,plain,
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% 2.86/3.09 inference(monotonicity,[status(thm)],[13003])).
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% 2.86/3.09 inference(modus_ponens,[status(thm)],[13006, 13005])).
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% 2.86/3.09 inference(rewrite,[status(thm)],[])).
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% 2.86/3.09 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
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% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[13013])).
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% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
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% 2.86/3.09 inference(modus_ponens,[status(thm)],[13016, 13015])).
% 2.86/3.09 tff(13018,plain,
% 2.86/3.09 (~r(s(s(s(s(s(z))))), s(s(z)))),
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% 2.86/3.09 tff(13021,plain,
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% 2.86/3.09 tff(13024,plain,
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% 2.86/3.09 tff(13025,plain,
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% 2.86/3.09 tff(13027,plain,
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% 2.86/3.09 tff(13028,plain,
% 2.86/3.09 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3841, 13027])).
% 2.86/3.09 tff(13029,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13030,plain,
% 2.86/3.09 (((~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13031,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[13030])).
% 2.86/3.09 tff(13032,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[13031, 13029])).
% 2.86/3.09 tff(13033,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(13034,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[13033, 13032])).
% 2.86/3.09 tff(13035,plain,
% 2.86/3.09 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13034, 163, 3066, 3272, 152])).
% 2.86/3.09 tff(13036,plain,
% 2.86/3.09 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13035])).
% 2.86/3.09 tff(13037,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13038,plain,
% 2.86/3.09 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13039,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[13038])).
% 2.86/3.09 tff(13040,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[13039, 13037])).
% 2.86/3.09 tff(13041,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(13042,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[13041, 13040])).
% 2.86/3.09 tff(13043,plain,
% 2.86/3.09 (~b(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13042, 198, 13026, 9403, 13036, 13024])).
% 2.86/3.09 tff(13044,plain,
% 2.86/3.09 (r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[4110, 13043])).
% 2.86/3.09 tff(13045,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13046,plain,
% 2.86/3.09 (((~r(z, 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(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13047,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[13046])).
% 2.86/3.09 tff(13048,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[13047, 13045])).
% 2.86/3.09 tff(13049,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(13050,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[13049, 13048])).
% 2.86/3.09 tff(13051,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13050, 163, 3066, 152, 13044, 13028])).
% 2.86/3.09 tff(13052,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(13053,plain,
% 2.86/3.09 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13052, 12871, 12942, 9363, 13022])).
% 2.86/3.09 tff(13054,plain,
% 2.86/3.09 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[374, 13053])).
% 2.86/3.09 tff(13055,plain,
% 2.86/3.09 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[9459, 13054, 9363, 3745])).
% 2.86/3.09 tff(13056,plain,
% 2.86/3.09 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[31, 13055])).
% 2.86/3.09 tff(13057,plain,
% 2.86/3.09 (~b(s(s(z)), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3626, 13054, 2, 3615])).
% 2.86/3.09 tff(13058,plain,
% 2.86/3.09 (r(s(s(z)), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[487, 13057])).
% 2.86/3.09 tff(13059,plain,
% 2.86/3.09 (~r(s(s(z)), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12790, 13058, 150, 13056])).
% 2.86/3.09 tff(13060,plain,
% 2.86/3.09 (b(s(s(z)), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[345, 13059])).
% 2.86/3.09 tff(13061,plain,
% 2.86/3.09 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[5347, 163, 12871, 13056, 12942])).
% 2.86/3.09 tff(13062,plain,
% 2.86/3.09 (~b(s(z), s(s(z)))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[8845, 13054, 3615, 3745])).
% 2.86/3.09 tff(13063,plain,
% 2.86/3.09 (r(s(z), s(s(z)))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[403, 13062])).
% 2.86/3.09 tff(13064,plain,
% 2.86/3.09 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13007, 163, 12871, 13056, 12942])).
% 2.86/3.09 tff(13065,plain,
% 2.86/3.09 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3841, 13064])).
% 2.86/3.09 tff(13066,plain,
% 2.86/3.09 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[4110, 13061])).
% 2.86/3.09 tff(13067,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13068,plain,
% 2.86/3.09 (((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(13069,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(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)))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[13068])).
% 2.86/3.09 tff(13070,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[13069, 13067])).
% 2.86/3.09 tff(13071,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(13072,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(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)))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[13071, 13070])).
% 2.86/3.09 tff(13073,plain,
% 2.86/3.09 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13072, 198, 13060, 9363, 13066, 13065])).
% 2.86/3.09 tff(13074,plain,
% 2.86/3.09 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13073])).
% 2.86/3.10 tff(13075,plain,
% 2.86/3.10 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12769, 198, 13060, 9363, 13065])).
% 2.86/3.10 tff(13076,plain,
% 2.86/3.10 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[511, 26, 508, 13075])).
% 2.86/3.10 tff(13077,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13078,plain,
% 2.86/3.10 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13079,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13078])).
% 2.86/3.10 tff(13080,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13079, 13077])).
% 2.86/3.10 tff(13081,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13082,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13081, 13080])).
% 2.86/3.10 tff(13083,plain,
% 2.86/3.10 (~r(s(z), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13082, 163, 13063, 13076, 13074])).
% 2.86/3.10 tff(13084,plain,
% 2.86/3.10 (b(s(z), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[3301, 13083])).
% 2.86/3.10 tff(13085,plain,
% 2.86/3.10 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[10612])).
% 2.86/3.10 tff(13086,plain,
% 2.86/3.10 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13085])).
% 2.86/3.10 tff(13087,plain,
% 2.86/3.10 (z = elem!1),
% 2.86/3.10 inference(symmetry,[status(thm)],[80])).
% 2.86/3.10 tff(13088,plain,
% 2.86/3.10 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13087, 13086])).
% 2.86/3.10 tff(13089,plain,
% 2.86/3.10 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13088])).
% 2.86/3.10 tff(13090,plain,
% 2.86/3.10 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.86/3.10 inference(commutativity,[status(thm)],[])).
% 2.86/3.10 tff(13091,plain,
% 2.86/3.10 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13090])).
% 2.86/3.10 tff(13092,plain,
% 2.86/3.10 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13087])).
% 2.86/3.10 tff(13093,plain,
% 2.86/3.10 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13092, 13091])).
% 2.86/3.10 tff(13094,plain,
% 2.86/3.10 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13093])).
% 2.86/3.10 tff(13095,plain,
% 2.86/3.10 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[5159, 13094])).
% 2.86/3.10 tff(13096,plain,
% 2.86/3.10 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[80, 13085])).
% 2.86/3.10 tff(13097,plain,
% 2.86/3.10 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13096])).
% 2.86/3.10 tff(13098,plain,
% 2.86/3.10 ((~r(z, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13097])).
% 2.86/3.10 tff(13099,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13086])).
% 2.86/3.10 tff(13100,plain,
% 2.86/3.10 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13099])).
% 2.86/3.10 tff(13101,plain,
% 2.86/3.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13086])).
% 2.86/3.10 tff(13102,plain,
% 2.86/3.10 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13101])).
% 2.86/3.10 tff(13103,plain,
% 2.86/3.10 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13086])).
% 2.86/3.10 tff(13104,plain,
% 2.86/3.10 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13103])).
% 2.86/3.10 tff(13105,plain,
% 2.86/3.10 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13104])).
% 2.86/3.10 tff(13106,plain,
% 2.86/3.10 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12261, 13086])).
% 2.86/3.10 tff(13107,plain,
% 2.86/3.10 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13106])).
% 2.86/3.10 tff(13108,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 2.86/3.10 tff(13109,plain,
% 2.86/3.10 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[10612, 13108, 13086])).
% 2.86/3.10 tff(13110,plain,
% 2.86/3.10 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[2736, 12238])).
% 2.86/3.10 tff(13111,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13110, 13109])).
% 2.86/3.10 tff(13112,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(13113,plain,
% 2.86/3.10 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13112, 80])).
% 2.86/3.10 tff(13114,plain,
% 2.86/3.10 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13113, 13107])).
% 2.86/3.10 tff(13115,plain,
% 2.86/3.10 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[6454, 13114, 10614])).
% 2.86/3.10 tff(13116,plain,
% 2.86/3.10 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13115, 13105])).
% 2.86/3.10 tff(13117,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.86/3.10 tff(13118,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13119,plain,
% 2.86/3.10 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(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(z), s(s(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(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13120,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13119])).
% 2.86/3.10 tff(13121,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13120, 13118])).
% 2.86/3.10 tff(13122,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13123,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13122, 13121])).
% 2.86/3.10 tff(13124,plain,
% 2.86/3.10 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13123, 198, 6262, 3615, 2, 559])).
% 2.86/3.10 tff(13125,plain,
% 2.86/3.10 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13124, 13117])).
% 2.86/3.10 tff(13126,plain,
% 2.86/3.10 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[2751, 26, 13125])).
% 2.86/3.10 tff(13127,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13126, 13116])).
% 2.86/3.10 tff(13128,plain,
% 2.86/3.10 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13086])).
% 2.86/3.10 tff(13129,plain,
% 2.86/3.10 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13128])).
% 2.86/3.10 tff(13130,plain,
% 2.86/3.10 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13129])).
% 2.86/3.10 tff(13131,plain,
% 2.86/3.10 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[3384, 10614])).
% 2.86/3.10 tff(13132,plain,
% 2.86/3.10 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[6386, 13131])).
% 2.86/3.10 tff(13133,plain,
% 2.86/3.10 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13132, 13130])).
% 2.86/3.10 tff(13134,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13135,plain,
% 2.86/3.10 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(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(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13136,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13135])).
% 2.86/3.10 tff(13137,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13136, 13134])).
% 2.86/3.10 tff(13138,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13139,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13138, 13137])).
% 2.86/3.10 tff(13140,plain,
% 2.86/3.10 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13139, 198, 3615, 2])).
% 2.86/3.10 tff(13141,plain,
% 2.86/3.10 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13140, 13117])).
% 2.86/3.10 tff(13142,plain,
% 2.86/3.10 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12501, 26, 13141])).
% 2.86/3.10 tff(13143,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13142, 13133])).
% 2.86/3.10 tff(13144,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13145,plain,
% 2.86/3.10 (((~r(s(s(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(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13146,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13145])).
% 2.86/3.10 tff(13147,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13146, 13144])).
% 2.86/3.10 tff(13148,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13149,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13148, 13147])).
% 2.86/3.10 tff(13150,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13149, 163, 12871, 152, 13143, 13127])).
% 2.86/3.10 tff(13151,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~(elem!1 = z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(13152,plain,
% 2.86/3.10 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13151, 80, 152, 6262, 3615, 2, 559])).
% 2.86/3.10 tff(13153,plain,
% 2.86/3.10 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13152, 13102])).
% 2.86/3.10 tff(13154,plain,
% 2.86/3.10 (r(s(s(s(s(elem!1)))), s(z))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[6436, 13153])).
% 2.86/3.10 tff(13155,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13154, 13100])).
% 2.86/3.10 tff(13156,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13157,plain,
% 2.86/3.10 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13158,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13157])).
% 2.86/3.10 tff(13159,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[13158, 13156])).
% 2.86/3.10 tff(13160,plain,
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% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13161,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13160, 13159])).
% 2.86/3.10 tff(13162,plain,
% 2.86/3.10 (~r(z, s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13161, 163, 150, 406, 13155])).
% 2.86/3.10 tff(13163,plain,
% 2.86/3.10 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13162, 13098])).
% 2.86/3.10 tff(13164,plain,
% 2.86/3.10 (((~![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))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(13165,plain,
% 2.86/3.10 ((~![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))))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(13166,plain,
% 2.86/3.10 ((~![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)))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13165, 13164])).
% 2.86/3.10 tff(13167,plain,
% 2.86/3.10 ((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)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13166, 26])).
% 2.86/3.10 tff(13168,plain,
% 2.86/3.10 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[13167, 13163, 13095])).
% 2.86/3.10 tff(13169,plain,
% 2.86/3.10 (b(z, s(s(s(s(z)))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[13168, 13089])).
% 2.86/3.10 tff(13170,plain,
% 2.86/3.10 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13085, 9558])).
% 2.86/3.10 tff(13171,plain,
% 2.86/3.10 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[2626, 10619])).
% 2.86/3.10 tff(13172,plain,
% 2.86/3.10 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[13085, 9558])).
% 2.86/3.10 tff(13173,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.86/3.10 inference(symmetry,[status(thm)],[13172])).
% 2.86/3.11 tff(13174,plain,
% 2.86/3.11 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13173])).
% 2.86/3.11 tff(13175,plain,
% 2.86/3.11 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13052, 12871, 152, 9363, 406])).
% 2.86/3.11 tff(13176,plain,
% 2.86/3.11 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[374, 13175])).
% 2.86/3.11 tff(13177,plain,
% 2.86/3.11 (~b(s(s(z)), s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[3626, 13176, 2, 3615])).
% 2.86/3.11 tff(13178,plain,
% 2.86/3.11 (r(s(s(z)), s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[487, 13177])).
% 2.86/3.11 tff(13179,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13180,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13181,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13180, 13179])).
% 2.86/3.11 tff(13182,plain,
% 2.86/3.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13181, 163, 150, 13155, 13178])).
% 2.86/3.11 tff(13183,plain,
% 2.86/3.11 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13182, 13174])).
% 2.86/3.11 tff(13184,plain,
% 2.86/3.11 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[2654, 13183, 13171])).
% 2.86/3.11 tff(13185,plain,
% 2.86/3.11 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13184, 13170])).
% 2.86/3.11 tff(13186,plain,
% 2.86/3.11 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[9558, 13085])).
% 2.86/3.11 tff(13187,plain,
% 2.86/3.11 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12244, 13086])).
% 2.86/3.11 tff(13188,plain,
% 2.86/3.11 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13187])).
% 2.86/3.11 tff(13189,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13190,plain,
% 2.86/3.11 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13191,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13190])).
% 2.86/3.11 tff(13192,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13191, 13189])).
% 2.86/3.11 tff(13193,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13194,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13193, 13192])).
% 2.86/3.11 tff(13195,plain,
% 2.86/3.11 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13194, 163, 150, 13155, 13178])).
% 2.86/3.11 tff(13196,plain,
% 2.86/3.11 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13195, 13188])).
% 2.86/3.11 tff(13197,plain,
% 2.86/3.11 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[5274, 13196, 10619])).
% 2.86/3.11 tff(13198,plain,
% 2.86/3.11 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13197, 13186])).
% 2.86/3.11 tff(13199,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13200,plain,
% 2.86/3.11 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13201,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13200])).
% 2.86/3.11 tff(13202,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13201, 13199])).
% 2.86/3.11 tff(13203,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13204,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13203, 13202])).
% 2.86/3.11 tff(13205,plain,
% 2.86/3.11 (~r(s(s(s(s(z)))), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13204, 163, 150, 406, 13155])).
% 2.86/3.11 tff(13206,plain,
% 2.86/3.11 (b(s(s(s(s(z)))), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12473, 26, 462, 13205])).
% 2.86/3.11 tff(13207,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13208,plain,
% 2.86/3.11 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13209,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13208])).
% 2.86/3.11 tff(13210,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13209, 13207])).
% 2.86/3.11 tff(13211,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13212,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13211, 13210])).
% 2.86/3.11 tff(13213,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13212, 198, 347, 13206, 13198, 13185, 13169])).
% 2.86/3.11 tff(13214,plain,((~(elem!1 = z)) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(13215,plain,
% 2.86/3.11 (~(elem!1 = z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13214, 13060, 150, 13022, 12942, 13084, 3615, 2, 559])).
% 2.86/3.11 tff(13216,plain,
% 2.86/3.11 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[4110, 4104])).
% 2.86/3.11 tff(13217,assumption,(~b(z, elem!1)), introduced(assumption)).
% 2.86/3.11 tff(13218,plain,
% 2.86/3.11 (r(z, elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[102, 1999, 13217])).
% 2.86/3.11 tff(13219,plain,
% 2.86/3.11 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[8030, 13218, 4104])).
% 2.86/3.11 tff(13220,plain,
% 2.86/3.11 (r(z, s(s(z))) <=> r(z, elem!1)),
% 2.86/3.11 inference(monotonicity,[status(thm)],[2082])).
% 2.86/3.11 tff(13221,plain,
% 2.86/3.11 (r(z, elem!1) <=> r(z, s(s(z)))),
% 2.86/3.11 inference(symmetry,[status(thm)],[13220])).
% 2.86/3.11 tff(13222,plain,
% 2.86/3.11 (r(z, s(s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[1475, 13221])).
% 2.86/3.11 tff(13223,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[49, 13222])).
% 2.86/3.11 tff(13224,plain,((~(s(s(z)) = elem!1)) | r(z, s(s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(13225,plain,
% 2.86/3.11 (~(s(s(z)) = elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13224, 13218, 49])).
% 2.86/3.11 tff(13226,plain,
% 2.86/3.11 (~(elem!1 = s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[8661, 13225])).
% 2.86/3.11 tff(13227,plain,
% 2.86/3.11 (~b(elem!1, s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12606, 198, 271, 347, 9403])).
% 2.86/3.11 tff(13228,plain,
% 2.86/3.11 (r(elem!1, s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[5572, 26, 5011, 13227])).
% 2.86/3.11 tff(13229,plain,
% 2.86/3.11 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13072, 198, 347, 9403, 5428, 4167])).
% 2.86/3.11 tff(13230,plain,
% 2.86/3.11 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13229])).
% 2.86/3.11 tff(13231,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13232,plain,
% 2.86/3.11 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13233,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13232])).
% 2.86/3.11 tff(13234,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13233, 13231])).
% 2.86/3.11 tff(13235,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13236,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13235, 13234])).
% 2.86/3.11 tff(13237,plain,
% 2.86/3.11 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13236, 198, 271, 347, 9403, 5428, 4167])).
% 2.86/3.11 tff(13238,plain,
% 2.86/3.11 (r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[4810, 13237, 5530])).
% 2.86/3.11 tff(13239,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13240,plain,
% 2.86/3.11 (((~r(s(s(s(s(s(z))))), s(s(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(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13241,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13240])).
% 2.86/3.11 tff(13242,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13241, 13239])).
% 2.86/3.11 tff(13243,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(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(elem!1, s(s(z)))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13244,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13243, 13242])).
% 2.86/3.11 tff(13245,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13244, 163, 3066, 13238, 13230, 13228])).
% 2.86/3.11 tff(13246,plain,((~b(elem!1, z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(13247,plain,
% 2.86/3.11 (~b(elem!1, z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13246, 13226, 3066, 13219, 347, 9363, 13216, 4167])).
% 2.86/3.11 tff(13248,plain,
% 2.86/3.11 (r(elem!1, z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[187, 13247, 76])).
% 2.86/3.11 tff(13249,plain,
% 2.86/3.11 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[13052, 3066, 12942, 9363, 406])).
% 2.86/3.11 tff(13250,plain,
% 2.86/3.11 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[374, 13249])).
% 2.86/3.11 tff(13251,plain,
% 2.86/3.11 (~b(s(s(z)), s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[3626, 13250, 2, 3615])).
% 2.86/3.11 tff(13252,plain,
% 2.86/3.11 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[5024])).
% 2.86/3.11 tff(13253,plain,
% 2.86/3.11 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.86/3.11 inference(symmetry,[status(thm)],[13252])).
% 2.86/3.11 tff(13254,plain,
% 2.86/3.11 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[825])).
% 2.86/3.11 tff(13255,plain,
% 2.86/3.11 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[9580, 13254])).
% 2.86/3.11 tff(13256,plain,
% 2.86/3.11 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13255, 13253])).
% 2.86/3.11 tff(13257,plain,
% 2.86/3.11 (r(elem!1, s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[5075, 2915, 328])).
% 2.86/3.11 tff(13258,plain,
% 2.86/3.11 (~r(z, s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[2523, 5079, 995, 13257])).
% 2.86/3.11 tff(13259,plain,
% 2.86/3.11 (b(z, s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1791, 13258])).
% 2.86/3.11 tff(13260,plain,
% 2.86/3.11 (~r(s(s(elem!1)), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[8726, 978, 152, 7346, 2834, 1475, 1103, 995, 5034])).
% 2.86/3.11 tff(13261,plain,
% 2.86/3.11 (b(s(s(elem!1)), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[801, 13260])).
% 2.86/3.11 tff(13262,plain,
% 2.86/3.11 (~r(s(elem!1), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[6771, 5079, 995, 406])).
% 2.86/3.11 tff(13263,plain,
% 2.86/3.11 (b(s(elem!1), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1217, 13262])).
% 2.86/3.11 tff(13264,plain,
% 2.86/3.11 (~b(s(s(elem!1)), s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[3549, 198, 13263, 13261, 13259])).
% 2.86/3.11 tff(13265,plain,
% 2.86/3.11 (r(s(s(elem!1)), s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1143, 13264, 5318])).
% 2.86/3.11 tff(13266,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13267,plain,
% 2.86/3.11 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), 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)))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(13268,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[13267])).
% 2.86/3.11 tff(13269,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[13268, 13266])).
% 2.86/3.11 tff(13270,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(13271,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[13270, 13269])).
% 2.86/3.11 tff(13272,plain,
% 2.86/3.12 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13271, 163, 5079, 13265, 13256])).
% 2.86/3.12 tff(13273,plain,
% 2.86/3.12 (b(s(s(s(s(elem!1)))), z)),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[4167, 5602])).
% 2.86/3.12 tff(13274,plain,
% 2.86/3.12 (b(z, s(s(s(s(elem!1)))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[5428, 5128])).
% 2.86/3.12 tff(13275,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13276,plain,
% 2.86/3.12 (((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13277,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[13276])).
% 2.86/3.12 tff(13278,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.86/3.12 inference(transitivity,[status(thm)],[13277, 13275])).
% 2.86/3.12 tff(13279,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(13280,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[13279, 13278])).
% 2.86/3.12 tff(13281,plain,
% 2.86/3.12 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13280, 198, 13263, 13261, 13259])).
% 2.86/3.12 tff(13282,plain,
% 2.86/3.12 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13281, 13274, 13273])).
% 2.86/3.12 tff(13283,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[5274, 13282, 13272, 5093])).
% 2.86/3.12 tff(13284,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | b(s(s(z)), s(z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(13285,plain,
% 2.86/3.12 (~(s(z) = elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13284, 13218, 13216, 12942, 4167, 12845, 3615, 406, 13251, 328, 150, 1999, 2])).
% 2.86/3.12 tff(13286,plain,
% 2.86/3.12 (r(s(z), elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[217, 225, 149])).
% 2.86/3.12 tff(13287,plain,
% 2.86/3.12 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[7778, 13286, 150, 1475])).
% 2.86/3.12 tff(13288,plain,
% 2.86/3.12 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[703, 13287, 12359])).
% 2.86/3.12 tff(13289,plain,
% 2.86/3.12 (~(s(s(z)) = s(elem!1))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[227, 225])).
% 2.86/3.12 tff(13290,plain,
% 2.86/3.12 (~(elem!1 = s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[234, 13289])).
% 2.86/3.12 tff(13291,plain,
% 2.86/3.12 (~r(elem!1, s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[7631, 13286, 150, 1475])).
% 2.86/3.12 tff(13292,plain,
% 2.86/3.12 (b(elem!1, s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[242, 13291, 13290])).
% 2.86/3.12 tff(13293,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[7791, 198, 13292, 13288, 3615, 2])).
% 2.86/3.12 tff(13294,plain,((s(z) = elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(13295,plain,
% 2.86/3.12 (b(s(z), elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13294, 13285, 2, 150, 13218, 3615])).
% 2.86/3.12 tff(13296,plain,
% 2.86/3.12 (~(s(s(z)) = s(elem!1))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[227, 13285])).
% 2.86/3.12 tff(13297,plain,
% 2.86/3.12 (~(elem!1 = s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[234, 13296])).
% 2.86/3.12 tff(13298,plain,
% 2.86/3.12 (~r(elem!1, s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[6651, 13248, 150, 406])).
% 2.86/3.12 tff(13299,plain,
% 2.86/3.12 (b(elem!1, s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[242, 13298, 13297])).
% 2.86/3.12 tff(13300,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13301,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(13302,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[13301, 13300])).
% 2.86/3.12 tff(13303,plain,
% 2.86/3.12 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13302, 163, 1475, 150, 152])).
% 2.86/3.12 tff(13304,plain,
% 2.86/3.12 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[3654, 13303])).
% 2.86/3.12 tff(13305,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13306,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(13307,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[13306, 13305])).
% 2.86/3.12 tff(13308,plain,
% 2.86/3.12 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13307, 163, 1475, 833, 152])).
% 2.86/3.12 tff(13309,plain,
% 2.86/3.12 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[256, 13308, 3790])).
% 2.86/3.12 tff(13310,plain,
% 2.86/3.12 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13311,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[13310])).
% 2.86/3.12 tff(13312,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.12 inference(transitivity,[status(thm)],[13311, 8178])).
% 2.86/3.12 tff(13313,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(13314,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[13313, 13312])).
% 2.86/3.12 tff(13315,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13314, 198, 5927, 320, 13309, 13304])).
% 2.86/3.12 tff(13316,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(13317,plain,
% 2.86/3.12 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13316, 13299, 12942, 13295, 13218, 150, 13248])).
% 2.86/3.12 tff(13318,plain,
% 2.86/3.12 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[9265, 13317])).
% 2.86/3.12 tff(13319,plain,
% 2.86/3.12 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[317, 13317])).
% 2.86/3.12 tff(13320,plain,
% 2.86/3.12 (b(s(s(elem!1)), elem!1)),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[602, 8717, 598])).
% 2.86/3.12 tff(13321,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13322,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(13323,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[13322, 13321])).
% 2.86/3.12 tff(13324,plain,
% 2.86/3.12 (~r(s(z), s(s(elem!1)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[13323, 163, 1475, 790, 150])).
% 2.86/3.12 tff(13325,plain,
% 2.86/3.12 (b(s(z), s(s(elem!1)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[642, 13324])).
% 2.86/3.12 tff(13326,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13327,plain,
% 2.86/3.12 (((~b(s(s(elem!1)), elem!1)) | (~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(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(13328,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[13327])).
% 2.86/3.12 tff(13329,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(transitivity,[status(thm)],[13328, 13326])).
% 2.86/3.12 tff(13330,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.97/3.12 tff(13331,plain,
% 2.97/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 2.97/3.12 inference(modus_ponens,[status(thm)],[13330, 13329])).
% 2.97/3.12 tff(13332,plain,
% 2.97/3.12 ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[13331, 198])).
% 2.97/3.12 tff(13333,plain,
% 2.97/3.12 ($false),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[13332, 13325, 13320, 5927, 8710])).
% 2.97/3.12 tff(13334,plain,((~r(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.12 tff(13335,plain,
% 2.97/3.12 (~r(s(s(elem!1)), z)),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[13334, 13295, 13218, 150, 13248, 13319])).
% 2.97/3.12 tff(13336,plain,
% 2.97/3.12 (b(s(s(elem!1)), z)),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[801, 13335])).
% 2.97/3.12 tff(13337,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.12 inference(rewrite,[status(thm)],[])).
% 2.97/3.12 tff(13338,plain,
% 2.97/3.12 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.12 inference(rewrite,[status(thm)],[])).
% 2.97/3.12 tff(13339,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.97/3.12 inference(monotonicity,[status(thm)],[13338])).
% 2.97/3.12 tff(13340,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.12 inference(transitivity,[status(thm)],[13339, 13337])).
% 2.97/3.12 tff(13341,plain,
% 2.97/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 2.97/3.12 inference(quant_inst,[status(thm)],[])).
% 2.97/3.12 tff(13342,plain,
% 2.97/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.97/3.12 inference(modus_ponens,[status(thm)],[13341, 13340])).
% 2.97/3.12 tff(13343,plain,
% 2.97/3.12 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[13342, 198, 13336, 347, 9363, 13216, 4167])).
% 2.97/3.12 tff(13344,plain,
% 2.97/3.12 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[3400, 13343, 13318])).
% 2.97/3.12 tff(13345,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.97/3.12 inference(rewrite,[status(thm)],[])).
% 2.97/3.12 tff(13346,plain,
% 2.97/3.12 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.97/3.12 inference(rewrite,[status(thm)],[])).
% 2.97/3.12 tff(13347,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.97/3.12 inference(monotonicity,[status(thm)],[13346])).
% 2.97/3.12 tff(13348,plain,
% 2.97/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.97/3.12 inference(transitivity,[status(thm)],[13347, 13345])).
% 2.97/3.12 tff(13349,plain,
% 2.97/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 2.97/3.12 inference(quant_inst,[status(thm)],[])).
% 2.97/3.12 tff(13350,plain,
% 2.97/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.97/3.12 inference(modus_ponens,[status(thm)],[13349, 13348])).
% 2.97/3.12 tff(13351,plain,
% 2.97/3.12 (~b(s(s(elem!1)), s(s(z)))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[13350, 198, 13336, 347, 9363])).
% 2.97/3.12 tff(13352,plain,
% 2.97/3.12 (r(s(s(elem!1)), s(s(z)))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[3497, 26, 12509, 13351])).
% 2.97/3.12 tff(13353,plain,
% 2.97/3.12 (r(s(s(z)), s(z))),
% 2.97/3.12 inference(unit_resolution,[status(thm)],[487, 13251])).
% 2.97/3.12 tff(13354,plain,
% 2.97/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13355,plain,
% 2.97/3.13 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13356,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13355])).
% 2.97/3.13 tff(13357,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[13356, 13354])).
% 2.97/3.13 tff(13358,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13359,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13358, 13357])).
% 2.97/3.13 tff(13360,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13359, 163, 13353, 13352, 12845, 13344])).
% 2.97/3.13 tff(13361,plain,((elem!1 = z) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | r(z, s(s(s(s(s(z)))))) | r(z, s(s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(13362,plain,
% 2.97/3.13 (b(z, elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13361, 13215, 13065, 150, 13022, 12871, 2, 3615, 13063, 13061, 49, 13060])).
% 2.97/3.13 tff(13363,plain,
% 2.97/3.13 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3468, 13362, 13055])).
% 2.97/3.13 tff(13364,plain,
% 2.97/3.13 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3792, 13363])).
% 2.97/3.13 tff(13365,plain,
% 2.97/3.13 (~(s(z) = elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[4600, 13362, 13021])).
% 2.97/3.13 tff(13366,plain,
% 2.97/3.13 (~(s(s(z)) = s(elem!1))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[227, 13365])).
% 2.97/3.13 tff(13367,plain,
% 2.97/3.13 (~(elem!1 = s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[234, 13366])).
% 2.97/3.13 tff(13368,plain,
% 2.97/3.13 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[9674, 149, 6262])).
% 2.97/3.13 tff(13369,plain,
% 2.97/3.13 (elem!1 = s(s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13246, 13368, 3066, 12369, 347, 9363, 5428, 4167])).
% 2.97/3.13 tff(13370,plain,
% 2.97/3.13 (s(elem!1) = s(s(s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13369])).
% 2.97/3.13 tff(13371,plain,
% 2.97/3.13 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13370])).
% 2.97/3.13 tff(13372,plain,
% 2.97/3.13 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13371])).
% 2.97/3.13 tff(13373,plain,
% 2.97/3.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13372])).
% 2.97/3.13 tff(13374,plain,
% 2.97/3.13 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13373])).
% 2.97/3.13 tff(13375,plain,
% 2.97/3.13 (s(s(z)) = elem!1),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8661, 13369])).
% 2.97/3.13 tff(13376,plain,
% 2.97/3.13 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8694, 13375])).
% 2.97/3.13 tff(13377,plain,
% 2.97/3.13 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3249, 13376])).
% 2.97/3.13 tff(13378,plain,
% 2.97/3.13 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13372])).
% 2.97/3.13 tff(13379,plain,
% 2.97/3.13 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13378])).
% 2.97/3.13 tff(13380,plain,
% 2.97/3.13 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13369])).
% 2.97/3.13 tff(13381,plain,
% 2.97/3.13 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[13380, 12409])).
% 2.97/3.13 tff(13382,plain,
% 2.97/3.13 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.97/3.13 inference(symmetry,[status(thm)],[13381])).
% 2.97/3.13 tff(13383,plain,
% 2.97/3.13 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13382])).
% 2.97/3.13 tff(13384,plain,
% 2.97/3.13 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[12415, 13383])).
% 2.97/3.13 tff(13385,plain,
% 2.97/3.13 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13371])).
% 2.97/3.13 tff(13386,plain,
% 2.97/3.13 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13385])).
% 2.97/3.13 tff(13387,plain,
% 2.97/3.13 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13386])).
% 2.97/3.13 tff(13388,plain,
% 2.97/3.13 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13387])).
% 2.97/3.13 tff(13389,plain,
% 2.97/3.13 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.97/3.13 inference(symmetry,[status(thm)],[9855])).
% 2.97/3.13 tff(13390,plain,
% 2.97/3.13 (~(s(s(z)) = elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[9862, 3380, 225])).
% 2.97/3.13 tff(13391,plain,
% 2.97/3.13 (~(elem!1 = s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8661, 13390])).
% 2.97/3.13 tff(13392,plain,
% 2.97/3.13 (elem!1 = s(s(s(s(s(z)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13246, 13391, 3066, 271, 347, 9403, 5428, 4167])).
% 2.97/3.13 tff(13393,plain,
% 2.97/3.13 (s(s(s(s(z)))) = s(elem!1)),
% 2.97/3.13 inference(transitivity,[status(thm)],[289, 13389, 134])).
% 2.97/3.13 tff(13394,plain,
% 2.97/3.13 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13393])).
% 2.97/3.13 tff(13395,plain,
% 2.97/3.13 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[294, 13394, 129, 13392])).
% 2.97/3.13 tff(13396,plain,
% 2.97/3.13 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13395])).
% 2.97/3.13 tff(13397,plain,
% 2.97/3.13 (s(s(z)) = s(elem!1)),
% 2.97/3.13 inference(transitivity,[status(thm)],[299, 13396, 13389, 134])).
% 2.97/3.13 tff(13398,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13289, 13397])).
% 2.97/3.13 tff(13399,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(13400,plain,
% 2.97/3.13 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13399, 12369, 3066, 347, 9363, 5428, 4167, 225])).
% 2.97/3.13 tff(13401,plain,
% 2.97/3.13 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13400, 13388])).
% 2.97/3.13 tff(13402,plain,
% 2.97/3.13 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13369])).
% 2.97/3.13 tff(13403,plain,
% 2.97/3.13 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13402])).
% 2.97/3.13 tff(13404,plain,
% 2.97/3.13 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13052, 3066, 152, 9363, 406])).
% 2.97/3.13 tff(13405,plain,
% 2.97/3.13 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[374, 13404])).
% 2.97/3.13 tff(13406,plain,
% 2.97/3.13 (~b(s(s(z)), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3626, 13405, 2, 3615])).
% 2.97/3.13 tff(13407,plain,
% 2.97/3.13 (r(s(s(z)), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[487, 13406])).
% 2.97/3.13 tff(13408,plain,
% 2.97/3.13 (r(elem!1, s(z))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13407, 13403])).
% 2.97/3.13 tff(13409,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[12427, 4926])).
% 2.97/3.13 tff(13410,plain,
% 2.97/3.13 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.97/3.13 inference(symmetry,[status(thm)],[13409])).
% 2.97/3.13 tff(13411,plain,
% 2.97/3.13 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[12769, 198, 347, 9403, 4167])).
% 2.97/3.13 tff(13412,plain,
% 2.97/3.13 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[511, 26, 508, 13411])).
% 2.97/3.13 tff(13413,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), elem!1)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13412, 13410])).
% 2.97/3.13 tff(13414,plain,
% 2.97/3.13 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[12423, 4926])).
% 2.97/3.13 tff(13415,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 2.97/3.13 inference(symmetry,[status(thm)],[13414])).
% 2.97/3.13 tff(13416,plain,
% 2.97/3.13 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13415])).
% 2.97/3.13 tff(13417,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.97/3.13 tff(13418,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[12480, 198, 347, 9403, 13417])).
% 2.97/3.13 tff(13419,plain,
% 2.97/3.13 (~b(s(s(elem!1)), elem!1)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13418, 13416])).
% 2.97/3.13 tff(13420,plain,
% 2.97/3.13 (r(s(s(elem!1)), elem!1)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[602, 13419, 138])).
% 2.97/3.13 tff(13421,plain,
% 2.97/3.13 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[12428])).
% 2.97/3.13 tff(13422,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[12425, 13421])).
% 2.97/3.13 tff(13423,plain,
% 2.97/3.13 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13422])).
% 2.97/3.13 tff(13424,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13425,plain,
% 2.97/3.13 (((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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))))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13426,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13425])).
% 2.97/3.13 tff(13427,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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))))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[13426, 13424])).
% 2.97/3.13 tff(13428,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13429,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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)))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13428, 13427])).
% 2.97/3.13 tff(13430,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13429, 198, 347, 9403, 13417, 5428, 4167])).
% 2.97/3.13 tff(13431,plain,
% 2.97/3.13 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13430, 13423])).
% 2.97/3.13 tff(13432,plain,
% 2.97/3.13 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1377, 13431, 1268])).
% 2.97/3.13 tff(13433,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13434,plain,
% 2.97/3.13 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13435,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13434])).
% 2.97/3.13 tff(13436,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[13435, 13433])).
% 2.97/3.13 tff(13437,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13438,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13437, 13436])).
% 2.97/3.13 tff(13439,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13438, 163, 1115, 1364, 1363, 259])).
% 2.97/3.13 tff(13440,plain,((~r(elem!1, s(z))) | (~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))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(13441,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13440, 13432, 13420, 13413, 259])).
% 2.97/3.13 tff(13442,plain,((~b(s(s(s(s(z)))), z)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~(elem!1 = s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(13443,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13442, 13408, 13401, 13384, 13369, 347, 9363, 5428, 4167])).
% 2.97/3.13 tff(13444,plain,
% 2.97/3.13 (r(s(s(s(s(z)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[12473, 26, 462, 13443])).
% 2.97/3.13 tff(13445,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13446,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13447,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13446, 13445])).
% 2.97/3.13 tff(13448,plain,
% 2.97/3.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13447, 163, 406, 152, 13444])).
% 2.97/3.13 tff(13449,plain,
% 2.97/3.13 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13448, 13379])).
% 2.97/3.13 tff(13450,plain,
% 2.97/3.13 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[4221, 13449, 13377])).
% 2.97/3.13 tff(13451,plain,
% 2.97/3.13 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13450, 13374])).
% 2.97/3.13 tff(13452,plain,
% 2.97/3.13 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13372])).
% 2.97/3.13 tff(13453,plain,
% 2.97/3.13 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13452])).
% 2.97/3.13 tff(13454,plain,
% 2.97/3.13 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13372])).
% 2.97/3.13 tff(13455,plain,
% 2.97/3.13 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(s(z), s(s(elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13454])).
% 2.97/3.13 tff(13456,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13457,plain,
% 2.97/3.13 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13458,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13457])).
% 2.97/3.13 tff(13459,plain,
% 2.97/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[13458, 13456])).
% 2.97/3.13 tff(13460,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13461,plain,
% 2.97/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13460, 13459])).
% 2.97/3.13 tff(13462,plain,
% 2.97/3.13 (~r(s(z), s(s(s(s(z)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13461, 163, 150, 406, 13444])).
% 2.97/3.13 tff(13463,plain,
% 2.97/3.13 (~r(s(z), s(s(elem!1)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13462, 13455])).
% 2.97/3.13 tff(13464,plain,
% 2.97/3.13 (b(s(z), s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[642, 13463])).
% 2.97/3.13 tff(13465,plain,
% 2.97/3.13 (b(s(z), s(s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13464, 13453])).
% 2.97/3.13 tff(13466,plain,
% 2.97/3.13 ((s(s(s(s(z)))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13372])).
% 2.97/3.13 tff(13467,plain,
% 2.97/3.13 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 2.97/3.13 inference(symmetry,[status(thm)],[13466])).
% 2.97/3.13 tff(13468,plain,
% 2.97/3.13 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[13467])).
% 2.97/3.13 tff(13469,plain,
% 2.97/3.13 (~(s(s(s(s(z)))) = s(z))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[620, 13468])).
% 2.97/3.13 tff(13470,plain,
% 2.97/3.13 (~r(s(s(s(s(z)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[12453, 163, 150, 406, 13444])).
% 2.97/3.13 tff(13471,plain,
% 2.97/3.13 (((~![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)))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(13472,plain,
% 2.97/3.13 ((~![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)))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(13473,plain,
% 2.97/3.13 ((~![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))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[13472, 13471])).
% 2.97/3.13 tff(13474,plain,
% 2.97/3.13 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13473, 26, 13470])).
% 2.97/3.13 tff(13475,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13474, 13469])).
% 2.97/3.13 tff(13476,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13477,plain,
% 2.97/3.14 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13478,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13477])).
% 2.97/3.14 tff(13479,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[13478, 13476])).
% 2.97/3.14 tff(13480,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(13481,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13480, 13479])).
% 2.97/3.14 tff(13482,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13481, 198, 3615, 2, 13475, 13465, 13451])).
% 2.97/3.14 tff(13483,plain,(b(s(z), elem!1) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (s(z) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13484,plain,
% 2.97/3.14 (b(s(z), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13483, 13060, 2, 13022, 12942, 150, 3615, 13066, 13065, 12871, 13084, 13365, 13215])).
% 2.97/3.14 tff(13485,plain,
% 2.97/3.14 (~(s(s(z)) = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12536, 13484, 13062])).
% 2.97/3.14 tff(13486,plain,
% 2.97/3.14 (~(elem!1 = s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[8661, 13485])).
% 2.97/3.14 tff(13487,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13488,plain,
% 2.97/3.14 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13489,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13488])).
% 2.97/3.14 tff(13490,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[13489, 13487])).
% 2.97/3.14 tff(13491,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(13492,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13491, 13490])).
% 2.97/3.14 tff(13493,plain,
% 2.97/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13492, 198, 13084, 3615, 2, 559])).
% 2.97/3.14 tff(13494,plain,
% 2.97/3.14 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3328, 26, 13493])).
% 2.97/3.14 tff(13495,plain,
% 2.97/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13494, 2935])).
% 2.97/3.14 tff(13496,plain,
% 2.97/3.14 (~(z = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[78, 13215])).
% 2.97/3.14 tff(13497,plain,
% 2.97/3.14 (~(s(elem!1) = s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[814, 13496])).
% 2.97/3.14 tff(13498,plain,
% 2.97/3.14 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13007, 163, 12871, 33, 152])).
% 2.97/3.14 tff(13499,plain,
% 2.97/3.14 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3841, 13498])).
% 2.97/3.14 tff(13500,plain,
% 2.97/3.14 (~r(z, s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[5347, 163, 12871, 33, 152])).
% 2.97/3.14 tff(13501,plain,
% 2.97/3.14 (b(z, s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4110, 13500])).
% 2.97/3.14 tff(13502,plain,
% 2.97/3.14 (~r(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12790, 13178, 150, 33])).
% 2.97/3.14 tff(13503,plain,
% 2.97/3.14 (b(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[345, 13502])).
% 2.97/3.14 tff(13504,plain,
% 2.97/3.14 (elem!1 = s(s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13246, 271, 12871, 5011, 13503, 9363, 13501, 13499])).
% 2.97/3.14 tff(13505,plain,
% 2.97/3.14 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13504])).
% 2.97/3.14 tff(13506,plain,
% 2.97/3.14 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13505])).
% 2.97/3.14 tff(13507,plain,
% 2.97/3.14 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13506])).
% 2.97/3.14 tff(13508,plain,
% 2.97/3.14 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13504])).
% 2.97/3.14 tff(13509,plain,
% 2.97/3.14 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 2.97/3.14 inference(symmetry,[status(thm)],[13508])).
% 2.97/3.14 tff(13510,plain,
% 2.97/3.14 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13509])).
% 2.97/3.14 tff(13511,plain,
% 2.97/3.14 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13399, 271, 12871, 13503, 9363, 13501, 13499, 225])).
% 2.97/3.14 tff(13512,plain,
% 2.97/3.14 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13511, 13510])).
% 2.97/3.14 tff(13513,plain,
% 2.97/3.14 (~(s(elem!1) = s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[140, 13512])).
% 2.97/3.14 tff(13514,plain,
% 2.97/3.14 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13506])).
% 2.97/3.14 tff(13515,plain,
% 2.97/3.14 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(elem!1)), z)),
% 2.97/3.14 inference(symmetry,[status(thm)],[13514])).
% 2.97/3.14 tff(13516,plain,
% 2.97/3.14 (r(s(s(elem!1)), z)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[152, 13515])).
% 2.97/3.14 tff(13517,plain,
% 2.97/3.14 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13506])).
% 2.97/3.14 tff(13518,plain,
% 2.97/3.14 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(elem!1)))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13517])).
% 2.97/3.14 tff(13519,plain,
% 2.97/3.14 (r(z, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[33, 13518])).
% 2.97/3.14 tff(13520,plain,
% 2.97/3.14 (~(s(elem!1) = elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1395, 13512])).
% 2.97/3.14 tff(13521,plain,
% 2.97/3.14 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13504])).
% 2.97/3.14 tff(13522,plain,
% 2.97/3.14 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13521])).
% 2.97/3.14 tff(13523,plain,
% 2.97/3.14 (b(elem!1, s(z))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[559, 13522])).
% 2.97/3.14 tff(13524,plain,
% 2.97/3.14 (~b(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6934, 13523, 150, 406, 820, 95, 5927, 271])).
% 2.97/3.14 tff(13525,plain,
% 2.97/3.14 (r(s(elem!1), elem!1)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[856, 13524, 13520])).
% 2.97/3.14 tff(13526,plain,
% 2.97/3.14 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13506])).
% 2.97/3.14 tff(13527,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13526])).
% 2.97/3.14 tff(13528,plain,
% 2.97/3.14 (b(s(s(elem!1)), s(z))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[2, 13527])).
% 2.97/3.14 tff(13529,plain,
% 2.97/3.14 (~r(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1530, 791, 790, 1098])).
% 2.97/3.14 tff(13530,plain,
% 2.97/3.14 (b(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[901, 13529, 890])).
% 2.97/3.14 tff(13531,plain,
% 2.97/3.14 (~r(s(s(elem!1)), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1781, 791, 790, 1474])).
% 2.97/3.14 tff(13532,plain,
% 2.97/3.14 (b(s(s(elem!1)), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1143, 13531, 2968])).
% 2.97/3.14 tff(13533,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1562, 13532, 13530, 820, 150, 790, 791, 722])).
% 2.97/3.14 tff(13534,plain,((~r(z, s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13535,plain,
% 2.97/3.14 (~r(z, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13534, 13516, 150, 820, 13528, 13513, 13525, 13519])).
% 2.97/3.14 tff(13536,plain,
% 2.97/3.14 (b(z, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1791, 13535])).
% 2.97/3.14 tff(13537,plain,
% 2.97/3.14 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13504])).
% 2.97/3.14 tff(13538,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13537])).
% 2.97/3.14 tff(13539,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13506])).
% 2.97/3.14 tff(13540,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13539])).
% 2.97/3.14 tff(13541,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(transitivity,[status(thm)],[13540, 13538])).
% 2.97/3.14 tff(13542,plain,
% 2.97/3.14 (r(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[12871, 13541])).
% 2.97/3.14 tff(13543,plain,
% 2.97/3.14 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(elem!1), s(z))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[5378])).
% 2.97/3.14 tff(13544,plain,
% 2.97/3.14 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13543])).
% 2.97/3.14 tff(13545,plain,
% 2.97/3.14 ((~r(s(elem!1), s(z))) <=> (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13544])).
% 2.97/3.14 tff(13546,plain,
% 2.97/3.14 (~r(s(elem!1), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3941, 1175, 150, 3450, 406, 232, 1801])).
% 2.97/3.14 tff(13547,plain,
% 2.97/3.14 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13546, 13545])).
% 2.97/3.14 tff(13548,plain,
% 2.97/3.14 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[5377, 5381])).
% 2.97/3.14 tff(13549,plain,
% 2.97/3.14 (~b(elem!1, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[8990, 1175, 271, 1801])).
% 2.97/3.14 tff(13550,plain,
% 2.97/3.14 (r(elem!1, s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1416, 13549, 1652])).
% 2.97/3.14 tff(13551,plain,
% 2.97/3.14 (~r(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[5315, 13550, 271, 95, 138, 405])).
% 2.97/3.14 tff(13552,plain,
% 2.97/3.14 (b(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[901, 13551, 6708])).
% 2.97/3.14 tff(13553,plain,
% 2.97/3.14 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13552, 13548])).
% 2.97/3.14 tff(13554,plain,
% 2.97/3.14 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12671, 198, 3615, 2, 13553])).
% 2.97/3.14 tff(13555,plain,
% 2.97/3.14 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4344, 26, 13554])).
% 2.97/3.14 tff(13556,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13555, 13547, 11021])).
% 2.97/3.14 tff(13557,plain,((~b(s(elem!1), z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13558,plain,
% 2.97/3.14 (~b(s(elem!1), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13557, 13504, 820, 3615, 2, 271, 95, 13512, 13542, 13536, 150, 13178, 406, 13289])).
% 2.97/3.14 tff(13559,plain,
% 2.97/3.14 (r(s(elem!1), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1217, 13558])).
% 2.97/3.14 tff(13560,plain,
% 2.97/3.14 (~b(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2303, 13559, 820, 150, 13519, 13516])).
% 2.97/3.14 tff(13561,plain,
% 2.97/3.14 (r(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[901, 13560, 13513])).
% 2.97/3.14 tff(13562,plain,
% 2.97/3.14 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13561, 13507])).
% 2.97/3.14 tff(13563,plain,
% 2.97/3.14 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13504])).
% 2.97/3.14 tff(13564,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(symmetry,[status(thm)],[13563])).
% 2.97/3.14 tff(13565,plain,
% 2.97/3.14 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[12871, 13564])).
% 2.97/3.14 tff(13566,plain,
% 2.97/3.14 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3376, 13525, 3368, 13565])).
% 2.97/3.14 tff(13567,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13566, 13562])).
% 2.97/3.14 tff(13568,plain,((~b(elem!1, z)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13569,plain,
% 2.97/3.14 (~b(elem!1, z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13568, 13497, 150, 3615, 2, 13362, 13022, 13495, 13484, 13056, 12942, 559, 13486, 13365])).
% 2.97/3.14 tff(13570,plain,
% 2.97/3.14 (r(elem!1, z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[187, 13569, 13215])).
% 2.97/3.14 tff(13571,plain,
% 2.97/3.14 (~r(elem!1, s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6651, 13570, 150, 13022])).
% 2.97/3.14 tff(13572,plain,
% 2.97/3.14 (b(elem!1, s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[242, 13571, 13367])).
% 2.97/3.14 tff(13573,plain,
% 2.97/3.14 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[7965, 198, 13484, 13572, 3615, 2])).
% 2.97/3.14 tff(13574,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13575,plain,
% 2.97/3.14 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13576,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13575])).
% 2.97/3.14 tff(13577,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[13576, 13574])).
% 2.97/3.14 tff(13578,plain,
% 2.97/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(13579,plain,
% 2.97/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13578, 13577])).
% 2.97/3.14 tff(13580,plain,
% 2.97/3.14 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13579, 163, 13570, 13022, 12942])).
% 2.97/3.14 tff(13581,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[703, 13580, 13573, 13364])).
% 2.97/3.14 tff(13582,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | r(z, s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13583,plain,
% 2.97/3.14 (~b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13582, 3745, 2, 150, 49, 3615])).
% 2.97/3.14 tff(13584,plain,
% 2.97/3.14 (r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[469, 13583])).
% 2.97/3.14 tff(13585,plain,
% 2.97/3.14 (~r(s(s(z)), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12747, 13584, 150, 13022])).
% 2.97/3.14 tff(13586,plain,
% 2.97/3.14 (b(s(s(z)), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[487, 13585])).
% 2.97/3.14 tff(13587,plain,
% 2.97/3.14 (~b(s(z), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3753, 13586, 3745, 2])).
% 2.97/3.14 tff(13588,plain,
% 2.97/3.14 (r(s(z), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[403, 13587])).
% 2.97/3.14 tff(13589,plain,
% 2.97/3.14 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3626, 13586, 2, 3615])).
% 2.97/3.14 tff(13590,plain,
% 2.97/3.14 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[374, 13589])).
% 2.97/3.14 tff(13591,plain,
% 2.97/3.14 (~r(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4031, 13590, 12942, 13022])).
% 2.97/3.14 tff(13592,plain,
% 2.97/3.14 (b(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[345, 13591])).
% 2.97/3.14 tff(13593,plain,
% 2.97/3.14 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12998, 13592, 13584, 13590, 9363, 13588, 150])).
% 2.97/3.14 tff(13594,plain,
% 2.97/3.14 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[31, 13593])).
% 2.97/3.14 tff(13595,plain,
% 2.97/3.14 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13052, 13590, 12942, 9363, 13022])).
% 2.97/3.14 tff(13596,plain,
% 2.97/3.14 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3098, 13595])).
% 2.97/3.14 tff(13597,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13598,plain,
% 2.97/3.14 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(13599,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[13598])).
% 2.97/3.14 tff(13600,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[13599, 13597])).
% 2.97/3.14 tff(13601,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(13602,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13601, 13600])).
% 2.97/3.14 tff(13603,plain,
% 2.97/3.14 (~b(z, s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13602, 198, 13596, 13594, 3745, 9363])).
% 2.97/3.14 tff(13604,plain,
% 2.97/3.14 (~r(z, s(s(s(s(s(z))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12124, 163, 150, 13022, 13584])).
% 2.97/3.14 tff(13605,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4110, 13604, 13603])).
% 2.97/3.14 tff(13606,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(13607,plain,
% 2.97/3.14 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13606, 3615, 2, 150, 49])).
% 2.97/3.14 tff(13608,plain,
% 2.97/3.14 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[420, 13607])).
% 2.97/3.14 tff(13609,plain,
% 2.97/3.14 (~r(s(s(z)), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12978, 12833, 2, 3615, 595, 152, 150])).
% 2.97/3.14 tff(13610,plain,
% 2.97/3.14 (b(s(s(z)), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[487, 13609])).
% 2.97/3.14 tff(13611,plain,
% 2.97/3.14 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[3626, 13610, 2, 3615])).
% 2.97/3.14 tff(13612,plain,
% 2.97/3.14 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[374, 13611])).
% 2.97/3.14 tff(13613,plain,
% 2.97/3.14 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[12950, 332, 152, 2, 3615, 150])).
% 2.97/3.14 tff(13614,plain,
% 2.97/3.14 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[31, 13613])).
% 2.97/3.15 tff(13615,plain,
% 2.97/3.15 (~b(z, s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3669, 198, 3615, 13614, 2])).
% 2.97/3.15 tff(13616,plain,
% 2.97/3.15 (r(z, s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[593, 13615])).
% 2.97/3.15 tff(13617,plain,
% 2.97/3.15 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[4031, 13616, 152, 332])).
% 2.97/3.15 tff(13618,plain,
% 2.97/3.15 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[374, 13617])).
% 2.97/3.15 tff(13619,plain,
% 2.97/3.15 (~b(s(s(z)), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3626, 13618, 2, 3615])).
% 2.97/3.15 tff(13620,plain,
% 2.97/3.15 (r(s(s(z)), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[487, 13619])).
% 2.97/3.15 tff(13621,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[544, 163, 150, 13616, 13620, 332])).
% 2.97/3.15 tff(13622,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(13623,plain,
% 2.97/3.15 (~r(s(s(z)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13622, 3615, 2, 150, 152])).
% 2.97/3.15 tff(13624,plain,
% 2.97/3.15 (b(s(s(z)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[345, 13623])).
% 2.97/3.15 tff(13625,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12986, 3828, 33, 150])).
% 2.97/3.15 tff(13626,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[469, 13625])).
% 2.97/3.15 tff(13627,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12754, 198, 3615, 2, 13626])).
% 2.97/3.15 tff(13628,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3098, 13627])).
% 2.97/3.15 tff(13629,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12762, 163, 13628, 33, 423, 3828])).
% 2.97/3.15 tff(13630,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(13631,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13630, 12833, 423, 3615, 2, 150])).
% 2.97/3.15 tff(13632,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3841, 13631])).
% 2.97/3.15 tff(13633,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12769, 198, 13624, 9363, 13632])).
% 2.97/3.15 tff(13634,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[511, 26, 508, 13633])).
% 2.97/3.15 tff(13635,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12919, 163, 13612, 423, 13634])).
% 2.97/3.15 tff(13636,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3098, 13635])).
% 2.97/3.15 tff(13637,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13638,plain,
% 2.97/3.15 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13639,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13638])).
% 2.97/3.15 tff(13640,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[13639, 13637])).
% 2.97/3.15 tff(13641,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(13642,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13641, 13640])).
% 2.97/3.15 tff(13643,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13642, 198, 595, 13636, 3615, 13632])).
% 2.97/3.15 tff(13644,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[469, 13643])).
% 2.97/3.15 tff(13645,plain,
% 2.97/3.15 (~r(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12998, 13644, 13624, 12833, 9363, 13612, 150])).
% 2.97/3.15 tff(13646,plain,
% 2.97/3.15 (b(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[403, 13645])).
% 2.97/3.15 tff(13647,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[9447, 198, 595, 13610, 13646, 9363])).
% 2.97/3.15 tff(13648,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(13649,plain,
% 2.97/3.15 (~b(z, s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13648, 3615, 150, 13608, 2, 12942])).
% 2.97/3.15 tff(13650,plain,
% 2.97/3.15 (r(z, s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[593, 13649])).
% 2.97/3.15 tff(13651,plain,
% 2.97/3.15 (~r(s(s(z)), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12747, 3827, 150, 13650])).
% 2.97/3.15 tff(13652,plain,
% 2.97/3.15 (b(s(s(z)), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[487, 13651])).
% 2.97/3.15 tff(13653,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12885, 13652, 150, 13608, 13650, 3615, 2])).
% 2.97/3.15 tff(13654,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3841, 13653])).
% 2.97/3.15 tff(13655,plain,
% 2.97/3.15 (~r(z, s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12124, 163, 150, 13650, 3827])).
% 2.97/3.15 tff(13656,plain,
% 2.97/3.15 (b(z, s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[4110, 13655])).
% 2.97/3.15 tff(13657,plain,
% 2.97/3.15 (~r(s(s(z)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13622, 3615, 2, 150, 12942])).
% 2.97/3.15 tff(13658,plain,
% 2.97/3.15 (b(s(s(z)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[345, 13657])).
% 2.97/3.15 tff(13659,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12769, 198, 13658, 9363, 13654])).
% 2.97/3.15 tff(13660,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[511, 26, 508, 13659])).
% 2.97/3.15 tff(13661,plain,
% 2.97/3.15 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3626, 13652, 2, 3615])).
% 2.97/3.15 tff(13662,plain,
% 2.97/3.15 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[374, 13661])).
% 2.97/3.15 tff(13663,plain,
% 2.97/3.15 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[5798, 163, 13662, 13608, 13660])).
% 2.97/3.15 tff(13664,plain,
% 2.97/3.15 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3328, 26, 13663])).
% 2.97/3.15 tff(13665,plain,
% 2.97/3.15 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13664, 2935])).
% 2.97/3.15 tff(13666,plain,
% 2.97/3.15 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12057, 198, 3819, 13656, 13665])).
% 2.97/3.15 tff(13667,plain,
% 2.97/3.15 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[31, 13666])).
% 2.97/3.15 tff(13668,plain,
% 2.97/3.15 (~r(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12998, 13667, 13658, 3827, 9363, 13662, 150])).
% 2.97/3.15 tff(13669,plain,
% 2.97/3.15 (b(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[403, 13668])).
% 2.97/3.15 tff(13670,plain,
% 2.97/3.15 (r(s(elem!1), z) <=> r(s(z), z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[1644])).
% 2.97/3.15 tff(13671,plain,
% 2.97/3.15 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.97/3.15 inference(symmetry,[status(thm)],[13670])).
% 2.97/3.15 tff(13672,plain,
% 2.97/3.15 (r(s(elem!1), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[150, 13671])).
% 2.97/3.15 tff(13673,plain,
% 2.97/3.15 (r(z, s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3155, 80, 13650])).
% 2.97/3.15 tff(13674,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[80])).
% 2.97/3.15 tff(13675,plain,
% 2.97/3.15 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[80])).
% 2.97/3.15 tff(13676,plain,
% 2.97/3.15 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[13675])).
% 2.97/3.15 tff(13677,plain,
% 2.97/3.15 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13676])).
% 2.97/3.15 tff(13678,plain,
% 2.97/3.15 (~(s(s(s(elem!1))) = elem!1)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[968, 13677])).
% 2.97/3.15 tff(13679,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12885, 560, 150, 13608, 13650, 3615, 2])).
% 2.97/3.15 tff(13680,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3841, 13679])).
% 2.97/3.15 tff(13681,plain,
% 2.97/3.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1874, 1310, 68, 12243])).
% 2.97/3.15 tff(13682,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1326, 13681, 12239])).
% 2.97/3.15 tff(13683,plain,
% 2.97/3.15 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13682, 12237])).
% 2.97/3.15 tff(13684,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13685,plain,
% 2.97/3.15 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(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))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13686,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13685])).
% 2.97/3.15 tff(13687,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[13686, 13684])).
% 2.97/3.15 tff(13688,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(13689,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13688, 13687])).
% 2.97/3.15 tff(13690,plain,
% 2.97/3.15 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13689, 163, 13683, 3272, 13412])).
% 2.97/3.15 tff(13691,plain,
% 2.97/3.15 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 2.97/3.15 inference(transitivity,[status(thm)],[12253, 12311])).
% 2.97/3.15 tff(13692,plain,
% 2.97/3.15 (b(s(s(s(z))), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[1310, 13691])).
% 2.97/3.15 tff(13693,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), 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))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13694,plain,
% 2.97/3.15 (((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), 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))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13695,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), 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)))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13694])).
% 2.97/3.15 tff(13696,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), 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))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[13695, 13693])).
% 2.97/3.15 tff(13697,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(13698,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13697, 13696])).
% 2.97/3.15 tff(13699,plain,
% 2.97/3.15 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13698, 198, 13692, 347, 9403, 5428, 4167])).
% 2.97/3.15 tff(13700,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[10626, 26, 12295, 13699, 13690])).
% 2.97/3.15 tff(13701,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~(elem!1 = z)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(13702,plain,
% 2.97/3.15 (~b(s(s(s(elem!1))), elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13701, 80, 13658, 9363, 5428, 13680, 7266, 12252])).
% 2.97/3.15 tff(13703,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1308, 13702, 13678])).
% 2.97/3.15 tff(13704,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13703, 13674])).
% 2.97/3.15 tff(13705,plain,
% 2.97/3.15 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1358, 13704, 13673, 13672])).
% 2.97/3.15 tff(13706,plain,
% 2.97/3.15 (b(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1339, 13705, 10618])).
% 2.97/3.15 tff(13707,plain,
% 2.97/3.15 (b(s(s(s(z))), s(z))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13706, 12265])).
% 2.97/3.15 tff(13708,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13709,plain,
% 2.97/3.15 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13710,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13709])).
% 2.97/3.15 tff(13711,plain,
% 2.97/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[13710, 13708])).
% 2.97/3.15 tff(13712,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(13713,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13712, 13711])).
% 2.97/3.15 tff(13714,plain,
% 2.97/3.15 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13713, 198, 560, 407, 3615, 2, 13707])).
% 2.97/3.15 tff(13715,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 2.97/3.15 inference(transitivity,[status(thm)],[13674, 12286])).
% 2.97/3.15 tff(13716,plain,
% 2.97/3.15 (r(s(s(s(z))), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13703, 13715])).
% 2.97/3.15 tff(13717,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13718,plain,
% 2.97/3.15 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, 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))))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(13719,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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)))))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[13718])).
% 2.97/3.15 tff(13720,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[13719, 13717])).
% 2.97/3.15 tff(13721,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(13722,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13721, 13720])).
% 2.97/3.15 tff(13723,plain,
% 2.97/3.15 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13722, 163, 13650, 12942, 13716])).
% 2.97/3.15 tff(13724,plain,
% 2.97/3.15 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[10593, 26, 13723])).
% 2.97/3.15 tff(13725,plain,
% 2.97/3.15 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13724, 13714])).
% 2.97/3.15 tff(13726,plain,
% 2.97/3.15 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[10612, 13725])).
% 2.97/3.15 tff(13727,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12323, 13726])).
% 2.97/3.15 tff(13728,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(13729,plain,
% 2.97/3.15 (~(elem!1 = z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13728, 13652, 13669, 3615, 2, 13656, 150, 49])).
% 2.97/3.15 tff(13730,plain,
% 2.97/3.15 (~(z = elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[78, 13729])).
% 2.97/3.15 tff(13731,plain,
% 2.97/3.15 (~(s(elem!1) = s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[814, 13730])).
% 2.97/3.15 tff(13732,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12769, 198, 13624, 9363, 4167])).
% 2.97/3.15 tff(13733,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[511, 26, 508, 13732])).
% 2.97/3.15 tff(13734,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13733, 13254])).
% 2.97/3.15 tff(13735,plain,
% 2.97/3.15 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13734, 13253])).
% 2.97/3.15 tff(13736,plain,
% 2.97/3.15 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[825, 5023])).
% 2.97/3.15 tff(13737,plain,
% 2.97/3.15 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[12141, 198, 13624, 5428, 4167])).
% 2.97/3.15 tff(13738,plain,
% 2.97/3.15 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13737])).
% 2.97/3.15 tff(13739,plain,
% 2.97/3.15 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13738, 13736])).
% 2.97/3.15 tff(13740,plain,
% 2.97/3.15 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[825])).
% 2.97/3.15 tff(13741,plain,
% 2.97/3.15 (b(z, s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[9363, 13740])).
% 2.97/3.15 tff(13742,plain,
% 2.97/3.15 (~b(z, elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[4600, 206, 4598])).
% 2.97/3.15 tff(13743,plain,
% 2.97/3.15 (r(z, elem!1)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[102, 13742, 3])).
% 2.97/3.15 tff(13744,plain,
% 2.97/3.15 (~r(s(s(elem!1)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[8726, 978, 152, 13743, 7346, 2834, 1103, 995, 5034])).
% 2.97/3.15 tff(13745,plain,
% 2.97/3.15 (b(s(s(elem!1)), z)),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[801, 13744])).
% 2.97/3.15 tff(13746,plain,
% 2.97/3.15 (b(s(elem!1), z)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[13624, 832])).
% 2.97/3.15 tff(13747,plain,
% 2.97/3.15 (~b(s(s(elem!1)), s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[3549, 198, 13746, 13745, 13741])).
% 2.97/3.15 tff(13748,plain,
% 2.97/3.15 (r(s(s(elem!1)), s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1143, 13747, 5318])).
% 2.97/3.16 tff(13749,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13750,plain,
% 2.97/3.16 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13751,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13750])).
% 2.97/3.16 tff(13752,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[13751, 13749])).
% 2.97/3.16 tff(13753,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(13754,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13753, 13752])).
% 2.97/3.16 tff(13755,plain,
% 2.97/3.16 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13754, 163, 13748, 13739, 13735])).
% 2.97/3.16 tff(13756,plain,
% 2.97/3.16 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13280, 198, 13746, 13745, 13741])).
% 2.97/3.16 tff(13757,plain,
% 2.97/3.16 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13756, 13274, 13273])).
% 2.97/3.16 tff(13758,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[5274, 13757, 13755, 5093])).
% 2.97/3.16 tff(13759,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (z = elem!1) | b(z, s(z)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(13760,plain,
% 2.97/3.16 (~(s(z) = elem!1)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13759, 13654, 13656, 12942, 3615, 13730, 13649, 150, 2])).
% 2.97/3.16 tff(13761,plain,
% 2.97/3.16 (~(s(s(z)) = s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[227, 13760])).
% 2.97/3.16 tff(13762,plain,
% 2.97/3.16 (r(s(s(elem!1)), z)),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[152, 5383])).
% 2.97/3.16 tff(13763,plain,
% 2.97/3.16 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.16 inference(symmetry,[status(thm)],[13548])).
% 2.97/3.16 tff(13764,plain,
% 2.97/3.16 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13763])).
% 2.97/3.16 tff(13765,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13766,plain,
% 2.97/3.16 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13767,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13766])).
% 2.97/3.16 tff(13768,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[13767, 13765])).
% 2.97/3.16 tff(13769,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(13770,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13769, 13768])).
% 2.97/3.16 tff(13771,plain,
% 2.97/3.16 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13770, 198, 3819, 3615, 2, 3404, 12653])).
% 2.97/3.16 tff(13772,plain,
% 2.97/3.16 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[4344, 26, 13771])).
% 2.97/3.16 tff(13773,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13772, 11021])).
% 2.97/3.16 tff(13774,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> r(s(elem!1), elem!1)),
% 2.97/3.16 inference(monotonicity,[status(thm)],[5378, 5435])).
% 2.97/3.16 tff(13775,plain,
% 2.97/3.16 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(symmetry,[status(thm)],[13774])).
% 2.97/3.16 tff(13776,plain,
% 2.97/3.16 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[5376])).
% 2.97/3.16 tff(13777,plain,
% 2.97/3.16 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.97/3.16 inference(symmetry,[status(thm)],[13776])).
% 2.97/3.16 tff(13778,plain,
% 2.97/3.16 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[5378])).
% 2.97/3.16 tff(13779,plain,
% 2.97/3.16 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.97/3.16 inference(transitivity,[status(thm)],[13778, 13777])).
% 2.97/3.16 tff(13780,plain,
% 2.97/3.16 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13779])).
% 2.97/3.16 tff(13781,plain,
% 2.97/3.16 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[11049, 198, 3819, 3404, 12653])).
% 2.97/3.16 tff(13782,plain,
% 2.97/3.16 (~b(s(elem!1), elem!1)),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13781, 13780])).
% 2.97/3.16 tff(13783,plain,
% 2.97/3.16 (r(s(elem!1), elem!1)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[856, 13782, 5434])).
% 2.97/3.16 tff(13784,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13783, 13775])).
% 2.97/3.16 tff(13785,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13786,plain,
% 2.97/3.16 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(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(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13787,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13786])).
% 2.97/3.16 tff(13788,plain,
% 2.97/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[13787, 13785])).
% 2.97/3.16 tff(13789,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(13790,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13789, 13788])).
% 2.97/3.16 tff(13791,plain,
% 2.97/3.16 (~b(s(z), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13790, 198, 3819, 3615, 3404])).
% 2.97/3.16 tff(13792,plain,
% 2.97/3.16 (r(s(z), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[3301, 13791])).
% 2.97/3.16 tff(13793,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13794,plain,
% 2.97/3.16 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13795,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13794])).
% 2.97/3.16 tff(13796,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[13795, 13793])).
% 2.97/3.16 tff(13797,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(13798,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13797, 13796])).
% 2.97/3.16 tff(13799,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13798, 163, 13792, 3827, 13784, 13773])).
% 2.97/3.16 tff(13800,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(13801,plain,
% 2.97/3.16 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13800, 5376, 820, 3819, 3615, 2, 3404])).
% 2.97/3.16 tff(13802,plain,
% 2.97/3.16 (~b(s(elem!1), s(s(elem!1)))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13801, 13764])).
% 2.97/3.16 tff(13803,plain,
% 2.97/3.16 (r(s(elem!1), s(s(elem!1)))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[901, 13802, 5418])).
% 2.97/3.16 tff(13804,plain,
% 2.97/3.16 (~r(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1530, 13803, 13762, 5387])).
% 2.97/3.16 tff(13805,plain,
% 2.97/3.16 (b(z, s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1791, 13804])).
% 2.97/3.16 tff(13806,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(elem!1), z)),
% 2.97/3.16 inference(symmetry,[status(thm)],[5427])).
% 2.97/3.16 tff(13807,plain,
% 2.97/3.16 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(elem!1), z))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13806])).
% 2.97/3.16 tff(13808,plain,
% 2.97/3.16 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(symmetry,[status(thm)],[5490])).
% 2.97/3.16 tff(13809,plain,
% 2.97/3.16 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13803, 5488])).
% 2.97/3.16 tff(13810,plain,
% 2.97/3.16 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13809, 13808])).
% 2.97/3.16 tff(13811,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13812,plain,
% 2.97/3.16 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(13813,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[13812])).
% 2.97/3.16 tff(13814,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[13813, 13811])).
% 2.97/3.16 tff(13815,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(13816,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13815, 13814])).
% 2.97/3.16 tff(13817,plain,
% 2.97/3.16 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13816, 163, 33, 423, 13810])).
% 2.97/3.16 tff(13818,plain,
% 2.97/3.16 (~r(s(elem!1), z)),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13817, 13807])).
% 2.97/3.16 tff(13819,plain,
% 2.97/3.16 (b(s(elem!1), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[1217, 13818])).
% 2.97/3.16 tff(13820,plain,
% 2.97/3.16 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[10997, 163, 3272, 423, 13810])).
% 2.97/3.16 tff(13821,plain,
% 2.97/3.16 (~r(s(s(z)), s(elem!1))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[13820, 5426])).
% 2.97/3.16 tff(13822,plain,
% 2.97/3.16 (b(s(s(z)), s(elem!1))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[2378, 13821, 232])).
% 2.97/3.16 tff(13823,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[6776, 13822, 13819, 347, 13805])).
% 2.97/3.16 tff(13824,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(13825,plain,
% 2.97/3.16 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13824, 13761, 13658, 13662, 13608, 13667, 13731, 3819, 3615, 2, 13665, 12942])).
% 2.97/3.16 tff(13826,plain,
% 2.97/3.16 (~(elem!1 = s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[234, 13761])).
% 2.97/3.16 tff(13827,plain,
% 2.97/3.16 (~b(z, s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[13648, 3615, 150, 423, 2, 152])).
% 2.97/3.16 tff(13828,plain,
% 2.97/3.16 (r(z, s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[593, 13827])).
% 2.97/3.16 tff(13829,plain,
% 2.97/3.16 (~r(s(s(z)), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[12747, 3827, 150, 13828])).
% 2.97/3.16 tff(13830,plain,
% 2.97/3.16 (b(s(s(z)), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[487, 13829])).
% 2.97/3.16 tff(13831,plain,
% 2.97/3.16 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[12885, 13830, 150, 423, 13828, 3615, 2])).
% 2.97/3.16 tff(13832,plain,
% 2.97/3.16 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[3841, 13831])).
% 2.97/3.16 tff(13833,plain,
% 2.97/3.16 (~r(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[12124, 163, 150, 13828, 3827])).
% 2.97/3.16 tff(13834,plain,
% 2.97/3.16 (b(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[4110, 13833])).
% 2.97/3.16 tff(13835,plain,
% 2.97/3.16 (~r(elem!1, z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[12367, 13286, 150, 13828])).
% 2.97/3.17 tff(13836,plain,
% 2.97/3.17 (b(elem!1, z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[187, 13835, 76])).
% 2.97/3.17 tff(13837,plain,
% 2.97/3.17 (~r(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13294, 225, 2, 150, 149, 3615])).
% 2.97/3.17 tff(13838,plain,
% 2.97/3.17 (b(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[102, 13837, 1999])).
% 2.97/3.17 tff(13839,plain,
% 2.97/3.17 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[5536, 198, 13838, 13836, 13834, 13832])).
% 2.97/3.17 tff(13840,plain,
% 2.97/3.17 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12769, 198, 13624, 9363, 13832])).
% 2.97/3.17 tff(13841,plain,
% 2.97/3.17 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[511, 26, 508, 13840])).
% 2.97/3.17 tff(13842,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3626, 13830, 2, 3615])).
% 2.97/3.17 tff(13843,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[374, 13842])).
% 2.97/3.17 tff(13844,plain,
% 2.97/3.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[5798, 163, 13843, 423, 13841])).
% 2.97/3.17 tff(13845,plain,
% 2.97/3.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3328, 26, 13844])).
% 2.97/3.17 tff(13846,plain,
% 2.97/3.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13845, 2935])).
% 2.97/3.17 tff(13847,plain,
% 2.97/3.17 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12057, 198, 3819, 13834, 13846])).
% 2.97/3.17 tff(13848,plain,
% 2.97/3.17 (r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[31, 13847])).
% 2.97/3.17 tff(13849,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13824, 13289, 13624, 13843, 423, 13848, 12414, 3819, 3615, 2, 13846, 152])).
% 2.97/3.17 tff(13850,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4810, 13849, 13839])).
% 2.97/3.17 tff(13851,plain,
% 2.97/3.17 (~b(s(z), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13790, 198, 3819, 3615, 13846])).
% 2.97/3.17 tff(13852,plain,
% 2.97/3.17 (r(s(z), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3301, 13851])).
% 2.97/3.17 tff(13853,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13854,plain,
% 2.97/3.17 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13855,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13854])).
% 2.97/3.17 tff(13856,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13855, 13853])).
% 2.97/3.17 tff(13857,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13858,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13857, 13856])).
% 2.97/3.17 tff(13859,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13858, 163, 13286, 13852, 3827, 13850])).
% 2.97/3.17 tff(13860,plain,((s(z) = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z) | (~r(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(13861,plain,
% 2.97/3.17 (b(s(z), elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13860, 13760, 3819, 3615, 2, 12942, 13729, 150, 13608])).
% 2.97/3.17 tff(13862,plain,
% 2.97/3.17 (~(s(s(z)) = elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13224, 1475, 49])).
% 2.97/3.17 tff(13863,plain,
% 2.97/3.17 (~(elem!1 = s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[8661, 13862])).
% 2.97/3.17 tff(13864,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12141, 198, 347, 5428, 4167])).
% 2.97/3.17 tff(13865,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13864])).
% 2.97/3.17 tff(13866,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13867,plain,
% 2.97/3.17 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13868,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13867])).
% 2.97/3.17 tff(13869,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13868, 13866])).
% 2.97/3.17 tff(13870,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13871,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13870, 13869])).
% 2.97/3.17 tff(13872,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13871, 163, 422, 13238, 13865, 13228])).
% 2.97/3.17 tff(13873,plain,((~b(elem!1, z)) | (~r(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(13874,plain,
% 2.97/3.17 (~b(elem!1, z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13873, 13863, 422, 5530, 347, 9403, 12745, 4167])).
% 2.97/3.17 tff(13875,plain,
% 2.97/3.17 (r(elem!1, z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[187, 13874, 76])).
% 2.97/3.17 tff(13876,plain,
% 2.97/3.17 (~r(elem!1, s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[6651, 13875, 150, 406])).
% 2.97/3.17 tff(13877,plain,
% 2.97/3.17 (b(elem!1, s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[242, 13876, 237])).
% 2.97/3.17 tff(13878,plain,
% 2.97/3.17 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13316, 13877, 152, 1475, 5927, 150, 13875])).
% 2.97/3.17 tff(13879,plain,
% 2.97/3.17 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[9265, 13878])).
% 2.97/3.17 tff(13880,plain,
% 2.97/3.17 (~(elem!1 = s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[317, 13878])).
% 2.97/3.17 tff(13881,plain,
% 2.97/3.17 (~r(s(s(elem!1)), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13334, 13880, 5927, 150, 1475, 13875])).
% 2.97/3.17 tff(13882,plain,
% 2.97/3.17 (b(s(s(elem!1)), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[801, 13881])).
% 2.97/3.17 tff(13883,plain,
% 2.97/3.17 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13342, 198, 13882, 347, 9403, 12745, 4167])).
% 2.97/3.17 tff(13884,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3400, 13883, 13879])).
% 2.97/3.17 tff(13885,plain,
% 2.97/3.17 (~b(s(s(elem!1)), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13350, 198, 13882, 347, 9403])).
% 2.97/3.17 tff(13886,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3497, 26, 12509, 13885])).
% 2.97/3.17 tff(13887,plain,
% 2.97/3.17 (~r(s(s(z)), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12747, 422, 150, 406])).
% 2.97/3.17 tff(13888,plain,
% 2.97/3.17 (b(s(s(z)), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[487, 13887])).
% 2.97/3.17 tff(13889,plain,
% 2.97/3.17 (~b(s(s(z)), elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[6661, 13877, 13888, 5927])).
% 2.97/3.17 tff(13890,plain,
% 2.97/3.17 (r(s(s(z)), elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2139, 13889, 13862])).
% 2.97/3.17 tff(13891,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13892,plain,
% 2.97/3.17 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13893,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13892])).
% 2.97/3.17 tff(13894,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13893, 13891])).
% 2.97/3.17 tff(13895,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13896,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13895, 13894])).
% 2.97/3.17 tff(13897,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13896, 163, 13890, 13886, 13412, 13884])).
% 2.97/3.17 tff(13898,plain,((~r(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (elem!1 = z) | (~r(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(13899,plain,
% 2.97/3.17 (~r(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13898, 13654, 9363, 13658, 13861, 150, 12942, 13826, 13650, 13729, 3827, 13825, 49])).
% 2.97/3.17 tff(13900,plain,
% 2.97/3.17 (b(z, elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[102, 13899, 13730])).
% 2.97/3.17 tff(13901,plain,
% 2.97/3.17 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3468, 13900, 13666])).
% 2.97/3.17 tff(13902,plain,
% 2.97/3.17 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3792, 13901])).
% 2.97/3.17 tff(13903,plain,
% 2.97/3.17 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13579, 163, 833, 406, 152])).
% 2.97/3.17 tff(13904,plain,
% 2.97/3.17 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[7965, 198, 5927, 6674, 3615, 2])).
% 2.97/3.17 tff(13905,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[703, 13904, 13903, 673])).
% 2.97/3.17 tff(13906,plain,((~r(elem!1, z)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(13907,plain,
% 2.97/3.17 (~r(elem!1, z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13906, 13902, 13861, 3615, 2, 13650, 12942, 13826, 150])).
% 2.97/3.17 tff(13908,plain,
% 2.97/3.17 (b(elem!1, z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[187, 13907, 13729])).
% 2.97/3.17 tff(13909,plain,
% 2.97/3.17 (elem!1 = s(s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13873, 13908, 3827, 13825, 13658, 9363, 13656, 13654])).
% 2.97/3.17 tff(13910,plain,
% 2.97/3.17 (s(s(z)) = elem!1),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[8661, 13909])).
% 2.97/3.17 tff(13911,plain,
% 2.97/3.17 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[8694, 13910])).
% 2.97/3.17 tff(13912,plain,
% 2.97/3.17 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3249, 13911])).
% 2.97/3.17 tff(13913,plain,
% 2.97/3.17 (s(s(s(z))) = s(elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13910])).
% 2.97/3.17 tff(13914,plain,
% 2.97/3.17 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13913])).
% 2.97/3.17 tff(13915,plain,
% 2.97/3.17 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13914])).
% 2.97/3.17 tff(13916,plain,
% 2.97/3.17 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13915])).
% 2.97/3.17 tff(13917,plain,
% 2.97/3.17 (b(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13656, 13916])).
% 2.97/3.17 tff(13918,plain,
% 2.97/3.17 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13915])).
% 2.97/3.17 tff(13919,plain,
% 2.97/3.17 (b(s(s(s(elem!1))), z)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13654, 13918])).
% 2.97/3.17 tff(13920,plain,
% 2.97/3.17 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13910])).
% 2.97/3.17 tff(13921,plain,
% 2.97/3.17 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.97/3.17 inference(transitivity,[status(thm)],[13920, 112])).
% 2.97/3.17 tff(13922,plain,
% 2.97/3.17 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13921])).
% 2.97/3.17 tff(13923,plain,
% 2.97/3.17 (~(s(s(z)) = s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[822, 13731])).
% 2.97/3.17 tff(13924,plain,
% 2.97/3.17 (~(s(s(elem!1)) = elem!1)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13923, 13922])).
% 2.97/3.17 tff(13925,plain,
% 2.97/3.17 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13915])).
% 2.97/3.17 tff(13926,plain,
% 2.97/3.17 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13925])).
% 2.97/3.17 tff(13927,plain,
% 2.97/3.17 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[9862, 13910, 13760])).
% 2.97/3.17 tff(13928,plain,
% 2.97/3.17 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13927, 13926])).
% 2.97/3.17 tff(13929,plain,
% 2.97/3.17 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[13915])).
% 2.97/3.17 tff(13930,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13929])).
% 2.97/3.17 tff(13931,plain,
% 2.97/3.17 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.97/3.17 inference(symmetry,[status(thm)],[13930])).
% 2.97/3.17 tff(13932,plain,
% 2.97/3.17 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13910])).
% 2.97/3.17 tff(13933,plain,
% 2.97/3.17 (r(s(s(s(s(s(z))))), elem!1)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13660, 13932])).
% 2.97/3.17 tff(13934,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), elem!1)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13933, 13931])).
% 2.97/3.17 tff(13935,plain,
% 2.97/3.17 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13929])).
% 2.97/3.17 tff(13936,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[13935])).
% 2.97/3.17 tff(13937,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13910])).
% 2.97/3.17 tff(13938,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12141, 198, 13658, 13656, 13654])).
% 2.97/3.17 tff(13939,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2715, 26, 507, 13938])).
% 2.97/3.17 tff(13940,plain,
% 2.97/3.17 (r(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13939, 13937])).
% 2.97/3.17 tff(13941,plain,
% 2.97/3.17 (r(elem!1, s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13940, 13936])).
% 2.97/3.17 tff(13942,plain,
% 2.97/3.17 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1384, 198, 95, 271, 723, 1311, 2545])).
% 2.97/3.17 tff(13943,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1377, 13942, 1268])).
% 2.97/3.17 tff(13944,plain,
% 2.97/3.17 (r(s(s(elem!1)), elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[602, 6965, 138])).
% 2.97/3.17 tff(13945,plain,
% 2.97/3.17 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13946,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13945])).
% 2.97/3.17 tff(13947,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13946, 9889])).
% 2.97/3.17 tff(13948,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13949,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13948, 13947])).
% 2.97/3.17 tff(13950,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13949, 163, 13944, 9149, 13943, 1363])).
% 2.97/3.17 tff(13951,plain,((~b(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(13952,plain,
% 2.97/3.17 (~b(s(s(elem!1)), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13951, 13941, 13934, 13928, 13924, 13900, 13908, 13919, 13917])).
% 2.97/3.17 tff(13953,plain,
% 2.97/3.17 (r(s(s(elem!1)), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[801, 13952])).
% 2.97/3.17 tff(13954,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13955,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13956,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13955, 13954])).
% 2.97/3.17 tff(13957,plain,
% 2.97/3.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13956, 163, 13953, 13650, 12942])).
% 2.97/3.17 tff(13958,plain,
% 2.97/3.17 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4221, 13957, 13912])).
% 2.97/3.17 tff(13959,plain,
% 2.97/3.17 (~r(s(s(elem!1)), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3719, 163, 13953, 150, 13650])).
% 2.97/3.17 tff(13960,plain,
% 2.97/3.17 (b(s(s(elem!1)), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[626, 13959])).
% 2.97/3.17 tff(13961,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13962,plain,
% 2.97/3.17 (((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13963,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13962])).
% 2.97/3.17 tff(13964,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13963, 13961])).
% 2.97/3.17 tff(13965,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13966,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[13965, 13964])).
% 2.97/3.17 tff(13967,plain,
% 2.97/3.17 (~r(s(z), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13966, 163, 13953, 150, 13650])).
% 2.97/3.17 tff(13968,plain,
% 2.97/3.17 (b(s(z), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[642, 13967])).
% 2.97/3.17 tff(13969,plain,
% 2.97/3.17 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(13970,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[13969])).
% 2.97/3.17 tff(13971,plain,
% 2.97/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(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(z))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[13970, 4212])).
% 2.97/3.17 tff(13972,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(13973,plain,
% 2.97/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[13972, 13971])).
% 2.97/3.18 tff(13974,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13973, 198, 13968, 13960, 2, 13958])).
% 2.97/3.18 tff(13975,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(13976,plain,
% 2.97/3.18 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13975, 3615, 150, 2, 49])).
% 2.97/3.18 tff(13977,plain,
% 2.97/3.18 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3098, 13976])).
% 2.97/3.18 tff(13978,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(13979,plain,
% 2.97/3.18 (((~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(13980,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[13979])).
% 2.97/3.18 tff(13981,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[13980, 13978])).
% 2.97/3.18 tff(13982,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(13983,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[13982, 13981])).
% 2.97/3.18 tff(13984,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13983, 163, 406, 3066, 152, 3828])).
% 2.97/3.18 tff(13985,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, 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))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(13986,plain,
% 2.97/3.18 (~r(s(s(s(s(s(z))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13985, 13650, 13977, 12942])).
% 2.97/3.18 tff(13987,plain,
% 2.97/3.18 (b(s(s(s(s(s(z))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3841, 13986])).
% 2.97/3.18 tff(13988,plain,
% 2.97/3.18 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12769, 198, 13658, 9363, 13987])).
% 2.97/3.18 tff(13989,plain,
% 2.97/3.18 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[511, 26, 508, 13988])).
% 2.97/3.18 tff(13990,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13052, 13977, 12942, 9363, 13650])).
% 2.97/3.18 tff(13991,plain,
% 2.97/3.18 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[374, 13990])).
% 2.97/3.18 tff(13992,plain,
% 2.97/3.18 (~b(s(s(z)), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3626, 13991, 2, 3615])).
% 2.97/3.18 tff(13993,plain,
% 2.97/3.18 (r(s(s(z)), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[487, 13992])).
% 2.97/3.18 tff(13994,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12777, 163, 13977, 13993, 13608, 13989])).
% 2.97/3.18 tff(13995,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(13996,plain,
% 2.97/3.18 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13995, 2, 150, 49])).
% 2.97/3.18 tff(13997,plain,
% 2.97/3.18 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3613, 13996])).
% 2.97/3.18 tff(13998,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(13999,plain,
% 2.97/3.18 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14000,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[13999])).
% 2.97/3.18 tff(14001,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[14000, 13998])).
% 2.97/3.18 tff(14002,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(14003,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[14002, 14001])).
% 2.97/3.18 tff(14004,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14003, 163, 150, 406, 151, 152])).
% 2.97/3.18 tff(14005,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(14006,plain,
% 2.97/3.18 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14005, 13997, 150, 406])).
% 2.97/3.18 tff(14007,plain,
% 2.97/3.18 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[176, 14006])).
% 2.97/3.18 tff(14008,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14009,plain,
% 2.97/3.18 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14010,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[14009])).
% 2.97/3.18 tff(14011,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[14010, 14008])).
% 2.97/3.18 tff(14012,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(14013,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[14012, 14011])).
% 2.97/3.18 tff(14014,plain,
% 2.97/3.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14013, 198, 407, 347, 2, 14007])).
% 2.97/3.18 tff(14015,plain,
% 2.97/3.18 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[420, 14014])).
% 2.97/3.18 tff(14016,plain,
% 2.97/3.18 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[7215, 14015, 150, 13997])).
% 2.97/3.18 tff(14017,plain,
% 2.97/3.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[31, 14016])).
% 2.97/3.18 tff(14018,plain,
% 2.97/3.18 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[356, 14017, 347, 14007])).
% 2.97/3.18 tff(14019,plain,
% 2.97/3.18 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[374, 14018])).
% 2.97/3.18 tff(14020,plain,
% 2.97/3.18 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12234, 14019, 407, 11721, 406, 14015])).
% 2.97/3.18 tff(14021,plain,
% 2.97/3.18 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3098, 14020])).
% 2.97/3.18 tff(14022,plain,
% 2.97/3.18 (~b(s(s(s(s(s(z))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[4174, 14021, 14007, 14017])).
% 2.97/3.18 tff(14023,plain,
% 2.97/3.18 (r(s(s(s(s(s(z))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3841, 14022])).
% 2.97/3.18 tff(14024,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[12116, 163, 150, 406, 422, 3828])).
% 2.97/3.18 tff(14025,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(14026,plain,
% 2.97/3.18 (~r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14025, 3828, 406, 150])).
% 2.97/3.18 tff(14027,plain,
% 2.97/3.18 (b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[469, 14026])).
% 2.97/3.18 tff(14028,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[12196, 198, 12461, 2, 14027, 3404])).
% 2.97/3.18 tff(14029,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(14030,plain,
% 2.97/3.18 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14029, 14023, 150, 406, 2])).
% 2.97/3.18 tff(14031,plain,
% 2.97/3.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[9643, 14030])).
% 2.97/3.18 tff(14032,plain,
% 2.97/3.18 (~r(s(s(s(s(s(z))))), s(z))),
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% 2.97/3.18 tff(14033,plain,
% 2.97/3.18 (b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[469, 14032])).
% 2.97/3.18 tff(14034,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[7694, 14019, 13997, 14015])).
% 2.97/3.18 tff(14035,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[487, 14034])).
% 2.97/3.18 tff(14036,plain,
% 2.97/3.18 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[494, 198, 14035, 407, 14033])).
% 2.97/3.18 tff(14037,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[9576, 14036])).
% 2.97/3.18 tff(14038,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[5798, 163, 14019, 14015, 14037, 14031])).
% 2.97/3.18 tff(14039,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(14040,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[14039, 347, 41, 406, 407, 49])).
% 2.97/3.18 tff(14041,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[3654, 14040])).
% 2.97/3.18 tff(14042,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[9541, 163, 41, 406, 14041])).
% 2.97/3.18 tff(14043,plain,
% 2.97/3.18 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[31, 14042])).
% 2.97/3.18 tff(14044,plain,
% 2.97/3.18 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[9533, 14041, 41])).
% 2.97/3.18 tff(14045,plain,
% 2.97/3.18 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[176, 14044])).
% 2.97/3.18 tff(14046,plain,
% 2.97/3.18 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(z)), z)) | (~b(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))))))), z)))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14047,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[14046])).
% 2.97/3.18 tff(14048,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.97/3.18 inference(transitivity,[status(thm)],[14047, 12104])).
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% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
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% 2.97/3.18 inference(modus_ponens,[status(thm)],[14049, 14048])).
% 2.97/3.18 tff(14051,plain,
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% 2.97/3.18 tff(14052,plain,
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% 2.97/3.18 tff(14055,plain,
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% 2.97/3.18 tff(14056,plain,
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% 2.97/3.18 tff(14057,plain,
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% 2.97/3.18 tff(14058,plain,
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% 2.97/3.18 tff(14059,plain,
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% 2.97/3.18 tff(14060,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[469, 14059])).
% 2.97/3.18 tff(14061,plain,
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% 2.97/3.18 tff(14062,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[487, 14061])).
% 2.97/3.18 tff(14063,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[11867, 14062, 407, 14060])).
% 2.97/3.18 tff(14064,plain,
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% 2.97/3.18 tff(14065,plain,
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% 2.97/3.18 tff(14066,plain,
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% 2.97/3.18 tff(14067,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[10515, 198, 14056, 14043, 14066])).
% 2.97/3.18 tff(14068,plain,
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% 2.97/3.18 tff(14069,plain,
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% 2.97/3.18 tff(14070,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[3301, 14069])).
% 2.97/3.18 tff(14071,plain,
% 2.97/3.18 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[9880, 198, 14062, 407, 14070, 14060])).
% 2.97/3.18 tff(14072,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[9885, 14071])).
% 2.97/3.18 tff(14073,plain,
% 2.97/3.18 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), 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(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14074,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[14073])).
% 2.97/3.18 tff(14075,plain,
% 2.97/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[14074, 13785])).
% 2.97/3.18 tff(14076,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(14077,plain,
% 2.97/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[14076, 14075])).
% 2.97/3.18 tff(14078,plain,
% 2.97/3.18 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14077, 198, 14056, 14070, 14066])).
% 2.97/3.18 tff(14079,plain,
% 2.97/3.18 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3613, 14078])).
% 2.97/3.18 tff(14080,plain,
% 2.97/3.18 (~r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14025, 3828, 150, 406])).
% 2.97/3.18 tff(14081,plain,
% 2.97/3.18 (b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[469, 14080])).
% 2.97/3.18 tff(14082,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14083,plain,
% 2.97/3.18 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(14084,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[14083])).
% 2.97/3.18 tff(14085,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[14084, 14082])).
% 2.97/3.18 tff(14086,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(14087,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[14086, 14085])).
% 2.97/3.18 tff(14088,plain,
% 2.97/3.18 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14087, 163, 790, 406, 3828])).
% 2.97/3.18 tff(14089,plain,
% 2.97/3.18 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3400, 14088, 3396])).
% 2.97/3.18 tff(14090,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[4125, 198, 722, 6262, 559, 3405])).
% 2.97/3.18 tff(14091,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(14092,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[14091, 14089, 3721, 12461, 14081])).
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% 2.97/3.18 tff(14094,plain,
% 2.97/3.18 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14093, 790, 406, 3828, 150])).
% 2.97/3.18 tff(14095,plain,
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% 2.97/3.18 tff(14098,plain,
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% 2.97/3.18 tff(14099,plain,
% 2.97/3.18 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[14098])).
% 2.97/3.18 tff(14100,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[3384, 14094])).
% 2.97/3.18 tff(14101,plain,
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% 2.97/3.18 inference(unit_resolution,[status(thm)],[1079, 14100])).
% 2.97/3.18 tff(14102,plain,
% 2.97/3.18 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
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% 2.97/3.18 tff(14103,plain,
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% 2.97/3.19 tff(14105,plain,
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% 2.97/3.19 tff(14106,plain,
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% 2.97/3.19 tff(14107,plain,
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% 2.97/3.19 tff(14109,plain,
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% 2.97/3.19 tff(14110,plain,
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% 2.97/3.19 tff(14111,plain,
% 2.97/3.19 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
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% 2.97/3.19 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
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% 2.97/3.19 tff(14113,plain,
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% 2.97/3.19 inference(monotonicity,[status(thm)],[14094])).
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% 2.97/3.19 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(elem!1)))))),
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% 2.97/3.19 tff(14119,plain,
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% 2.97/3.19 inference(modus_ponens,[status(thm)],[151, 14118])).
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% 2.97/3.19 inference(monotonicity,[status(thm)],[14120])).
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% 2.97/3.19 inference(unit_resolution,[status(thm)],[636, 14123])).
% 2.97/3.19 tff(14125,plain,((~r(s(z), s(s(s(s(elem!1)))))) | r(s(z), s(s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(14126,plain,
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% 2.97/3.19 inference(unit_resolution,[status(thm)],[2064, 14126])).
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% 2.97/3.19 inference(unit_resolution,[status(thm)],[676, 14127])).
% 2.97/3.19 tff(14129,plain,
% 2.97/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14094])).
% 2.97/3.19 tff(14130,plain,
% 2.97/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.19 inference(symmetry,[status(thm)],[14129])).
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% 2.97/3.19 inference(monotonicity,[status(thm)],[14130])).
% 2.97/3.19 tff(14132,plain,
% 2.97/3.19 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[9641, 14131])).
% 2.97/3.19 tff(14133,plain,
% 2.97/3.19 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[11484])).
% 2.97/3.19 tff(14134,plain,
% 2.97/3.19 (~(s(z) = elem!1)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[10804, 14133])).
% 2.97/3.19 tff(14135,plain,
% 2.97/3.19 (~(s(s(z)) = elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9862, 14134, 3380])).
% 2.97/3.19 tff(14136,plain,
% 2.97/3.19 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[11482])).
% 2.97/3.19 tff(14137,plain,
% 2.97/3.19 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 2.97/3.19 inference(symmetry,[status(thm)],[14136])).
% 2.97/3.19 tff(14138,plain,
% 2.97/3.19 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(s(z)), elem!1))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14137])).
% 2.97/3.19 tff(14139,plain,
% 2.97/3.19 (r(elem!1, s(s(elem!1)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[147, 85, 116])).
% 2.97/3.19 tff(14140,plain,
% 2.97/3.19 (r(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14139, 10822])).
% 2.97/3.19 tff(14141,plain,
% 2.97/3.19 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14140, 11497])).
% 2.97/3.19 tff(14142,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14143,plain,
% 2.97/3.19 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14144,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14143])).
% 2.97/3.19 tff(14145,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[14144, 14142])).
% 2.97/3.19 tff(14146,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(14147,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14146, 14145])).
% 2.97/3.19 tff(14148,plain,
% 2.97/3.19 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14147, 163, 9580, 9472])).
% 2.97/3.19 tff(14149,plain,
% 2.97/3.19 (~r(s(s(z)), s(s(s(z))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14148, 14141])).
% 2.97/3.19 tff(14150,plain,
% 2.97/3.19 (~r(s(s(z)), elem!1)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14149, 14138])).
% 2.97/3.19 tff(14151,plain,
% 2.97/3.19 (b(s(s(z)), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[2139, 14150, 14135])).
% 2.97/3.19 tff(14152,plain,
% 2.97/3.19 (~(z = elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3384, 3380])).
% 2.97/3.19 tff(14153,plain,
% 2.97/3.19 (~(elem!1 = z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[1079, 14152])).
% 2.97/3.19 tff(14154,plain,
% 2.97/3.19 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 2.97/3.19 inference(monotonicity,[status(thm)],[11482])).
% 2.97/3.19 tff(14155,plain,
% 2.97/3.19 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 2.97/3.19 inference(symmetry,[status(thm)],[14154])).
% 2.97/3.19 tff(14156,plain,
% 2.97/3.19 ((~r(s(s(s(z))), z)) <=> (~r(elem!1, z))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14155])).
% 2.97/3.19 tff(14157,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14158,plain,
% 2.97/3.19 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14159,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14158])).
% 2.97/3.19 tff(14160,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[14159, 14157])).
% 2.97/3.19 tff(14161,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(14162,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14161, 14160])).
% 2.97/3.19 tff(14163,plain,
% 2.97/3.19 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14162, 163, 9580, 7912])).
% 2.97/3.19 tff(14164,plain,
% 2.97/3.19 (~r(s(s(s(z))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14163, 14141])).
% 2.97/3.19 tff(14165,plain,
% 2.97/3.19 (~r(elem!1, z)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14164, 14156])).
% 2.97/3.19 tff(14166,plain,
% 2.97/3.19 (b(elem!1, z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[187, 14165, 14153])).
% 2.97/3.19 tff(14167,plain,
% 2.97/3.19 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9533, 3639, 150])).
% 2.97/3.19 tff(14168,plain,
% 2.97/3.19 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[176, 14167])).
% 2.97/3.19 tff(14169,plain,
% 2.97/3.19 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[11482])).
% 2.97/3.19 tff(14170,plain,
% 2.97/3.19 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 2.97/3.19 inference(symmetry,[status(thm)],[14169])).
% 2.97/3.19 tff(14171,plain,
% 2.97/3.19 ((~r(z, s(s(s(z))))) <=> (~r(z, elem!1))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14170])).
% 2.97/3.19 tff(14172,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(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(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14173,plain,
% 2.97/3.19 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(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(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14174,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z, s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14173])).
% 2.97/3.19 tff(14175,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(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(z, s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[14174, 14172])).
% 2.97/3.19 tff(14176,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(14177,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14176, 14175])).
% 2.97/3.19 tff(14178,plain,
% 2.97/3.19 ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14177, 163, 9580, 7912])).
% 2.97/3.19 tff(14179,plain,
% 2.97/3.19 (~r(z, s(s(s(z))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14178, 14141])).
% 2.97/3.19 tff(14180,plain,
% 2.97/3.19 (~r(z, elem!1)),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14179, 14171])).
% 2.97/3.19 tff(14181,plain,
% 2.97/3.19 (b(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[102, 14180, 14152])).
% 2.97/3.19 tff(14182,plain,
% 2.97/3.19 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9622, 14181, 14168, 14166])).
% 2.97/3.19 tff(14183,plain,
% 2.97/3.19 (~(elem!1 = s(s(elem!1)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[7865, 244, 669])).
% 2.97/3.19 tff(14184,plain,
% 2.97/3.19 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[3441, 405, 151, 236])).
% 2.97/3.19 tff(14185,plain,
% 2.97/3.19 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[256, 14184, 244])).
% 2.97/3.19 tff(14186,plain,
% 2.97/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14185])).
% 2.97/3.19 tff(14187,plain,
% 2.97/3.19 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.19 inference(symmetry,[status(thm)],[14186])).
% 2.97/3.19 tff(14188,plain,
% 2.97/3.19 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[405, 14187])).
% 2.97/3.19 tff(14189,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[669, 14188])).
% 2.97/3.19 tff(14190,plain,((~r(elem!1, s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), elem!1) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(14191,plain,
% 2.97/3.19 (~r(elem!1, s(s(elem!1)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14190, 244, 669, 151, 236])).
% 2.97/3.19 tff(14192,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[147, 14191, 14183, 85])).
% 2.97/3.19 tff(14193,plain,(b(s(s(s(s(s(s(s(z))))))), elem!1) | b(elem!1, s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(14194,plain,
% 2.97/3.19 (~r(s(z), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14193, 14182, 85, 151, 669])).
% 2.97/3.19 tff(14195,plain,
% 2.97/3.19 (b(s(z), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[217, 14194, 14134])).
% 2.97/3.19 tff(14196,plain,
% 2.97/3.19 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9265, 3380])).
% 2.97/3.19 tff(14197,plain,
% 2.97/3.19 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[256, 14182, 14196])).
% 2.97/3.19 tff(14198,plain,
% 2.97/3.19 (~r(elem!1, s(z))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9665, 14197, 150, 3639])).
% 2.97/3.19 tff(14199,plain,
% 2.97/3.19 (b(elem!1, s(z))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[242, 14198, 11487])).
% 2.97/3.19 tff(14200,plain,
% 2.97/3.19 ($false),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[6661, 14199, 14195, 560, 14151])).
% 2.97/3.19 tff(14201,plain,(b(elem!1, s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.19 tff(14202,plain,
% 2.97/3.19 (b(elem!1, s(s(elem!1)))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14201, 14132, 150, 3639, 151, 560, 14094, 9580, 9472, 7912, 14128])).
% 2.97/3.19 tff(14203,plain,
% 2.97/3.19 (b(elem!1, s(s(s(s(s(z))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14202, 14113])).
% 2.97/3.19 tff(14204,plain,
% 2.97/3.19 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14203, 14112])).
% 2.97/3.19 tff(14205,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14206,plain,
% 2.97/3.19 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(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))))))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14207,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14206])).
% 2.97/3.19 tff(14208,plain,
% 2.97/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[14207, 14205])).
% 2.97/3.19 tff(14209,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.19 tff(14210,plain,
% 2.97/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14209, 14208])).
% 2.97/3.19 tff(14211,plain,
% 2.97/3.19 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14210, 198, 12461, 14081])).
% 2.97/3.19 tff(14212,plain,
% 2.97/3.19 (~b(s(s(s(z))), s(z))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[14211, 14204])).
% 2.97/3.19 tff(14213,plain,
% 2.97/3.19 (~b(elem!1, s(z))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14212, 14110])).
% 2.97/3.19 tff(14214,plain,
% 2.97/3.19 (r(elem!1, s(z))),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[242, 14213, 14107])).
% 2.97/3.19 tff(14215,plain,
% 2.97/3.19 (~r(elem!1, z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[6651, 14214, 150, 406])).
% 2.97/3.19 tff(14216,plain,
% 2.97/3.19 (b(elem!1, z)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[187, 14215, 14101])).
% 2.97/3.19 tff(14217,plain,
% 2.97/3.19 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9265, 14094])).
% 2.97/3.19 tff(14218,plain,
% 2.97/3.19 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9665, 14214, 150, 3639])).
% 2.97/3.19 tff(14219,plain,
% 2.97/3.19 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[256, 14218, 14217])).
% 2.97/3.19 tff(14220,plain,
% 2.97/3.19 (~b(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[9622, 14219, 14168, 14216])).
% 2.97/3.19 tff(14221,plain,
% 2.97/3.19 (r(z, elem!1)),
% 2.97/3.19 inference(unit_resolution,[status(thm)],[102, 14220, 14100])).
% 2.97/3.19 tff(14222,plain,
% 2.97/3.19 (r(z, s(s(s(z))))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14221, 14099])).
% 2.97/3.19 tff(14223,plain,
% 2.97/3.19 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14098])).
% 2.97/3.19 tff(14224,plain,
% 2.97/3.19 (r(s(s(s(z))), s(z))),
% 2.97/3.19 inference(modus_ponens,[status(thm)],[14214, 14223])).
% 2.97/3.19 tff(14225,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14226,plain,
% 2.97/3.19 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.97/3.19 inference(rewrite,[status(thm)],[])).
% 2.97/3.19 tff(14227,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.97/3.19 inference(monotonicity,[status(thm)],[14226])).
% 2.97/3.19 tff(14228,plain,
% 2.97/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.97/3.19 inference(transitivity,[status(thm)],[14227, 14225])).
% 2.97/3.19 tff(14229,plain,
% 2.97/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.97/3.19 inference(quant_inst,[status(thm)],[])).
% 2.97/3.20 tff(14230,plain,
% 2.97/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.97/3.20 inference(modus_ponens,[status(thm)],[14229, 14228])).
% 2.97/3.20 tff(14231,plain,
% 2.97/3.20 ($false),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[14230, 163, 150, 406, 14224, 14222])).
% 2.97/3.20 tff(14232,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.20 tff(14233,plain,
% 2.97/3.20 (~r(s(s(elem!1)), z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[14232, 14041, 406, 41, 14079, 14062, 14064, 14072, 14068, 14065, 14058])).
% 2.97/3.20 tff(14234,plain,
% 2.97/3.20 (b(s(s(elem!1)), z)),
% 2.97/3.20 inference(unit_resolution,[status(thm)],[801, 14233])).
% 2.97/3.20 tff(14235,plain,
% 2.97/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(14236,plain,
% 2.97/3.20 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(rewrite,[status(thm)],[])).
% 2.97/3.20 tff(14237,plain,
% 2.97/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.97/3.20 inference(monotonicity,[status(thm)],[14236])).
% 2.97/3.20 tff(14238,plain,
% 2.97/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.97/3.20 inference(transitivity,[status(thm)],[14237, 14235])).
% 2.97/3.20 tff(14239,plain,
% 2.97/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14240,plain,
% 3.05/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14239, 14238])).
% 3.05/3.20 tff(14241,plain,
% 3.05/3.20 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14240, 198, 14234, 347, 14043, 14045, 11721])).
% 3.05/3.20 tff(14242,plain,
% 3.05/3.20 (r(z, s(s(s(s(s(z))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[4110, 4105])).
% 3.05/3.20 tff(14243,plain,
% 3.05/3.20 (~(s(s(elem!1)) = s(s(z)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[3493, 5276])).
% 3.05/3.20 tff(14244,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14245,plain,
% 3.05/3.20 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14246,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14245])).
% 3.05/3.20 tff(14247,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14246, 14244])).
% 3.05/3.20 tff(14248,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14249,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14248, 14247])).
% 3.05/3.20 tff(14250,plain,
% 3.05/3.20 (~r(s(s(elem!1)), s(s(z)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14249, 163, 9580, 9472, 3386])).
% 3.05/3.20 tff(14251,plain,
% 3.05/3.20 (b(s(s(elem!1)), s(s(z)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[3497, 26, 14250, 10705])).
% 3.05/3.20 tff(14252,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14253,plain,
% 3.05/3.20 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14254,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14253])).
% 3.05/3.20 tff(14255,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14254, 14252])).
% 3.05/3.20 tff(14256,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(elem!1)))))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14257,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14256, 14255])).
% 3.05/3.20 tff(14258,plain,
% 3.05/3.20 (~r(z, s(s(elem!1)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14257, 163, 9580, 7912, 3386])).
% 3.05/3.20 tff(14259,plain,
% 3.05/3.20 (b(z, s(s(elem!1)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[1096, 14258])).
% 3.05/3.20 tff(14260,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14261,plain,
% 3.05/3.20 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14262,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14261])).
% 3.05/3.20 tff(14263,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14262, 14260])).
% 3.05/3.20 tff(14264,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), z)))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14265,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14264, 14263])).
% 3.05/3.20 tff(14266,plain,
% 3.05/3.20 (~r(s(s(elem!1)), z)),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14265, 163, 9580, 7912, 3386])).
% 3.05/3.20 tff(14267,plain,
% 3.05/3.20 (b(s(s(elem!1)), z)),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[801, 14266])).
% 3.05/3.20 tff(14268,plain,
% 3.05/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14269,plain,
% 3.05/3.20 (((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14270,plain,
% 3.05/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14269])).
% 3.05/3.20 tff(14271,plain,
% 3.05/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14270, 14268])).
% 3.05/3.20 tff(14272,plain,
% 3.05/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14273,plain,
% 3.05/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14272, 14271])).
% 3.05/3.20 tff(14274,plain,
% 3.05/3.20 ($false),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14273, 198, 14267, 14259, 347, 9403, 14251])).
% 3.05/3.20 tff(14275,plain,((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.20 tff(14276,plain,
% 3.05/3.20 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14275, 14243, 9403, 347, 9580, 14242, 9472])).
% 3.05/3.20 tff(14277,plain,
% 3.05/3.20 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[3400, 14276, 3396])).
% 3.05/3.20 tff(14278,plain,
% 3.05/3.20 (~b(s(s(elem!1)), s(z))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14091, 14277, 6262, 559])).
% 3.05/3.20 tff(14279,plain,
% 3.05/3.20 (r(s(s(elem!1)), s(z))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[626, 14278])).
% 3.05/3.20 tff(14280,plain,
% 3.05/3.20 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[9837, 14279, 150, 3639])).
% 3.05/3.20 tff(14281,plain,
% 3.05/3.20 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[935, 14280])).
% 3.05/3.20 tff(14282,plain,
% 3.05/3.20 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14281])).
% 3.05/3.20 tff(14283,plain,
% 3.05/3.20 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 3.05/3.20 inference(symmetry,[status(thm)],[14282])).
% 3.05/3.20 tff(14284,plain,
% 3.05/3.20 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14283])).
% 3.05/3.20 tff(14285,plain,
% 3.05/3.20 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.05/3.20 inference(symmetry,[status(thm)],[14284])).
% 3.05/3.20 tff(14286,plain,
% 3.05/3.20 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14283])).
% 3.05/3.20 tff(14287,plain,
% 3.05/3.20 ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14286])).
% 3.05/3.20 tff(14288,plain,
% 3.05/3.20 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14282])).
% 3.05/3.20 tff(14289,plain,
% 3.05/3.20 (~(s(s(z)) = elem!1)),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[8694, 14281])).
% 3.05/3.20 tff(14290,plain,
% 3.05/3.20 (~(s(s(s(elem!1))) = elem!1)),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[11360, 14281, 14289])).
% 3.05/3.20 tff(14291,plain,
% 3.05/3.20 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14281])).
% 3.05/3.20 tff(14292,plain,
% 3.05/3.20 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.05/3.20 inference(symmetry,[status(thm)],[14291])).
% 3.05/3.20 tff(14293,plain,
% 3.05/3.20 (s(s(s(s(s(z))))) = elem!1),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[10750, 14281])).
% 3.05/3.20 tff(14294,plain,
% 3.05/3.20 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.20 tff(14295,plain,
% 3.05/3.20 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), elem!1)),
% 3.05/3.20 inference(transitivity,[status(thm)],[14294, 14292])).
% 3.05/3.20 tff(14296,plain,
% 3.05/3.20 (b(s(s(elem!1)), elem!1)),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[3404, 14295])).
% 3.05/3.20 tff(14297,plain,
% 3.05/3.20 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14281])).
% 3.05/3.20 tff(14298,plain,
% 3.05/3.20 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.05/3.20 inference(symmetry,[status(thm)],[14297])).
% 3.05/3.20 tff(14299,plain,
% 3.05/3.20 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.20 tff(14300,plain,
% 3.05/3.20 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14299, 14298])).
% 3.05/3.20 tff(14301,plain,
% 3.05/3.20 (b(elem!1, s(s(elem!1)))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[3819, 14300])).
% 3.05/3.20 tff(14302,plain,
% 3.05/3.20 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.20 tff(14303,plain,
% 3.05/3.20 (b(elem!1, s(z))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[559, 14302])).
% 3.05/3.20 tff(14304,plain,
% 3.05/3.20 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14077, 198, 3819, 6262, 3404])).
% 3.05/3.20 tff(14305,plain,
% 3.05/3.20 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[3613, 14304])).
% 3.05/3.20 tff(14306,plain,
% 3.05/3.20 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[14050, 198, 347, 14168, 9403])).
% 3.05/3.20 tff(14307,plain,
% 3.05/3.20 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[420, 14306])).
% 3.05/3.20 tff(14308,plain,
% 3.05/3.20 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), elem!1)),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.20 tff(14309,plain,
% 3.05/3.20 (b(s(z), elem!1)),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[6262, 14308])).
% 3.05/3.20 tff(14310,plain,
% 3.05/3.20 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[1874, 1310, 68, 1128])).
% 3.05/3.20 tff(14311,plain,
% 3.05/3.20 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.05/3.20 inference(unit_resolution,[status(thm)],[1326, 14310, 11422])).
% 3.05/3.20 tff(14312,plain,
% 3.05/3.20 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14311, 11421])).
% 3.05/3.20 tff(14313,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14314,plain,
% 3.05/3.20 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.20 inference(rewrite,[status(thm)],[])).
% 3.05/3.20 tff(14315,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.20 inference(monotonicity,[status(thm)],[14314])).
% 3.05/3.20 tff(14316,plain,
% 3.05/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.20 inference(transitivity,[status(thm)],[14315, 14313])).
% 3.05/3.20 tff(14317,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 3.05/3.20 inference(quant_inst,[status(thm)],[])).
% 3.05/3.20 tff(14318,plain,
% 3.05/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.20 inference(modus_ponens,[status(thm)],[14317, 14316])).
% 3.05/3.20 tff(14319,plain,
% 3.05/3.20 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14318, 163, 151, 423])).
% 3.05/3.21 tff(14320,plain,
% 3.05/3.21 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14319, 14312])).
% 3.05/3.21 tff(14321,plain,
% 3.05/3.21 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[11338])).
% 3.05/3.21 tff(14322,plain,
% 3.05/3.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.05/3.21 inference(symmetry,[status(thm)],[14321])).
% 3.05/3.21 tff(14323,plain,
% 3.05/3.21 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[1310, 14322])).
% 3.05/3.21 tff(14324,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14325,plain,
% 3.05/3.21 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14326,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14325])).
% 3.05/3.21 tff(14327,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(transitivity,[status(thm)],[14326, 14324])).
% 3.05/3.21 tff(14328,plain,
% 3.05/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14329,plain,
% 3.05/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14328, 14327])).
% 3.05/3.21 tff(14330,plain,
% 3.05/3.21 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14329, 198, 5927, 320])).
% 3.05/3.21 tff(14331,plain,
% 3.05/3.21 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14330, 14323])).
% 3.05/3.21 tff(14332,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(z)), introduced(assumption)).
% 3.05/3.21 tff(14333,plain,
% 3.05/3.21 (s(s(s(elem!1))) = s(z)),
% 3.05/3.21 inference(transitivity,[status(thm)],[11337, 14332])).
% 3.05/3.21 tff(14334,plain,
% 3.05/3.21 ($false),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1282, 14333])).
% 3.05/3.21 tff(14335,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.21 tff(14336,plain,
% 3.05/3.21 (~(s(s(s(s(s(s(s(s(z)))))))) = s(z))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14335, 2840])).
% 3.05/3.21 tff(14337,plain,
% 3.05/3.21 ($false),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[11403, 26, 14336, 14331, 14320])).
% 3.05/3.21 tff(14338,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.21 tff(14339,plain,
% 3.05/3.21 (~b(s(s(s(elem!1))), elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14338, 14309, 14307, 14305, 14303, 14281, 11422, 14301, 14296])).
% 3.05/3.21 tff(14340,plain,
% 3.05/3.21 (r(s(s(s(elem!1))), elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1308, 14339, 14290])).
% 3.05/3.21 tff(14341,plain,
% 3.05/3.21 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14340, 14288])).
% 3.05/3.21 tff(14342,plain,
% 3.05/3.21 (r(s(s(s(s(s(z))))), z) <=> r(elem!1, z)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.21 tff(14343,plain,
% 3.05/3.21 (r(elem!1, z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[3828, 14342])).
% 3.05/3.21 tff(14344,plain,
% 3.05/3.21 (~b(z, elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[10743, 14293, 4105])).
% 3.05/3.21 tff(14345,plain,
% 3.05/3.21 (r(z, elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[102, 14344, 3])).
% 3.05/3.21 tff(14346,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14347,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z)))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14348,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), z))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14347, 14346])).
% 3.05/3.21 tff(14349,plain,
% 3.05/3.21 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14348, 163, 14345, 14343, 14341])).
% 3.05/3.21 tff(14350,plain,
% 3.05/3.21 (~r(s(s(s(elem!1))), z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14349, 14287])).
% 3.05/3.21 tff(14351,plain,
% 3.05/3.21 (b(s(s(s(elem!1))), z)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1295, 14350])).
% 3.05/3.21 tff(14352,plain,
% 3.05/3.21 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14351, 14285])).
% 3.05/3.21 tff(14353,plain,
% 3.05/3.21 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14293])).
% 3.05/3.21 tff(14354,plain,
% 3.05/3.21 (r(s(s(z)), elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[9472, 14353])).
% 3.05/3.21 tff(14355,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14356,plain,
% 3.05/3.21 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14357,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14356])).
% 3.05/3.21 tff(14358,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.05/3.21 inference(transitivity,[status(thm)],[14357, 14355])).
% 3.05/3.21 tff(14359,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14360,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14359, 14358])).
% 3.05/3.21 tff(14361,plain,
% 3.05/3.21 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14360, 163, 14343, 14354, 14341])).
% 3.05/3.21 tff(14362,plain,
% 3.05/3.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14363,plain,
% 3.05/3.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14364,plain,
% 3.05/3.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14363, 14362])).
% 3.05/3.21 tff(14365,plain,
% 3.05/3.21 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14364, 26, 11379, 14361])).
% 3.05/3.21 tff(14366,plain,
% 3.05/3.21 (r(z, s(s(s(s(s(s(s(s(z))))))))) <=> r(z, s(s(s(elem!1))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14283])).
% 3.05/3.21 tff(14367,plain,
% 3.05/3.21 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14366])).
% 3.05/3.21 tff(14368,plain,
% 3.05/3.21 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14367])).
% 3.05/3.21 tff(14369,plain,
% 3.05/3.21 (~r(z, s(s(s(elem!1))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[8223, 14340, 14343, 14345])).
% 3.05/3.21 tff(14370,plain,
% 3.05/3.21 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14369, 14368])).
% 3.05/3.21 tff(14371,plain,
% 3.05/3.21 ((z = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = z)),
% 3.05/3.21 inference(commutativity,[status(thm)],[])).
% 3.05/3.21 tff(14372,plain,
% 3.05/3.21 ((s(s(s(s(s(s(s(s(z)))))))) = z) <=> (z = s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14371])).
% 3.05/3.21 tff(14373,plain,
% 3.05/3.21 ((~(s(s(s(s(s(s(s(s(z)))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14372])).
% 3.05/3.21 tff(14374,plain,
% 3.05/3.21 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(z)))))))) = z))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14375,plain,
% 3.05/3.21 (~(s(s(s(s(s(s(s(s(z)))))))) = z)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14374, 13])).
% 3.05/3.21 tff(14376,plain,
% 3.05/3.21 (~(z = s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14375, 14373])).
% 3.05/3.21 tff(14377,plain,
% 3.05/3.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14378,plain,
% 3.05/3.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14379,plain,
% 3.05/3.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14378, 14377])).
% 3.05/3.21 tff(14380,plain,
% 3.05/3.21 ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14379, 26])).
% 3.05/3.21 tff(14381,plain,
% 3.05/3.21 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14380, 14376, 14370])).
% 3.05/3.21 tff(14382,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14383,plain,
% 3.05/3.21 (((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14384,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14383])).
% 3.05/3.21 tff(14385,plain,
% 3.05/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.21 inference(transitivity,[status(thm)],[14384, 14382])).
% 3.05/3.21 tff(14386,plain,
% 3.05/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14387,plain,
% 3.05/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(s(z)))))))), z)) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14386, 14385])).
% 3.05/3.21 tff(14388,plain,
% 3.05/3.21 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14387, 198, 347, 14381, 14365])).
% 3.05/3.21 tff(14389,plain,
% 3.05/3.21 ($false),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14388, 14352])).
% 3.05/3.21 tff(14390,plain,((z = elem!1) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(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(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.21 tff(14391,plain,
% 3.05/3.21 (z = elem!1),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14390, 1866, 347, 14058, 14066, 14072, 14060, 14070, 14056, 14067, 14241, 41, 14041, 3396, 11721, 14064])).
% 3.05/3.21 tff(14392,plain,
% 3.05/3.21 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14393,plain,
% 3.05/3.21 (b(elem!1, s(s(z)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[11721, 14392])).
% 3.05/3.21 tff(14394,plain,
% 3.05/3.21 (elem!1 = z),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[78, 14391])).
% 3.05/3.21 tff(14395,plain,
% 3.05/3.21 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1032, 14394, 14045])).
% 3.05/3.21 tff(14396,plain,
% 3.05/3.21 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14397,plain,
% 3.05/3.21 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14043, 14396])).
% 3.05/3.21 tff(14398,plain,
% 3.05/3.21 (~r(s(s(elem!1)), s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[4766, 14391, 14061])).
% 3.05/3.21 tff(14399,plain,
% 3.05/3.21 (b(s(s(elem!1)), s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1143, 14398, 6709])).
% 3.05/3.21 tff(14400,plain,
% 3.05/3.21 (b(s(s(elem!1)), s(z))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[2972, 14399, 14391])).
% 3.05/3.21 tff(14401,plain,
% 3.05/3.21 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14091, 14400, 14070, 14060])).
% 3.05/3.21 tff(14402,plain,
% 3.05/3.21 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[3400, 14401, 3396])).
% 3.05/3.21 tff(14403,plain,
% 3.05/3.21 (s(s(elem!1)) = s(s(z))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14275, 14402, 11721, 347, 14064, 14068, 14072])).
% 3.05/3.21 tff(14404,plain,
% 3.05/3.21 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14403])).
% 3.05/3.21 tff(14405,plain,
% 3.05/3.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14404])).
% 3.05/3.21 tff(14406,plain,
% 3.05/3.21 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14407,plain,
% 3.05/3.21 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14406])).
% 3.05/3.21 tff(14408,plain,
% 3.05/3.21 (~(s(s(s(elem!1))) = elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[968, 14407])).
% 3.05/3.21 tff(14409,plain,
% 3.05/3.21 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14410,plain,
% 3.05/3.21 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 3.05/3.21 inference(symmetry,[status(thm)],[14409])).
% 3.05/3.21 tff(14411,plain,
% 3.05/3.21 (s(z) = s(elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14412,plain,
% 3.05/3.21 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14411])).
% 3.05/3.21 tff(14413,plain,
% 3.05/3.21 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 3.05/3.21 inference(transitivity,[status(thm)],[14412, 14410])).
% 3.05/3.21 tff(14414,plain,
% 3.05/3.21 (~b(s(z), elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[5930, 14391, 34])).
% 3.05/3.21 tff(14415,plain,
% 3.05/3.21 (~(s(z) = elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[9821, 14395, 14040])).
% 3.05/3.21 tff(14416,plain,
% 3.05/3.21 (r(s(z), elem!1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[217, 14415, 14414])).
% 3.05/3.21 tff(14417,plain,
% 3.05/3.21 (r(s(elem!1), z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14416, 14413])).
% 3.05/3.21 tff(14418,plain,
% 3.05/3.21 (r(z, s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[3155, 14394, 406])).
% 3.05/3.21 tff(14419,plain,
% 3.05/3.21 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.21 tff(14420,plain,
% 3.05/3.21 (r(s(s(s(s(s(z))))), elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14058, 14419])).
% 3.05/3.21 tff(14421,plain,
% 3.05/3.21 (s(elem!1) = s(z)),
% 3.05/3.21 inference(symmetry,[status(thm)],[14411])).
% 3.05/3.21 tff(14422,plain,
% 3.05/3.21 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14421, 14403])).
% 3.05/3.21 tff(14423,plain,
% 3.05/3.21 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14422])).
% 3.05/3.21 tff(14424,plain,
% 3.05/3.21 (b(s(elem!1), s(s(elem!1)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[407, 14423])).
% 3.05/3.21 tff(14425,plain,
% 3.05/3.21 (b(s(elem!1), s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[6266, 14391, 14070])).
% 3.05/3.21 tff(14426,plain,
% 3.05/3.21 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14411])).
% 3.05/3.21 tff(14427,plain,
% 3.05/3.21 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14060, 14426])).
% 3.05/3.21 tff(14428,plain,
% 3.05/3.21 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14403])).
% 3.05/3.21 tff(14429,plain,
% 3.05/3.21 (b(s(s(z)), s(elem!1))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14399, 14428])).
% 3.05/3.21 tff(14430,plain,
% 3.05/3.21 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[5827])).
% 3.05/3.21 tff(14431,plain,
% 3.05/3.21 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 3.05/3.21 inference(symmetry,[status(thm)],[14430])).
% 3.05/3.21 tff(14432,plain,
% 3.05/3.21 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.05/3.21 inference(monotonicity,[status(thm)],[4889, 57])).
% 3.05/3.21 tff(14433,plain,
% 3.05/3.21 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 3.05/3.21 inference(symmetry,[status(thm)],[14432])).
% 3.05/3.21 tff(14434,plain,
% 3.05/3.21 (r(s(s(s(z))), z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[1363, 14433])).
% 3.05/3.21 tff(14435,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 3.05/3.21 tff(14436,plain,
% 3.05/3.21 ($false),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14435, 14434])).
% 3.05/3.21 tff(14437,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(z))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.21 tff(14438,plain,
% 3.05/3.21 (r(s(s(s(z))), z)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14437, 1363, 57])).
% 3.05/3.21 tff(14439,plain,
% 3.05/3.21 (r(s(s(s(z))), elem!1)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14438, 14431])).
% 3.05/3.21 tff(14440,plain,
% 3.05/3.21 (r(elem!1, s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[3231, 791, 79])).
% 3.05/3.21 tff(14441,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14442,plain,
% 3.05/3.21 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(14443,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[14442])).
% 3.05/3.21 tff(14444,plain,
% 3.05/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 3.05/3.21 inference(transitivity,[status(thm)],[14443, 14441])).
% 3.05/3.21 tff(14445,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(14446,plain,
% 3.05/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14445, 14444])).
% 3.05/3.21 tff(14447,plain,
% 3.05/3.21 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14446, 163, 14440, 3109])).
% 3.05/3.21 tff(14448,plain,
% 3.05/3.21 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[14447, 14439])).
% 3.05/3.21 tff(14449,plain,
% 3.05/3.21 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[10622, 79])).
% 3.05/3.21 tff(14450,plain,
% 3.05/3.21 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[10626, 26, 14449, 14448])).
% 3.05/3.21 tff(14451,plain,
% 3.05/3.21 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[3491])).
% 3.05/3.21 tff(14452,plain,
% 3.05/3.21 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14451])).
% 3.05/3.21 tff(14453,plain,
% 3.05/3.21 (b(s(elem!1), s(s(z)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[1328, 14452])).
% 3.05/3.21 tff(14454,plain,
% 3.05/3.21 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[2936])).
% 3.05/3.21 tff(14455,plain,
% 3.05/3.21 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14454])).
% 3.05/3.21 tff(14456,plain,
% 3.05/3.21 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[10525, 58])).
% 3.05/3.21 tff(14457,plain,
% 3.05/3.21 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 3.05/3.21 inference(symmetry,[status(thm)],[14456])).
% 3.05/3.21 tff(14458,plain,
% 3.05/3.21 (r(s(s(s(elem!1))), z)),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[1363, 10555])).
% 3.05/3.21 tff(14459,plain,
% 3.05/3.21 (~r(s(s(s(elem!1))), s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1358, 14458, 791, 1221])).
% 3.05/3.21 tff(14460,plain,
% 3.05/3.21 (b(s(s(s(elem!1))), s(elem!1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[1339, 14459, 1256])).
% 3.05/3.21 tff(14461,plain,
% 3.05/3.21 (b(s(s(s(z))), s(z))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[14460, 14457])).
% 3.05/3.21 tff(14462,plain,
% 3.05/3.21 (b(s(s(s(z))), s(elem!1))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14461, 14455])).
% 3.05/3.22 tff(14463,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14464,plain,
% 3.05/3.22 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14465,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14464])).
% 3.05/3.22 tff(14466,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[14465, 14463])).
% 3.05/3.22 tff(14467,plain,
% 3.05/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(14468,plain,
% 3.05/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14467, 14466])).
% 3.05/3.22 tff(14469,plain,
% 3.05/3.22 ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14468, 198, 6774, 3169, 6276])).
% 3.05/3.22 tff(14470,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14469, 14462, 14453, 14450])).
% 3.05/3.22 tff(14471,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~(z = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14472,plain,
% 3.05/3.22 (~r(s(s(s(elem!1))), elem!1)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14471, 14429, 14427, 14425, 14391, 14424, 14403, 14420, 1846, 14418, 14417])).
% 3.05/3.22 tff(14473,plain,
% 3.05/3.22 (b(s(s(s(elem!1))), elem!1)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[1308, 14472, 14408])).
% 3.05/3.22 tff(14474,plain,
% 3.05/3.22 (b(s(s(s(z))), elem!1)),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14473, 14405])).
% 3.05/3.22 tff(14475,plain,
% 3.05/3.22 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14391])).
% 3.05/3.22 tff(14476,plain,
% 3.05/3.22 (b(s(s(z)), elem!1)),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[347, 14475])).
% 3.05/3.22 tff(14477,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14478,plain,
% 3.05/3.22 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14479,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14478])).
% 3.05/3.22 tff(14480,plain,
% 3.05/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[14479, 14477])).
% 3.05/3.22 tff(14481,plain,
% 3.05/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(14482,plain,
% 3.05/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14481, 14480])).
% 3.05/3.22 tff(14483,plain,
% 3.05/3.22 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14482, 198, 14476, 14474, 14397, 14395, 14393])).
% 3.05/3.22 tff(14484,plain,
% 3.05/3.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14404, 14403])).
% 3.05/3.22 tff(14485,plain,
% 3.05/3.22 (b(s(s(elem!1)), elem!1)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[2982, 14391, 14234])).
% 3.05/3.22 tff(14486,plain,
% 3.05/3.22 (~r(z, s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[12249, 14394, 49])).
% 3.05/3.22 tff(14487,plain,
% 3.05/3.22 (b(z, s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[1096, 14486])).
% 3.05/3.22 tff(14488,plain,
% 3.05/3.22 (b(elem!1, s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[87, 14487, 14394])).
% 3.05/3.22 tff(14489,plain,
% 3.05/3.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[1874, 14473, 14488, 14485])).
% 3.05/3.22 tff(14490,plain,
% 3.05/3.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[1326, 14489, 1866])).
% 3.05/3.22 tff(14491,plain,
% 3.05/3.22 (r(s(s(s(z))), s(s(z)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14490, 14484])).
% 3.05/3.22 tff(14492,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14493,plain,
% 3.05/3.22 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14494,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14493])).
% 3.05/3.22 tff(14495,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[14494, 14492])).
% 3.05/3.22 tff(14496,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(14497,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14496, 14495])).
% 3.05/3.22 tff(14498,plain,
% 3.05/3.22 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14497, 163, 14491, 14054, 14052])).
% 3.05/3.22 tff(14499,plain,
% 3.05/3.22 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[10589, 14403])).
% 3.05/3.22 tff(14500,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[10593, 26, 14499, 14498, 14483])).
% 3.05/3.22 tff(14501,plain,((s(s(elem!1)) = elem!1) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | r(z, s(s(z))) | (~r(z, s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14502,plain,
% 3.05/3.22 (s(s(elem!1)) = elem!1),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14501, 3396, 347, 407, 49, 406, 34])).
% 3.05/3.22 tff(14503,plain,
% 3.05/3.22 (b(elem!1, z)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[6671, 14502, 14234])).
% 3.05/3.22 tff(14504,plain,
% 3.05/3.22 (elem!1 = s(s(elem!1))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[118, 14502])).
% 3.05/3.22 tff(14505,plain,
% 3.05/3.22 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[317, 14504])).
% 3.05/3.22 tff(14506,plain,
% 3.05/3.22 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[3792, 14505])).
% 3.05/3.22 tff(14507,plain,
% 3.05/3.22 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[711, 14504, 14241])).
% 3.05/3.22 tff(14508,plain,
% 3.05/3.22 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[703, 14507, 14506])).
% 3.05/3.22 tff(14509,plain,
% 3.05/3.22 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[698, 14508, 14502])).
% 3.05/3.22 tff(14510,plain,
% 3.05/3.22 (~r(s(s(elem!1)), s(z))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[9837, 14509, 41, 14041])).
% 3.05/3.22 tff(14511,plain,
% 3.05/3.22 (b(s(s(elem!1)), s(z))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[626, 14510])).
% 3.05/3.22 tff(14512,plain,
% 3.05/3.22 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14091, 14511, 14070, 14060])).
% 3.05/3.22 tff(14513,plain,
% 3.05/3.22 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[3400, 14512, 3396])).
% 3.05/3.22 tff(14514,plain,
% 3.05/3.22 (s(s(elem!1)) = s(s(z))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14275, 14513, 11721, 347, 14064, 14068, 14072])).
% 3.05/3.22 tff(14515,plain,
% 3.05/3.22 (s(s(z)) = s(s(elem!1))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[3493, 14514])).
% 3.05/3.22 tff(14516,plain,
% 3.05/3.22 (s(elem!1) = s(z)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[822, 14515])).
% 3.05/3.22 tff(14517,plain,
% 3.05/3.22 (z = elem!1),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[814, 14516])).
% 3.05/3.22 tff(14518,plain,
% 3.05/3.22 (~r(z, elem!1)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[7300, 14517])).
% 3.05/3.22 tff(14519,plain,
% 3.05/3.22 (b(z, s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[110, 14518, 14504])).
% 3.05/3.22 tff(14520,plain,
% 3.05/3.22 (elem!1 = z),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[78, 14517])).
% 3.05/3.22 tff(14521,plain,
% 3.05/3.22 (b(elem!1, s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[87, 14519, 14520])).
% 3.05/3.22 tff(14522,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[1071, 14521, 14519, 14503, 14234])).
% 3.05/3.22 tff(14523,plain,((s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | r(z, s(s(z))) | (~r(z, s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14524,plain,
% 3.05/3.22 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14523, 347, 407, 49, 406, 34])).
% 3.05/3.22 tff(14525,plain,
% 3.05/3.22 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14524])).
% 3.05/3.22 tff(14526,plain,
% 3.05/3.22 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 3.05/3.22 inference(symmetry,[status(thm)],[14525])).
% 3.05/3.22 tff(14527,plain,
% 3.05/3.22 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(elem!1)), z))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14526])).
% 3.05/3.22 tff(14528,plain,
% 3.05/3.22 (~b(s(s(elem!1)), z)),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14057, 14527])).
% 3.05/3.22 tff(14529,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14234, 14528])).
% 3.05/3.22 tff(14530,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | r(z, s(s(z))) | (~r(z, s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14531,plain,
% 3.05/3.22 (~b(s(s(z)), z)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14530, 406, 49, 407, 34])).
% 3.05/3.22 tff(14532,plain,
% 3.05/3.22 (r(s(s(z)), z)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[345, 14531])).
% 3.05/3.22 tff(14533,plain,
% 3.05/3.22 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[13995, 41, 2, 49])).
% 3.05/3.22 tff(14534,plain,
% 3.05/3.22 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[3613, 14533])).
% 3.05/3.22 tff(14535,plain,
% 3.05/3.22 (~b(s(z), s(s(z)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[7219, 3745, 330, 2, 595])).
% 3.05/3.22 tff(14536,plain,
% 3.05/3.22 (r(s(z), s(s(z)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[403, 14535])).
% 3.05/3.22 tff(14537,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14538,plain,
% 3.05/3.22 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14539,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14538])).
% 3.05/3.22 tff(14540,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[14539, 14537])).
% 3.05/3.22 tff(14541,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(14542,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14541, 14540])).
% 3.05/3.22 tff(14543,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14542, 163, 150, 328, 332, 33])).
% 3.05/3.22 tff(14544,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14545,plain,
% 3.05/3.22 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14544, 14536, 41, 332])).
% 3.05/3.22 tff(14546,plain,
% 3.05/3.22 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[31, 14545])).
% 3.05/3.22 tff(14547,plain,
% 3.05/3.22 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[9459, 14546, 9363, 3745])).
% 3.05/3.22 tff(14548,plain,
% 3.05/3.22 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[374, 14547])).
% 3.05/3.22 tff(14549,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14550,plain,
% 3.05/3.22 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14551,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[14550])).
% 3.05/3.22 tff(14552,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[14551, 14549])).
% 3.05/3.22 tff(14553,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(14554,plain,
% 3.05/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[14553, 14552])).
% 3.05/3.22 tff(14555,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14554, 163, 328, 151, 3272, 680])).
% 3.05/3.22 tff(14556,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(14557,plain,
% 3.05/3.22 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[14556, 14536, 14534, 14548])).
% 3.05/3.22 tff(14558,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14559,plain,
% 3.05/3.22 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(14560,plain,
% 3.05/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14559])).
% 3.05/3.23 tff(14561,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14560, 14558])).
% 3.05/3.23 tff(14562,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14563,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14562, 14561])).
% 3.05/3.23 tff(14564,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14563, 163, 1098, 150, 328, 332])).
% 3.05/3.23 tff(14565,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14566,plain,
% 3.05/3.23 (~r(z, s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14565, 14536, 41, 332])).
% 3.05/3.23 tff(14567,plain,
% 3.05/3.23 (b(z, s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[1096, 14566])).
% 3.05/3.23 tff(14568,plain,
% 3.05/3.23 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3249, 7346])).
% 3.05/3.23 tff(14569,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[4221, 14568, 669])).
% 3.05/3.23 tff(14570,plain,
% 3.05/3.23 (b(z, s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[9403, 13740])).
% 3.05/3.23 tff(14571,plain,
% 3.05/3.23 (~(s(s(elem!1)) = s(elem!1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[1138, 1002])).
% 3.05/3.23 tff(14572,plain,
% 3.05/3.23 (r(s(z), s(elem!1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[5120, 2915, 328])).
% 3.05/3.23 tff(14573,plain,
% 3.05/3.23 (~r(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[5201, 840, 595, 83, 14572])).
% 3.05/3.23 tff(14574,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[1143, 14573, 14571])).
% 3.05/3.23 tff(14575,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14576,plain,
% 3.05/3.23 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14577,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14576])).
% 3.05/3.23 tff(14578,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14577, 14575])).
% 3.05/3.23 tff(14579,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14580,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14579, 14578])).
% 3.05/3.23 tff(14581,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14580, 198, 14574, 14570, 83, 331, 14569])).
% 3.05/3.23 tff(14582,plain,((~(s(z) = elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14583,plain,
% 3.05/3.23 (~(s(z) = elem!1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14582, 14567, 14546, 595, 9363, 332, 14557, 14536])).
% 3.05/3.23 tff(14584,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14585,plain,
% 3.05/3.23 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14586,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14585])).
% 3.05/3.23 tff(14587,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14586, 14584])).
% 3.05/3.23 tff(14588,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14589,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14588, 14587])).
% 3.05/3.23 tff(14590,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14589, 163, 1475, 150, 328, 332])).
% 3.05/3.23 tff(14591,plain,((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14592,plain,
% 3.05/3.23 (~r(z, elem!1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14591, 14536, 41, 332])).
% 3.05/3.23 tff(14593,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14594,plain,
% 3.05/3.23 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14595,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14594])).
% 3.05/3.23 tff(14596,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14595, 14593])).
% 3.05/3.23 tff(14597,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14598,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14597, 14596])).
% 3.05/3.23 tff(14599,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14598, 163, 150, 328, 332, 7912])).
% 3.05/3.23 tff(14600,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14601,plain,
% 3.05/3.23 (~r(z, s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14600, 14536, 41, 332])).
% 3.05/3.23 tff(14602,plain,
% 3.05/3.23 (b(z, s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[4110, 14601])).
% 3.05/3.23 tff(14603,plain,
% 3.05/3.23 (~b(s(z), elem!1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[5930, 57, 34])).
% 3.05/3.23 tff(14604,plain,
% 3.05/3.23 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[13995, 150, 2, 49])).
% 3.05/3.23 tff(14605,plain,
% 3.05/3.23 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3613, 14604])).
% 3.05/3.23 tff(14606,plain,
% 3.05/3.23 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[2942, 57, 14605])).
% 3.05/3.23 tff(14607,plain,
% 3.05/3.23 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[58])).
% 3.05/3.23 tff(14608,plain,
% 3.05/3.23 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 3.05/3.23 inference(symmetry,[status(thm)],[14607])).
% 3.05/3.23 tff(14609,plain,
% 3.05/3.23 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 3.05/3.23 inference(transitivity,[status(thm)],[4761, 14608])).
% 3.05/3.23 tff(14610,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[1644])).
% 3.05/3.23 tff(14611,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.05/3.23 inference(symmetry,[status(thm)],[14610])).
% 3.05/3.23 tff(14612,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[2, 14611])).
% 3.05/3.23 tff(14613,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[1032, 80, 330])).
% 3.05/3.23 tff(14614,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[1644])).
% 3.05/3.23 tff(14615,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(symmetry,[status(thm)],[14614])).
% 3.05/3.23 tff(14616,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[9558])).
% 3.05/3.23 tff(14617,plain,
% 3.05/3.23 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.05/3.23 inference(symmetry,[status(thm)],[14616])).
% 3.05/3.23 tff(14618,plain,
% 3.05/3.23 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14617, 14615])).
% 3.05/3.23 tff(14619,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[560, 14618])).
% 3.05/3.23 tff(14620,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[9558])).
% 3.05/3.23 tff(14621,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.23 inference(symmetry,[status(thm)],[14620])).
% 3.05/3.23 tff(14622,plain,
% 3.05/3.23 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[3745, 14621])).
% 3.05/3.23 tff(14623,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[8565, 14622, 14619, 14613, 12252, 14612])).
% 3.05/3.23 tff(14624,plain,((~(elem!1 = z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14625,plain,
% 3.05/3.23 (~b(s(s(z)), s(z))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14624, 79, 3745, 2, 330, 49])).
% 3.05/3.23 tff(14626,plain,
% 3.05/3.23 (r(s(s(z)), s(z))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[487, 14625])).
% 3.05/3.23 tff(14627,plain,
% 3.05/3.23 (r(s(s(z)), s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14626, 4759])).
% 3.05/3.23 tff(14628,plain,
% 3.05/3.23 (r(s(s(elem!1)), s(z))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14627, 14609])).
% 3.05/3.23 tff(14629,plain,
% 3.05/3.23 (r(s(s(elem!1)), s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14627, 4761])).
% 3.05/3.23 tff(14630,plain,
% 3.05/3.23 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[57])).
% 3.05/3.23 tff(14631,plain,
% 3.05/3.23 (b(elem!1, s(s(s(s(s(z))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[5428, 14630])).
% 3.05/3.23 tff(14632,plain,
% 3.05/3.23 (b(elem!1, s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[87, 79, 83])).
% 3.05/3.23 tff(14633,plain,
% 3.05/3.23 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3858, 422, 1219, 150])).
% 3.05/3.23 tff(14634,plain,
% 3.05/3.23 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3086, 26, 4865, 14633])).
% 3.05/3.23 tff(14635,plain,
% 3.05/3.23 (r(s(s(s(s(s(z))))), s(elem!1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3205, 422, 57])).
% 3.05/3.23 tff(14636,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14637,plain,
% 3.05/3.23 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14638,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14637])).
% 3.05/3.23 tff(14639,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14638, 14636])).
% 3.05/3.23 tff(14640,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14641,plain,
% 3.05/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14640, 14639])).
% 3.05/3.23 tff(14642,plain,
% 3.05/3.23 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14641, 163, 1474, 1773, 14635])).
% 3.05/3.23 tff(14643,plain,
% 3.05/3.23 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3400, 14642, 3385])).
% 3.05/3.23 tff(14644,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 3.05/3.23 tff(14645,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14646,plain,
% 3.05/3.23 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14647,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14646])).
% 3.05/3.23 tff(14648,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14647, 14645])).
% 3.05/3.23 tff(14649,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14650,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14649, 14648])).
% 3.05/3.23 tff(14651,plain,
% 3.05/3.23 ($false),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14650, 198, 68, 14644, 14643, 14634])).
% 3.05/3.23 tff(14652,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.23 tff(14653,plain,
% 3.05/3.23 (~r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14652, 14632, 14631, 2952, 14629, 14628, 150, 57])).
% 3.05/3.23 tff(14654,plain,
% 3.05/3.23 (b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[469, 14653])).
% 3.05/3.23 tff(14655,plain,
% 3.05/3.23 (b(s(s(s(s(s(z))))), s(elem!1))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14654, 4861])).
% 3.05/3.23 tff(14656,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14657,plain,
% 3.05/3.23 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14658,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[14657])).
% 3.05/3.23 tff(14659,plain,
% 3.05/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[14658, 14656])).
% 3.05/3.23 tff(14660,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(14661,plain,
% 3.05/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14660, 14659])).
% 3.05/3.23 tff(14662,plain,
% 3.05/3.23 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14661, 198, 2950, 14631, 14655, 4705])).
% 3.05/3.23 tff(14663,plain,
% 3.05/3.23 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3328, 26, 14662])).
% 3.05/3.23 tff(14664,plain,
% 3.05/3.23 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[14663, 2935])).
% 3.05/3.23 tff(14665,plain,
% 3.05/3.23 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[3275, 57, 3272])).
% 3.05/3.23 tff(14666,plain,
% 3.05/3.23 (r(s(elem!1), s(s(z)))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[328, 6033])).
% 3.05/3.23 tff(14667,plain,
% 3.05/3.23 (r(s(elem!1), s(s(elem!1)))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[14666, 6032])).
% 3.05/3.23 tff(14668,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14669,plain,
% 3.05/3.23 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(14670,plain,
% 3.05/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14669])).
% 3.05/3.24 tff(14671,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14670, 14668])).
% 3.05/3.24 tff(14672,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(14673,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14672, 14671])).
% 3.05/3.24 tff(14674,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14673, 163, 14667, 14665, 14664, 14606])).
% 3.05/3.24 tff(14675,plain,((~(z = elem!1)) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14676,plain,
% 3.05/3.24 (~r(s(z), elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14675, 57, 2, 328, 41, 5428, 83, 3745, 330, 49, 3272])).
% 3.05/3.24 tff(14677,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[217, 14676, 14603, 225])).
% 3.05/3.24 tff(14678,plain,((~(z = elem!1)) | (s(z) = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14679,plain,
% 3.05/3.24 (~(z = elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14678, 14583, 2, 14536, 14602, 14567, 3745, 330, 49, 14548, 34])).
% 3.05/3.24 tff(14680,plain,
% 3.05/3.24 (b(z, elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[102, 14679, 14592])).
% 3.05/3.24 tff(14681,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[7099, 198, 95, 5927, 595, 331, 2, 330])).
% 3.05/3.24 tff(14682,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14683,plain,
% 3.05/3.24 (~b(s(z), elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14682, 14680, 595, 14546, 2, 330])).
% 3.05/3.24 tff(14684,plain,
% 3.05/3.24 (r(s(z), elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[217, 14683, 14583])).
% 3.05/3.24 tff(14685,plain,
% 3.05/3.24 (~(s(elem!1) = s(z))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[814, 14679])).
% 3.05/3.24 tff(14686,plain,
% 3.05/3.24 (~(s(s(z)) = s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[822, 14685])).
% 3.05/3.24 tff(14687,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 3.05/3.24 tff(14688,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14689,plain,
% 3.05/3.24 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14690,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14689])).
% 3.05/3.24 tff(14691,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14690, 14688])).
% 3.05/3.24 tff(14692,plain,
% 3.05/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(14693,plain,
% 3.05/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14692, 14691])).
% 3.05/3.24 tff(14694,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14693, 198, 83, 331, 3745, 14687, 9403])).
% 3.05/3.24 tff(14695,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14696,plain,
% 3.05/3.24 (~b(s(s(z)), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14695, 14567, 14546, 3745, 9363])).
% 3.05/3.24 tff(14697,plain,
% 3.05/3.24 ((s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[2161, 26, 14696])).
% 3.05/3.24 tff(14698,plain,
% 3.05/3.24 (r(s(s(z)), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14697, 14686])).
% 3.05/3.24 tff(14699,plain,
% 3.05/3.24 (~(elem!1 = z)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1079, 14679])).
% 3.05/3.24 tff(14700,plain,
% 3.05/3.24 (~(s(s(z)) = s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[227, 14583])).
% 3.05/3.24 tff(14701,plain,
% 3.05/3.24 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[9459, 331, 9363, 3745])).
% 3.05/3.24 tff(14702,plain,
% 3.05/3.24 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[374, 14701])).
% 3.05/3.24 tff(14703,plain,
% 3.05/3.24 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14556, 328, 151, 14702])).
% 3.05/3.24 tff(14704,plain,
% 3.05/3.24 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[9622, 271, 95, 330])).
% 3.05/3.24 tff(14705,plain,
% 3.05/3.24 (~(elem!1 = s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[7865, 14704, 14703])).
% 3.05/3.24 tff(14706,plain,
% 3.05/3.24 (~(s(s(elem!1)) = elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[118, 14705])).
% 3.05/3.24 tff(14707,plain,
% 3.05/3.24 (b(elem!1, s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14193, 14704, 14703, 151, 236])).
% 3.05/3.24 tff(14708,plain,
% 3.05/3.24 (b(elem!1, s(z))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[269, 14704, 151, 236, 6642, 2])).
% 3.05/3.24 tff(14709,plain,
% 3.05/3.24 (~(s(elem!1) = elem!1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1395, 14706])).
% 3.05/3.24 tff(14710,plain,
% 3.05/3.24 (~(elem!1 = s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1400, 14709])).
% 3.05/3.24 tff(14711,plain,
% 3.05/3.24 (~(s(elem!1) = s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[140, 14706])).
% 3.05/3.24 tff(14712,plain,
% 3.05/3.24 (~b(s(s(elem!1)), z)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1071, 14707, 83, 271])).
% 3.05/3.24 tff(14713,plain,
% 3.05/3.24 (r(s(s(elem!1)), z)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[801, 14712])).
% 3.05/3.24 tff(14714,plain,
% 3.05/3.24 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[3788])).
% 3.05/3.24 tff(14715,plain,
% 3.05/3.24 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 3.05/3.24 inference(symmetry,[status(thm)],[14714])).
% 3.05/3.24 tff(14716,plain,
% 3.05/3.24 (b(z, s(s(s(s(s(s(s(s(z))))))))) <=> b(z, s(elem!1))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14715])).
% 3.05/3.24 tff(14717,plain,
% 3.05/3.24 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(symmetry,[status(thm)],[14716])).
% 3.05/3.24 tff(14718,plain,
% 3.05/3.24 (r(z, s(s(s(s(s(s(s(s(z))))))))) <=> r(z, s(elem!1))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14715])).
% 3.05/3.24 tff(14719,plain,
% 3.05/3.24 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(symmetry,[status(thm)],[14718])).
% 3.05/3.24 tff(14720,plain,
% 3.05/3.24 (r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[791, 14719])).
% 3.05/3.24 tff(14721,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14722,plain,
% 3.05/3.24 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), 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)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14723,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14722])).
% 3.05/3.24 tff(14724,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14723, 14721])).
% 3.05/3.24 tff(14725,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(14726,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14725, 14724])).
% 3.05/3.24 tff(14727,plain,
% 3.05/3.24 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14726, 163, 790, 2894, 332])).
% 3.05/3.24 tff(14728,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14727, 14720])).
% 3.05/3.24 tff(14729,plain,((~r(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14730,plain,
% 3.05/3.24 (~r(z, s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14729, 3788, 790, 2894, 332])).
% 3.05/3.24 tff(14731,plain,
% 3.05/3.24 (b(z, s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1791, 14730])).
% 3.05/3.24 tff(14732,plain,
% 3.05/3.24 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14731, 14717])).
% 3.05/3.24 tff(14733,plain,
% 3.05/3.24 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(elem!1))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14715])).
% 3.05/3.24 tff(14734,plain,
% 3.05/3.24 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(symmetry,[status(thm)],[14733])).
% 3.05/3.24 tff(14735,plain,
% 3.05/3.24 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(elem!1))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14715])).
% 3.05/3.24 tff(14736,plain,
% 3.05/3.24 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(s(z)), s(elem!1)))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14735])).
% 3.05/3.24 tff(14737,plain,
% 3.05/3.24 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14715])).
% 3.05/3.24 tff(14738,plain,
% 3.05/3.24 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 3.05/3.24 inference(symmetry,[status(thm)],[14737])).
% 3.05/3.24 tff(14739,plain,
% 3.05/3.24 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[3788])).
% 3.05/3.24 tff(14740,plain,
% 3.05/3.24 (r(s(s(z)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(z)), elem!1)),
% 3.05/3.24 inference(symmetry,[status(thm)],[14739])).
% 3.05/3.24 tff(14741,plain,
% 3.05/3.24 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[9459, 331, 9403, 3745])).
% 3.05/3.24 tff(14742,plain,
% 3.05/3.24 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[374, 14741])).
% 3.05/3.24 tff(14743,plain,
% 3.05/3.24 (r(s(s(z)), elem!1)),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14742, 14740])).
% 3.05/3.24 tff(14744,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14745,plain,
% 3.05/3.24 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14746,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14745])).
% 3.05/3.24 tff(14747,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14746, 14744])).
% 3.05/3.24 tff(14748,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(14749,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14748, 14747])).
% 3.05/3.24 tff(14750,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14749, 163, 1473, 236, 2113, 328])).
% 3.05/3.24 tff(14751,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(14752,plain,
% 3.05/3.24 (~r(elem!1, s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14751, 14743, 328, 236])).
% 3.05/3.24 tff(14753,plain,
% 3.05/3.24 (b(elem!1, s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1416, 14752, 1409])).
% 3.05/3.24 tff(14754,plain,
% 3.05/3.24 (~b(s(elem!1), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[1833, 14731, 95, 83, 14753])).
% 3.05/3.24 tff(14755,plain,
% 3.05/3.24 (r(s(elem!1), s(s(elem!1)))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[901, 14754, 890])).
% 3.05/3.24 tff(14756,plain,
% 3.05/3.24 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14755, 14738])).
% 3.05/3.24 tff(14757,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14758,plain,
% 3.05/3.24 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14759,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14758])).
% 3.05/3.24 tff(14760,plain,
% 3.05/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14759, 14757])).
% 3.05/3.24 tff(14761,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(14762,plain,
% 3.05/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14761, 14760])).
% 3.05/3.24 tff(14763,plain,
% 3.05/3.24 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14762, 163, 790, 2894])).
% 3.05/3.24 tff(14764,plain,
% 3.05/3.24 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[14763, 14756])).
% 3.05/3.24 tff(14765,plain,
% 3.05/3.24 (~r(s(s(z)), s(elem!1))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14764, 14736])).
% 3.05/3.24 tff(14766,plain,
% 3.05/3.24 (b(s(s(z)), s(elem!1))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[2378, 14765, 232])).
% 3.05/3.24 tff(14767,plain,
% 3.05/3.24 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[14766, 14734])).
% 3.05/3.24 tff(14768,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14769,plain,
% 3.05/3.24 (((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(14770,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[14769])).
% 3.05/3.24 tff(14771,plain,
% 3.05/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[14770, 14768])).
% 3.05/3.25 tff(14772,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14773,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14772, 14771])).
% 3.05/3.25 tff(14774,plain,
% 3.05/3.25 (~b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14773, 198, 331, 3745, 9403, 14767])).
% 3.05/3.25 tff(14775,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14774, 14732])).
% 3.05/3.25 tff(14776,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (s(s(z)) = s(elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (elem!1 = s(elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14777,plain,
% 3.05/3.25 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14776, 14713, 3745, 9363, 232, 331, 2894, 14711, 95, 83, 332, 14710, 328, 236])).
% 3.05/3.25 tff(14778,plain,
% 3.05/3.25 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[703, 14777, 12540])).
% 3.05/3.25 tff(14779,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14780,plain,
% 3.05/3.25 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14781,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14780])).
% 3.05/3.25 tff(14782,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14781, 14779])).
% 3.05/3.25 tff(14783,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14784,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14783, 14782])).
% 3.05/3.25 tff(14785,plain,
% 3.05/3.25 (~r(s(s(elem!1)), s(z))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14784, 163, 1115, 236, 694])).
% 3.05/3.25 tff(14786,plain,
% 3.05/3.25 (b(s(s(elem!1)), s(z))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[626, 14785])).
% 3.05/3.25 tff(14787,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14788,plain,
% 3.05/3.25 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), 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)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14789,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14788])).
% 3.05/3.25 tff(14790,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14789, 14787])).
% 3.05/3.25 tff(14791,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14792,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14791, 14790])).
% 3.05/3.25 tff(14793,plain,
% 3.05/3.25 (~r(s(z), s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14792, 163, 1115, 236, 694])).
% 3.05/3.25 tff(14794,plain,
% 3.05/3.25 (b(s(z), s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[642, 14793])).
% 3.05/3.25 tff(14795,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[1059, 198, 14794, 68, 14786, 320])).
% 3.05/3.25 tff(14796,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14797,plain,
% 3.05/3.25 (~r(s(s(elem!1)), elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14796, 14778, 14708, 236, 14707])).
% 3.05/3.25 tff(14798,plain,
% 3.05/3.25 (b(s(s(elem!1)), elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[602, 14797, 14706])).
% 3.05/3.25 tff(14799,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14800,plain,
% 3.05/3.25 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14801,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14800])).
% 3.05/3.25 tff(14802,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14801, 14799])).
% 3.05/3.25 tff(14803,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14804,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14803, 14802])).
% 3.05/3.25 tff(14805,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14804, 198, 95, 1128, 83, 331, 6080])).
% 3.05/3.25 tff(14806,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14807,plain,
% 3.05/3.25 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14806, 14798, 83, 331, 95])).
% 3.05/3.25 tff(14808,plain,
% 3.05/3.25 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[4221, 14807, 14703])).
% 3.05/3.25 tff(14809,plain,
% 3.05/3.25 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14808])).
% 3.05/3.25 tff(14810,plain,
% 3.05/3.25 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.25 inference(symmetry,[status(thm)],[14809])).
% 3.05/3.25 tff(14811,plain,
% 3.05/3.25 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14707, 14810])).
% 3.05/3.25 tff(14812,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[12540, 14811])).
% 3.05/3.25 tff(14813,plain,((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (s(s(z)) = s(elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14814,plain,
% 3.05/3.25 (~b(elem!1, z)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14813, 14567, 14546, 14680, 14684, 3745, 14700, 14698, 332, 14536, 330, 14534, 2])).
% 3.05/3.25 tff(14815,plain,
% 3.05/3.25 (r(elem!1, z)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[187, 14814, 14699])).
% 3.05/3.25 tff(14816,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14817,plain,
% 3.05/3.25 (((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14818,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14817])).
% 3.05/3.25 tff(14819,plain,
% 3.05/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14818, 14816])).
% 3.05/3.25 tff(14820,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14821,plain,
% 3.05/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14820, 14819])).
% 3.05/3.25 tff(14822,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14821, 163, 833, 236, 2113, 328])).
% 3.05/3.25 tff(14823,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14824,plain,
% 3.05/3.25 (~r(s(s(z)), elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14823, 14815, 14684, 14536])).
% 3.05/3.25 tff(14825,plain,
% 3.05/3.25 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 3.05/3.25 inference(symmetry,[status(thm)],[4013])).
% 3.05/3.25 tff(14826,plain,
% 3.05/3.25 (r(s(s(z)), elem!1)),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[2894, 14825])).
% 3.05/3.25 tff(14827,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[6889, 14826])).
% 3.05/3.25 tff(14828,plain,((~(elem!1 = s(s(elem!1)))) | r(s(s(z)), elem!1) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14829,plain,
% 3.05/3.25 (~(elem!1 = s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14828, 14824, 14698])).
% 3.05/3.25 tff(14830,plain,
% 3.05/3.25 (~(s(s(elem!1)) = elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[118, 14829])).
% 3.05/3.25 tff(14831,plain,
% 3.05/3.25 (~(s(elem!1) = s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[140, 14830])).
% 3.05/3.25 tff(14832,plain,
% 3.05/3.25 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[3249, 3246])).
% 3.05/3.25 tff(14833,plain,
% 3.05/3.25 (~(s(s(z)) = elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[8694, 14832])).
% 3.05/3.25 tff(14834,plain,
% 3.05/3.25 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[3247])).
% 3.05/3.25 tff(14835,plain,
% 3.05/3.25 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 3.05/3.25 inference(symmetry,[status(thm)],[14834])).
% 3.05/3.25 tff(14836,plain,
% 3.05/3.25 (b(s(s(elem!1)), s(s(z)))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[3745, 14835])).
% 3.05/3.25 tff(14837,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 3.05/3.25 tff(14838,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14837, 14836])).
% 3.05/3.25 tff(14839,plain,(b(s(s(elem!1)), s(s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14840,plain,
% 3.05/3.25 (b(s(s(elem!1)), s(s(z)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14839, 3246, 3745])).
% 3.05/3.25 tff(14841,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14842,plain,
% 3.05/3.25 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14843,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14842])).
% 3.05/3.25 tff(14844,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14843, 14841])).
% 3.05/3.25 tff(14845,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14846,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[14845, 14844])).
% 3.05/3.25 tff(14847,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14846, 198, 95, 2682, 83, 9403, 9840])).
% 3.05/3.25 tff(14848,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14849,plain,
% 3.05/3.25 (~b(s(s(z)), elem!1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14848, 14840, 83, 9403, 95])).
% 3.05/3.25 tff(14850,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[2139, 14849, 14833, 6889])).
% 3.05/3.25 tff(14851,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))) | r(s(s(z)), elem!1) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(14852,plain,
% 3.05/3.25 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[14851, 14824, 14567, 9363, 14680, 3745])).
% 3.05/3.25 tff(14853,plain,
% 3.05/3.25 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[4221, 14852, 14557])).
% 3.05/3.25 tff(14854,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14855,plain,
% 3.05/3.25 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(14856,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[14855])).
% 3.05/3.25 tff(14857,plain,
% 3.05/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[14856, 14854])).
% 3.05/3.25 tff(14858,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(14859,plain,
% 3.05/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14858, 14857])).
% 3.05/3.26 tff(14860,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14859, 198, 723, 595, 2, 330, 6080])).
% 3.05/3.26 tff(14861,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14862,plain,
% 3.05/3.26 (~b(s(s(elem!1)), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14861, 14853, 2, 330, 595])).
% 3.05/3.26 tff(14863,plain,
% 3.05/3.26 (r(s(s(elem!1)), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[801, 14862])).
% 3.05/3.26 tff(14864,plain,
% 3.05/3.26 (~(s(elem!1) = elem!1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[1395, 14830])).
% 3.05/3.26 tff(14865,plain,
% 3.05/3.26 (~(elem!1 = s(elem!1))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[1400, 14864])).
% 3.05/3.26 tff(14866,plain,
% 3.05/3.26 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14776, 14865, 3745, 9363, 14700, 14546, 14698, 14863, 14680, 14567, 332, 14831, 14536, 14684])).
% 3.05/3.26 tff(14867,plain,
% 3.05/3.26 (~b(s(s(elem!1)), elem!1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14806, 14853, 14567, 14546, 14680])).
% 3.05/3.26 tff(14868,plain,
% 3.05/3.26 (b(elem!1, s(s(elem!1)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[651, 14829, 595, 14567, 14684, 14867])).
% 3.05/3.26 tff(14869,plain,
% 3.05/3.26 (r(s(s(elem!1)), elem!1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[602, 14830, 14867])).
% 3.05/3.26 tff(14870,plain,
% 3.05/3.26 (~(elem!1 = s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[234, 14700])).
% 3.05/3.26 tff(14871,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14872,plain,
% 3.05/3.26 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14873,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.05/3.26 inference(monotonicity,[status(thm)],[14872])).
% 3.05/3.26 tff(14874,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.05/3.26 inference(transitivity,[status(thm)],[14873, 14871])).
% 3.05/3.26 tff(14875,plain,
% 3.05/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(14876,plain,
% 3.05/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14875, 14874])).
% 3.05/3.26 tff(14877,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14876, 198, 14680, 14868, 330, 14853])).
% 3.05/3.26 tff(14878,plain,
% 3.05/3.26 (b(elem!1, s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[269, 14877, 14534, 14684, 14870, 2])).
% 3.05/3.26 tff(14879,plain,
% 3.05/3.26 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14796, 14878, 14869, 14684, 14868])).
% 3.05/3.26 tff(14880,plain,
% 3.05/3.26 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[703, 14879, 14866])).
% 3.05/3.26 tff(14881,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14882,plain,
% 3.05/3.26 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14883,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.26 inference(monotonicity,[status(thm)],[14882])).
% 3.05/3.26 tff(14884,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(transitivity,[status(thm)],[14883, 14881])).
% 3.05/3.26 tff(14885,plain,
% 3.05/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(z, elem!1)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(14886,plain,
% 3.05/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14885, 14884])).
% 3.05/3.26 tff(14887,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14886, 198, 14680, 14880, 14546, 3745, 9363])).
% 3.05/3.26 tff(14888,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~b(z, s(z))) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14889,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14888, 595, 330, 332, 2, 49, 34])).
% 3.05/3.26 tff(14890,plain,
% 3.05/3.26 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[420, 14889])).
% 3.05/3.26 tff(14891,plain,
% 3.05/3.26 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[7215, 14890, 41, 14534])).
% 3.05/3.26 tff(14892,plain,
% 3.05/3.26 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[31, 14891])).
% 3.05/3.26 tff(14893,plain,
% 3.05/3.26 (~r(s(z), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9330, 14890, 14534, 332])).
% 3.05/3.26 tff(14894,plain,
% 3.05/3.26 (b(s(z), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[403, 14893])).
% 3.05/3.26 tff(14895,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[11747, 198, 595, 14894, 14892, 2, 9363])).
% 3.05/3.26 tff(14896,plain,((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14897,plain,
% 3.05/3.26 (~b(z, s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14896, 332, 2, 330, 49, 34])).
% 3.05/3.26 tff(14898,plain,
% 3.05/3.26 (r(z, s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[593, 14897])).
% 3.05/3.26 tff(14899,plain,
% 3.05/3.26 (~r(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[7140, 14898, 14534, 332])).
% 3.05/3.26 tff(14900,plain,
% 3.05/3.26 (b(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[487, 14899])).
% 3.05/3.26 tff(14901,plain,
% 3.05/3.26 (~r(s(z), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[12895, 163, 41, 14898, 332])).
% 3.05/3.26 tff(14902,plain,
% 3.05/3.26 (b(s(z), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[403, 14901])).
% 3.05/3.26 tff(14903,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3753, 14902, 14900, 2])).
% 3.05/3.26 tff(14904,plain,
% 3.05/3.26 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[420, 14903])).
% 3.05/3.26 tff(14905,plain,
% 3.05/3.26 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[7215, 14904, 41, 14534])).
% 3.05/3.26 tff(14906,plain,
% 3.05/3.26 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[31, 14905])).
% 3.05/3.26 tff(14907,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[456, 14906, 14534, 14898, 14904, 330])).
% 3.05/3.26 tff(14908,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[469, 14907])).
% 3.05/3.26 tff(14909,plain,
% 3.05/3.26 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[494, 198, 14900, 14902, 14908])).
% 3.05/3.26 tff(14910,plain,
% 3.05/3.26 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[511, 26, 508, 14909])).
% 3.05/3.26 tff(14911,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9588, 163, 332, 14904, 14910])).
% 3.05/3.26 tff(14912,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3098, 14911])).
% 3.05/3.26 tff(14913,plain,
% 3.05/3.26 (~b(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[4174, 14912, 330, 14906])).
% 3.05/3.26 tff(14914,plain,
% 3.05/3.26 (r(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3841, 14913])).
% 3.05/3.26 tff(14915,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[10122, 163, 14898, 332, 14910, 14914])).
% 3.05/3.26 tff(14916,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14917,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14916, 2, 34, 49, 332])).
% 3.05/3.26 tff(14918,plain,
% 3.05/3.26 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[176, 14917])).
% 3.05/3.26 tff(14919,plain,
% 3.05/3.26 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[13995, 2, 41, 49])).
% 3.05/3.26 tff(14920,plain,
% 3.05/3.26 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3613, 14919])).
% 3.05/3.26 tff(14921,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14005, 14920, 14918, 41, 406])).
% 3.05/3.26 tff(14922,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | r(z, s(s(z))) | b(s(z), z) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14923,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14922, 406, 49, 34, 14532])).
% 3.05/3.26 tff(14924,plain,
% 3.05/3.26 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3654, 14923])).
% 3.05/3.26 tff(14925,plain,
% 3.05/3.26 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9541, 163, 41, 406, 14924])).
% 3.05/3.26 tff(14926,plain,
% 3.05/3.26 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[31, 14925])).
% 3.05/3.26 tff(14927,plain,
% 3.05/3.26 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9533, 14924, 41])).
% 3.05/3.26 tff(14928,plain,
% 3.05/3.26 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[176, 14927])).
% 3.05/3.26 tff(14929,plain,
% 3.05/3.26 (~r(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[544, 163, 41, 406, 14532])).
% 3.05/3.26 tff(14930,plain,
% 3.05/3.26 (b(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[487, 14929])).
% 3.05/3.26 tff(14931,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14025, 422, 150, 406])).
% 3.05/3.26 tff(14932,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3841, 14931])).
% 3.05/3.26 tff(14933,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9546, 422, 150, 3639])).
% 3.05/3.26 tff(14934,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3098, 14933])).
% 3.05/3.26 tff(14935,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[4174, 14934, 14932, 14168, 9625])).
% 3.05/3.26 tff(14936,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14937,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14936, 14924, 41, 406])).
% 3.05/3.26 tff(14938,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[469, 14937])).
% 3.05/3.26 tff(14939,plain,
% 3.05/3.26 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[11867, 14938, 407, 14930])).
% 3.05/3.26 tff(14940,plain,
% 3.05/3.26 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9576, 14939])).
% 3.05/3.26 tff(14941,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[11957, 14532, 14940, 11721, 14926, 14924])).
% 3.05/3.26 tff(14942,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3098, 14941])).
% 3.05/3.26 tff(14943,plain,
% 3.05/3.26 (~b(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[4174, 14942, 14928, 14926])).
% 3.05/3.26 tff(14944,plain,
% 3.05/3.26 (r(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3841, 14943])).
% 3.05/3.26 tff(14945,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[10122, 163, 406, 14532, 14940, 14944])).
% 3.05/3.26 tff(14946,plain,((~r(z, s(z))) | (~b(s(z), s(s(z)))) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14947,plain,
% 3.05/3.26 (~r(z, s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14946, 34, 49, 407])).
% 3.05/3.26 tff(14948,plain,
% 3.05/3.26 (b(z, s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[593, 14947])).
% 3.05/3.26 tff(14949,plain,
% 3.05/3.26 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[11747, 198, 595, 407, 2, 11721])).
% 3.05/3.26 tff(14950,plain,
% 3.05/3.26 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[31, 14949])).
% 3.05/3.26 tff(14951,plain,
% 3.05/3.26 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[7215, 14950, 150, 13997])).
% 3.05/3.26 tff(14952,plain,
% 3.05/3.26 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[420, 14951])).
% 3.05/3.26 tff(14953,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14954,plain,
% 3.05/3.26 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14955,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.26 inference(monotonicity,[status(thm)],[14954])).
% 3.05/3.26 tff(14956,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.26 inference(transitivity,[status(thm)],[14955, 14953])).
% 3.05/3.26 tff(14957,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(14958,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14957, 14956])).
% 3.05/3.26 tff(14959,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14958, 163, 150, 151, 33, 152])).
% 3.05/3.26 tff(14960,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14961,plain,
% 3.05/3.26 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14960, 14950, 150, 13997])).
% 3.05/3.26 tff(14962,plain,
% 3.05/3.26 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[176, 14961])).
% 3.05/3.26 tff(14963,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[7219, 14962, 14952, 407, 595, 2])).
% 3.05/3.26 tff(14964,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z)) | r(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14965,plain,
% 3.05/3.26 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14964, 14948, 407, 41, 49])).
% 3.05/3.26 tff(14966,plain,
% 3.05/3.26 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3654, 14965])).
% 3.05/3.26 tff(14967,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[12986, 422, 150, 33])).
% 3.05/3.26 tff(14968,plain,
% 3.05/3.26 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[10303, 33, 150, 3639])).
% 3.05/3.26 tff(14969,plain,
% 3.05/3.26 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3613, 14968])).
% 3.05/3.26 tff(14970,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14971,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(14972,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14971, 14970])).
% 3.05/3.26 tff(14973,plain,
% 3.05/3.26 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14972, 163, 150, 3639, 422])).
% 3.05/3.26 tff(14974,plain,
% 3.05/3.26 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9643, 14973])).
% 3.05/3.26 tff(14975,plain,
% 3.05/3.26 (~b(z, s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[9634, 14974, 14168, 4167])).
% 3.05/3.26 tff(14976,plain,
% 3.05/3.26 (r(z, s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[4110, 14975])).
% 3.05/3.26 tff(14977,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14978,plain,
% 3.05/3.26 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(14979,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.05/3.26 inference(monotonicity,[status(thm)],[14978])).
% 3.05/3.26 tff(14980,plain,
% 3.05/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.05/3.26 inference(transitivity,[status(thm)],[14979, 14977])).
% 3.05/3.26 tff(14981,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(14982,plain,
% 3.05/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[14981, 14980])).
% 3.05/3.26 tff(14983,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14982, 163, 150, 6249, 422, 7912])).
% 3.05/3.26 tff(14984,plain,((~r(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))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14985,plain,
% 3.05/3.26 (~r(s(z), s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14984, 14976, 150, 422])).
% 3.05/3.26 tff(14986,plain,
% 3.05/3.26 (b(s(z), s(s(s(s(s(z))))))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3301, 14985])).
% 3.05/3.26 tff(14987,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[13790, 198, 14934, 14986, 3615, 14974])).
% 3.05/3.26 tff(14988,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14989,plain,
% 3.05/3.26 (~b(s(s(s(s(s(z))))), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14988, 422, 150, 14969, 3639])).
% 3.05/3.26 tff(14990,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3841, 14989, 14967])).
% 3.05/3.26 tff(14991,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(14992,plain,
% 3.05/3.26 (~r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[14991, 33, 3639, 150])).
% 3.05/3.26 tff(14993,plain,
% 3.05/3.26 (b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[469, 14992])).
% 3.05/3.26 tff(14994,plain,
% 3.05/3.26 (~b(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[11867, 559, 407, 4049])).
% 3.05/3.26 tff(14995,plain,
% 3.05/3.26 (r(s(s(z)), s(z))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[487, 14994])).
% 3.05/3.26 tff(14996,plain,
% 3.05/3.26 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[3644, 14995, 3639, 150])).
% 3.05/3.26 tff(14997,plain,
% 3.05/3.26 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[420, 14996])).
% 3.05/3.26 tff(14998,plain,
% 3.05/3.26 (~r(s(s(z)), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[12790, 14995, 150, 33])).
% 3.05/3.26 tff(14999,plain,
% 3.05/3.26 (b(s(s(z)), z)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[345, 14998])).
% 3.05/3.26 tff(15000,plain,
% 3.05/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(15001,plain,
% 3.05/3.26 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15002,plain,
% 3.05/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.05/3.27 inference(monotonicity,[status(thm)],[15001])).
% 3.05/3.27 tff(15003,plain,
% 3.05/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.27 inference(transitivity,[status(thm)],[15002, 15000])).
% 3.05/3.27 tff(15004,plain,
% 3.05/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(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(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(quant_inst,[status(thm)],[])).
% 3.05/3.27 tff(15005,plain,
% 3.05/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.05/3.27 inference(modus_ponens,[status(thm)],[15004, 15003])).
% 3.05/3.27 tff(15006,plain,
% 3.05/3.27 ($false),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15005, 198, 347, 3745, 330, 3404, 4049])).
% 3.05/3.27 tff(15007,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.27 tff(15008,plain,
% 3.05/3.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15007, 14999, 4049, 14168, 14997])).
% 3.05/3.27 tff(15009,plain,
% 3.05/3.27 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[11833, 7912, 3368, 33])).
% 3.05/3.27 tff(15010,plain,
% 3.05/3.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[9576, 15009])).
% 3.05/3.27 tff(15011,plain,
% 3.05/3.27 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[8132, 198, 595, 347, 559])).
% 3.05/3.27 tff(15012,plain,
% 3.05/3.27 (~b(s(s(s(s(s(z))))), z)),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15011, 15010])).
% 3.05/3.27 tff(15013,plain,
% 3.05/3.27 (r(s(s(s(s(s(z))))), z)),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3841, 15012])).
% 3.05/3.27 tff(15014,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15015,plain,
% 3.05/3.27 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15016,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.27 inference(monotonicity,[status(thm)],[15015])).
% 3.05/3.27 tff(15017,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(transitivity,[status(thm)],[15016, 15014])).
% 3.05/3.27 tff(15018,plain,
% 3.05/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(quant_inst,[status(thm)],[])).
% 3.05/3.27 tff(15019,plain,
% 3.05/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.27 inference(modus_ponens,[status(thm)],[15018, 15017])).
% 3.05/3.27 tff(15020,plain,
% 3.05/3.27 ($false),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15019, 163, 33, 3368, 7912, 15013])).
% 3.05/3.27 tff(15021,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.27 tff(15022,plain,
% 3.05/3.27 (~r(z, s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15021, 3368, 33, 595, 347, 559])).
% 3.05/3.27 tff(15023,plain,
% 3.05/3.27 (b(z, s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[4110, 15022])).
% 3.05/3.27 tff(15024,plain,
% 3.05/3.27 (~b(s(z), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[11269, 15023, 559, 595])).
% 3.05/3.27 tff(15025,plain,
% 3.05/3.27 (r(s(z), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3301, 15024])).
% 3.05/3.27 tff(15026,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15027,plain,
% 3.05/3.27 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15028,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.27 inference(monotonicity,[status(thm)],[15027])).
% 3.05/3.27 tff(15029,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(transitivity,[status(thm)],[15028, 15026])).
% 3.05/3.27 tff(15030,plain,
% 3.05/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(quant_inst,[status(thm)],[])).
% 3.05/3.27 tff(15031,plain,
% 3.05/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.27 inference(modus_ponens,[status(thm)],[15030, 15029])).
% 3.05/3.27 tff(15032,plain,
% 3.05/3.27 ($false),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15031, 163, 150, 6249, 33, 3828])).
% 3.05/3.27 tff(15033,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.27 tff(15034,plain,
% 3.05/3.27 (~r(s(s(s(s(s(z))))), z)),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15033, 15025, 150, 33])).
% 3.05/3.27 tff(15035,plain,
% 3.05/3.27 (b(s(s(s(s(s(z))))), z)),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3841, 15034])).
% 3.05/3.27 tff(15036,plain,
% 3.05/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15037,plain,
% 3.05/3.27 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15038,plain,
% 3.05/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 3.05/3.27 inference(monotonicity,[status(thm)],[15037])).
% 3.05/3.27 tff(15039,plain,
% 3.05/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.05/3.27 inference(transitivity,[status(thm)],[15038, 15036])).
% 3.05/3.27 tff(15040,plain,
% 3.05/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.27 inference(quant_inst,[status(thm)],[])).
% 3.05/3.27 tff(15041,plain,
% 3.05/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.05/3.27 inference(modus_ponens,[status(thm)],[15040, 15039])).
% 3.05/3.27 tff(15042,plain,
% 3.05/3.27 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15041, 198, 595, 14168, 559])).
% 3.05/3.27 tff(15043,plain,
% 3.05/3.27 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15042, 15035])).
% 3.05/3.27 tff(15044,plain,
% 3.05/3.27 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3098, 15043])).
% 3.05/3.27 tff(15045,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15046,plain,
% 3.05/3.27 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(rewrite,[status(thm)],[])).
% 3.05/3.27 tff(15047,plain,
% 3.05/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 3.05/3.27 inference(monotonicity,[status(thm)],[15046])).
% 3.05/3.27 tff(15048,plain,
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% 3.05/3.27 inference(transitivity,[status(thm)],[15047, 15045])).
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% 3.05/3.27 inference(quant_inst,[status(thm)],[])).
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% 3.05/3.27 inference(modus_ponens,[status(thm)],[15049, 15048])).
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% 3.05/3.27 ($false),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15050, 163, 15044, 15025, 3639, 3368])).
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% 3.05/3.27 tff(15053,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15052, 14999, 150, 595, 3639, 33, 559])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[9643, 15053, 15008])).
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% 3.05/3.27 tff(15056,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15055, 14993, 595, 3639, 33, 150, 407])).
% 3.05/3.27 tff(15057,plain,
% 3.05/3.27 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[9576, 15056])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[11823, 198, 595, 407, 14993, 11721])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[4110, 15058])).
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% 3.05/3.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[11833, 15059, 33, 15057])).
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% 3.05/3.27 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[9643, 15060])).
% 3.05/3.27 tff(15062,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[11987, 15059, 33, 3639])).
% 3.05/3.27 tff(15063,plain,
% 3.05/3.27 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3098, 15062])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15041, 198, 595, 14168, 14993])).
% 3.05/3.27 tff(15065,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15064, 15063])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3841, 15065])).
% 3.05/3.27 tff(15067,plain,
% 3.05/3.27 (~r(s(z), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15033, 15066, 150, 33])).
% 3.05/3.27 tff(15068,plain,
% 3.05/3.27 (b(s(z), s(s(s(s(s(z))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3301, 15067])).
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% 3.05/3.27 tff(15070,plain,((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.27 tff(15071,plain,
% 3.05/3.27 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[15070, 41, 14948, 14966, 407])).
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% 3.05/3.27 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[31, 15071])).
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% 3.05/3.27 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[9469, 15072, 407, 11721, 14948])).
% 3.05/3.27 tff(15074,plain,
% 3.05/3.27 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[374, 15073])).
% 3.05/3.27 tff(15075,plain,
% 3.05/3.27 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[9423, 15072, 11721, 41, 14948, 14966])).
% 3.05/3.27 tff(15076,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3613, 15075])).
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% 3.05/3.27 tff(15079,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15078, 12102, 407])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[7283, 331, 15079, 12103, 2])).
% 3.05/3.27 tff(15081,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[176, 15080])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[593, 11749])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[6539, 15082, 15079, 12103])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[487, 15083])).
% 3.05/3.27 tff(15085,plain,
% 3.05/3.27 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[356, 15081, 347, 331])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[374, 15085])).
% 3.05/3.27 tff(15087,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[6822, 15086, 15079, 15084, 12103])).
% 3.05/3.27 tff(15088,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3841, 15087])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[4174, 15088, 15081, 331])).
% 3.05/3.27 tff(15090,plain,
% 3.05/3.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[6545, 15086, 15079, 12103, 2, 15082])).
% 3.05/3.27 tff(15091,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[420, 15090])).
% 3.05/3.27 tff(15092,plain,
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[12234, 15091, 407, 11721, 15082, 15086])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15094, 2, 407, 347])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[31, 15095])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[487, 15097])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3753, 15098, 407, 2])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[420, 15099])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[374, 15101])).
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% 3.05/3.27 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[3613, 15103])).
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% 3.05/3.27 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3654, 15107])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[9533, 15108, 12103])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[176, 15109])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[15114, 15108, 407])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[31, 15115])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[176, 15135])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[420, 15137])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[9576, 15139])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[11867, 15140, 407, 15134])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[469, 15141])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3841, 15143])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[4174, 15144, 15136, 331])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3098, 15145])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[11747, 198, 407, 331, 2, 11721])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[593, 15147])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[12234, 15148, 407, 11721, 15138, 15146])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[374, 15149])).
% 3.05/3.27 tff(15151,plain,
% 3.05/3.27 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.27 inference(unit_resolution,[status(thm)],[456, 15148, 15136, 15142, 15138, 331])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3613, 15151])).
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% 3.05/3.27 inference(unit_resolution,[status(thm)],[3626, 15152, 15150, 2, 15134])).
% 3.05/3.27 tff(15154,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15155,plain,
% 3.05/3.28 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15154, 331, 407])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[3654, 15155])).
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% 3.05/3.28 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[9533, 15156, 12103])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[176, 15157])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[9556, 559, 15079, 15132, 407, 15134])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[4110, 15159])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[11867, 559, 407, 15134])).
% 3.05/3.28 tff(15162,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[9576, 15161])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[9592, 15162, 15079, 15132, 331])).
% 3.05/3.28 tff(15164,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[420, 15163])).
% 3.05/3.28 tff(15165,plain,
% 3.05/3.28 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[11957, 15162, 15132, 11721, 331, 15156])).
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% 3.05/3.28 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3098, 15165])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[13602, 198, 3819, 331, 3745, 9403, 5428])).
% 3.05/3.28 tff(15168,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15169,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[15168, 15166, 15164, 11721, 331, 15160])).
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% 3.05/3.28 tff(15171,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[15170, 331, 407])).
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% 3.05/3.28 (r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[469, 15171])).
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% 3.05/3.28 (~r(s(s(s(s(s(z))))), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3836, 15172, 12103, 15079])).
% 3.05/3.28 tff(15174,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[3841, 15173])).
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% 3.05/3.28 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[9546, 15172, 12103, 15156])).
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% 3.05/3.28 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3098, 15175])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[4174, 15176, 15174, 15158, 331])).
% 3.05/3.28 tff(15178,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[15178, 407])).
% 3.05/3.28 tff(15180,plain,
% 3.05/3.28 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[31, 15179])).
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[15114, 15180, 407])).
% 3.05/3.28 tff(15182,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[3654, 15181])).
% 3.05/3.28 tff(15183,plain,
% 3.05/3.28 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3753, 15182, 407, 15134])).
% 3.05/3.28 tff(15184,plain,
% 3.05/3.28 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[420, 15183])).
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% 3.05/3.28 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[7215, 15184, 12103, 15180])).
% 3.05/3.28 tff(15186,plain,
% 3.05/3.28 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[8399, 15182, 15079, 12103, 15180])).
% 3.05/3.28 tff(15187,plain,
% 3.05/3.28 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[374, 15186])).
% 3.05/3.28 tff(15188,plain,
% 3.05/3.28 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3626, 15187, 15182, 15134])).
% 3.05/3.28 tff(15189,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[3613, 15188, 15185])).
% 3.05/3.28 tff(15190,plain,(~b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15191,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[403, 15190])).
% 3.05/3.28 tff(15192,plain,
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% 3.05/3.28 inference(unit_resolution,[status(thm)],[54, 49])).
% 3.05/3.28 tff(15193,plain,
% 3.05/3.28 (~r(s(s(z)), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[14916, 330, 2, 49, 34])).
% 3.05/3.28 tff(15194,plain,
% 3.05/3.28 (b(s(s(z)), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[345, 15193])).
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% 3.05/3.28 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[356, 331, 330, 347])).
% 3.05/3.28 tff(15196,plain,
% 3.05/3.28 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[374, 15195])).
% 3.05/3.28 tff(15197,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15198,plain,
% 3.05/3.28 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15199,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.28 inference(monotonicity,[status(thm)],[15198])).
% 3.05/3.28 tff(15200,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(transitivity,[status(thm)],[15199, 15197])).
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% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))))),
% 3.05/3.28 inference(quant_inst,[status(thm)],[])).
% 3.05/3.28 tff(15202,plain,
% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.28 inference(modus_ponens,[status(thm)],[15201, 15200])).
% 3.05/3.28 tff(15203,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15202, 163, 328, 151, 3272, 3368])).
% 3.05/3.28 tff(15204,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15205,plain,
% 3.05/3.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15204, 15196, 328, 151])).
% 3.05/3.28 tff(15206,plain,
% 3.05/3.28 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[9643, 15205])).
% 3.05/3.28 tff(15207,plain,
% 3.05/3.28 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15208,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.28 inference(monotonicity,[status(thm)],[15207])).
% 3.05/3.28 tff(15209,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(transitivity,[status(thm)],[15208, 5783])).
% 3.05/3.28 tff(15210,plain,
% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(quant_inst,[status(thm)],[])).
% 3.05/3.28 tff(15211,plain,
% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.28 inference(modus_ponens,[status(thm)],[15210, 15209])).
% 3.05/3.28 tff(15212,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15211, 163, 328, 151, 3272, 423])).
% 3.05/3.28 tff(15213,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15214,plain,
% 3.05/3.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15213, 15196, 151, 328])).
% 3.05/3.28 tff(15215,plain,
% 3.05/3.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[420, 15214])).
% 3.05/3.28 tff(15216,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15217,plain,
% 3.05/3.28 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15218,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 3.05/3.28 inference(monotonicity,[status(thm)],[15217])).
% 3.05/3.28 tff(15219,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 3.05/3.28 inference(transitivity,[status(thm)],[15218, 15216])).
% 3.05/3.28 tff(15220,plain,
% 3.05/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.05/3.28 inference(quant_inst,[status(thm)],[])).
% 3.05/3.28 tff(15221,plain,
% 3.05/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 3.05/3.28 inference(modus_ponens,[status(thm)],[15220, 15219])).
% 3.05/3.28 tff(15222,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15221, 198, 347, 3745, 330, 5428, 3404])).
% 3.05/3.28 tff(15223,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15224,plain,
% 3.05/3.28 (~b(z, s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15223, 15215, 347, 330, 15206])).
% 3.05/3.28 tff(15225,plain,
% 3.05/3.28 (r(z, s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[4110, 15224])).
% 3.05/3.28 tff(15226,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3961, 198, 595, 347, 3745, 2, 330])).
% 3.05/3.28 tff(15227,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15228,plain,
% 3.05/3.28 (~b(z, s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15227, 15215, 347, 2, 330])).
% 3.05/3.28 tff(15229,plain,
% 3.05/3.28 (r(z, s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[593, 15228])).
% 3.05/3.28 tff(15230,plain,
% 3.05/3.28 (~r(s(s(s(s(s(z))))), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[14029, 15206, 2, 150, 15229])).
% 3.05/3.28 tff(15231,plain,
% 3.05/3.28 (b(s(s(s(s(s(z))))), z)),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3841, 15230])).
% 3.05/3.28 tff(15232,plain,
% 3.05/3.28 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[4174, 15231, 330, 331])).
% 3.05/3.28 tff(15233,plain,
% 3.05/3.28 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3098, 15232])).
% 3.05/3.28 tff(15234,plain,
% 3.05/3.28 (~r(s(z), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[10459, 15233, 150, 15225])).
% 3.05/3.28 tff(15235,plain,
% 3.05/3.28 (b(s(z), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3301, 15234])).
% 3.05/3.28 tff(15236,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[12196, 198, 6262, 2, 559, 3404])).
% 3.05/3.28 tff(15237,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15238,plain,
% 3.05/3.28 (~b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15237, 15235, 2, 15206])).
% 3.05/3.28 tff(15239,plain,
% 3.05/3.28 (r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[469, 15238])).
% 3.05/3.28 tff(15240,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[12124, 163, 150, 15229, 15239, 15225])).
% 3.05/3.28 tff(15241,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15242,plain,
% 3.05/3.28 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15241, 330, 2, 41, 15194, 14920, 328])).
% 3.05/3.28 tff(15243,plain,
% 3.05/3.28 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[31, 15242])).
% 3.05/3.28 tff(15244,plain,
% 3.05/3.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[7215, 15243, 41, 14920])).
% 3.05/3.28 tff(15245,plain,
% 3.05/3.28 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[420, 15244])).
% 3.05/3.28 tff(15246,plain,
% 3.05/3.28 (~b(z, s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15227, 15245, 15194, 2, 330])).
% 3.05/3.28 tff(15247,plain,
% 3.05/3.28 (r(z, s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[593, 15246])).
% 3.05/3.28 tff(15248,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15249,plain,
% 3.05/3.28 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15250,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.28 inference(monotonicity,[status(thm)],[15249])).
% 3.05/3.28 tff(15251,plain,
% 3.05/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.28 inference(transitivity,[status(thm)],[15250, 15248])).
% 3.05/3.28 tff(15252,plain,
% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 3.05/3.28 inference(quant_inst,[status(thm)],[])).
% 3.05/3.28 tff(15253,plain,
% 3.05/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.28 inference(modus_ponens,[status(thm)],[15252, 15251])).
% 3.05/3.28 tff(15254,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15253, 163, 406, 151, 33, 3368])).
% 3.05/3.28 tff(15255,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15256,plain,
% 3.05/3.28 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15255, 15247, 14920, 15243])).
% 3.05/3.28 tff(15257,plain,
% 3.05/3.28 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[9643, 15256])).
% 3.05/3.28 tff(15258,plain,
% 3.05/3.28 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15007, 15194, 15245, 330, 15257])).
% 3.05/3.28 tff(15259,plain,
% 3.05/3.28 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[9576, 15258])).
% 3.05/3.28 tff(15260,plain,
% 3.05/3.28 (~b(z, s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15223, 15257, 15194, 330, 15245])).
% 3.05/3.28 tff(15261,plain,
% 3.05/3.28 (r(z, s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[4110, 15260])).
% 3.05/3.28 tff(15262,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[12124, 163, 150, 406, 422, 7912])).
% 3.05/3.28 tff(15263,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.28 tff(15264,plain,
% 3.05/3.28 (~r(s(s(s(s(s(z))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15263, 15247, 41, 15261])).
% 3.05/3.28 tff(15265,plain,
% 3.05/3.28 (b(s(s(s(s(s(z))))), s(z))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[469, 15264])).
% 3.05/3.28 tff(15266,plain,
% 3.05/3.28 (~b(s(z), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15237, 15265, 2, 15257])).
% 3.05/3.28 tff(15267,plain,
% 3.05/3.28 (r(s(z), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3301, 15266])).
% 3.05/3.28 tff(15268,plain,
% 3.05/3.28 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[10459, 15267, 41, 15261])).
% 3.05/3.28 tff(15269,plain,
% 3.05/3.28 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[3098, 15268])).
% 3.05/3.28 tff(15270,plain,
% 3.05/3.28 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[10372, 198, 3819, 347, 330])).
% 3.05/3.28 tff(15271,plain,
% 3.05/3.28 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15270, 348])).
% 3.05/3.28 tff(15272,plain,
% 3.05/3.28 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[2715, 26, 507, 15271])).
% 3.05/3.28 tff(15273,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15274,plain,
% 3.05/3.28 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.28 inference(rewrite,[status(thm)],[])).
% 3.05/3.28 tff(15275,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.05/3.28 inference(monotonicity,[status(thm)],[15274])).
% 3.05/3.28 tff(15276,plain,
% 3.05/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.28 inference(transitivity,[status(thm)],[15275, 15273])).
% 3.05/3.28 tff(15277,plain,
% 3.05/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.05/3.28 inference(quant_inst,[status(thm)],[])).
% 3.05/3.28 tff(15278,plain,
% 3.05/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.05/3.28 inference(modus_ponens,[status(thm)],[15277, 15276])).
% 3.05/3.28 tff(15279,plain,
% 3.05/3.28 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[15278, 198, 3819, 348, 2, 559])).
% 3.05/3.28 tff(15280,plain,
% 3.05/3.28 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[511, 26, 508, 15279])).
% 3.05/3.28 tff(15281,plain,
% 3.05/3.28 ($false),
% 3.05/3.28 inference(unit_resolution,[status(thm)],[13082, 163, 328, 6249, 15280, 15272])).
% 3.05/3.29 tff(15282,plain,((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), 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(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.29 tff(15283,plain,
% 3.05/3.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15282, 15267, 328, 15269, 2, 15265, 15194, 330])).
% 3.05/3.29 tff(15284,plain,
% 3.05/3.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15283])).
% 3.05/3.29 tff(15285,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15286,plain,
% 3.05/3.29 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15287,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.29 inference(monotonicity,[status(thm)],[15286])).
% 3.05/3.29 tff(15288,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(transitivity,[status(thm)],[15287, 15285])).
% 3.05/3.29 tff(15289,plain,
% 3.05/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(quant_inst,[status(thm)],[])).
% 3.05/3.29 tff(15290,plain,
% 3.05/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.29 inference(modus_ponens,[status(thm)],[15289, 15288])).
% 3.05/3.29 tff(15291,plain,
% 3.05/3.29 ($false),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15290, 163, 328, 15267, 15284, 15259])).
% 3.05/3.29 tff(15292,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.29 tff(15293,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15292, 2, 328, 49, 34])).
% 3.05/3.29 tff(15294,plain,
% 3.05/3.29 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[176, 15293])).
% 3.05/3.29 tff(15295,plain,
% 3.05/3.29 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[14960, 15294, 14920, 41])).
% 3.05/3.29 tff(15296,plain,
% 3.05/3.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[31, 15295])).
% 3.05/3.29 tff(15297,plain,
% 3.05/3.29 ($false),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[5747, 163, 328, 151, 3272, 152])).
% 3.05/3.29 tff(15298,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.29 tff(15299,plain,
% 3.05/3.29 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15298, 14920, 328, 15294])).
% 3.05/3.29 tff(15300,plain,
% 3.05/3.29 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15299])).
% 3.05/3.29 tff(15301,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9459, 15300, 15192, 15296])).
% 3.05/3.29 tff(15302,plain,
% 3.05/3.29 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15301])).
% 3.05/3.29 tff(15303,plain,
% 3.05/3.29 (~r(s(s(z)), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9330, 15302, 328, 14920])).
% 3.05/3.29 tff(15304,plain,
% 3.05/3.29 (b(s(s(z)), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[345, 15303])).
% 3.05/3.29 tff(15305,plain,
% 3.05/3.29 (~r(z, s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[14005, 15294, 14920, 41])).
% 3.05/3.29 tff(15306,plain,
% 3.05/3.29 (b(z, s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[593, 15305])).
% 3.05/3.29 tff(15307,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15308,plain,
% 3.05/3.29 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15309,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.29 inference(monotonicity,[status(thm)],[15308])).
% 3.05/3.29 tff(15310,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(transitivity,[status(thm)],[15309, 15307])).
% 3.05/3.29 tff(15311,plain,
% 3.05/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 3.05/3.29 inference(quant_inst,[status(thm)],[])).
% 3.05/3.29 tff(15312,plain,
% 3.05/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.29 inference(modus_ponens,[status(thm)],[15311, 15310])).
% 3.05/3.29 tff(15313,plain,
% 3.05/3.29 ($false),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15312, 198, 15306, 15300, 15304, 15296, 2, 15192])).
% 3.05/3.29 tff(15314,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(z)))) | r(z, s(s(z))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.29 tff(15315,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15314, 34, 49, 328])).
% 3.05/3.29 tff(15316,plain,
% 3.05/3.29 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3654, 15315])).
% 3.05/3.29 tff(15317,plain,
% 3.05/3.29 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[14544, 332, 328, 150])).
% 3.05/3.29 tff(15318,plain,
% 3.05/3.29 (b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[31, 15317])).
% 3.05/3.29 tff(15319,plain,
% 3.05/3.29 (~b(z, s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9423, 15318, 9403, 3639, 3615, 150])).
% 3.05/3.29 tff(15320,plain,
% 3.05/3.29 (r(z, s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[593, 15319])).
% 3.05/3.29 tff(15321,plain,
% 3.05/3.29 ($false),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[12895, 163, 150, 15320, 328, 332])).
% 3.05/3.29 tff(15322,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.29 tff(15323,plain,
% 3.05/3.29 (~r(s(s(z)), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15322, 3615, 328, 9403, 3639, 150])).
% 3.05/3.29 tff(15324,plain,
% 3.05/3.29 (b(s(s(z)), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[345, 15323])).
% 3.05/3.29 tff(15325,plain,
% 3.05/3.29 (~r(s(s(z)), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3644, 423, 150, 3639])).
% 3.05/3.29 tff(15326,plain,
% 3.05/3.29 (b(s(s(z)), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[487, 15325])).
% 3.05/3.29 tff(15327,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15328,plain,
% 3.05/3.29 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15329,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.29 inference(monotonicity,[status(thm)],[15328])).
% 3.05/3.29 tff(15330,plain,
% 3.05/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(transitivity,[status(thm)],[15329, 15327])).
% 3.05/3.29 tff(15331,plain,
% 3.05/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))))),
% 3.05/3.29 inference(quant_inst,[status(thm)],[])).
% 3.05/3.29 tff(15332,plain,
% 3.05/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.29 inference(modus_ponens,[status(thm)],[15331, 15330])).
% 3.05/3.29 tff(15333,plain,
% 3.05/3.29 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15332, 198, 3615, 347, 14168])).
% 3.05/3.29 tff(15334,plain,
% 3.05/3.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15333, 15326])).
% 3.05/3.29 tff(15335,plain,
% 3.05/3.29 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15334])).
% 3.05/3.29 tff(15336,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15337,plain,
% 3.05/3.29 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(rewrite,[status(thm)],[])).
% 3.05/3.29 tff(15338,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.05/3.29 inference(monotonicity,[status(thm)],[15337])).
% 3.05/3.29 tff(15339,plain,
% 3.05/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.05/3.29 inference(transitivity,[status(thm)],[15338, 15336])).
% 3.05/3.29 tff(15340,plain,
% 3.05/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.05/3.29 inference(quant_inst,[status(thm)],[])).
% 3.05/3.29 tff(15341,plain,
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% 3.05/3.29 inference(modus_ponens,[status(thm)],[15340, 15339])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15343, 3615, 3639, 328, 15324, 150])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15344])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15347, 15316, 15192, 328, 41])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15348])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[10303, 15349, 41, 15316])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[31, 15350])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9533, 15316, 41])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[176, 15352])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15347, 3639, 9403, 328, 150])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15354])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[10303, 15355, 150, 3639])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[31, 15356])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9505, 332, 328, 3639])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15358])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9459, 15359, 9403, 15357])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15360])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9449, 15361, 9403, 3639, 15355])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[593, 15362])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15365, 41, 328, 15192, 15316])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[345, 15366])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[356, 15367, 15353, 15351])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15368])).
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% 3.05/3.29 tff(15372,plain,
% 3.05/3.29 (b(s(z), z) | r(z, s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15371, 15191])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15372, 34])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[8381, 15373, 41, 2, 152, 33])).
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% 3.05/3.29 tff(15376,plain,
% 3.05/3.29 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15375, 34, 2, 33])).
% 3.05/3.29 tff(15377,plain,
% 3.05/3.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[176, 15376])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[14050, 198, 347, 3745, 330, 9403])).
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% 3.05/3.29 tff(15380,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15379, 15377, 347, 9363])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15380])).
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% 3.05/3.29 tff(15384,plain,
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15383, 34, 2, 33])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[487, 15384])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3712, 15191])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15386, 15373, 41])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15387])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3626, 15388, 2, 15385])).
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% 3.05/3.29 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15389])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[7215, 15390, 15381, 41, 33])).
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% 3.05/3.29 tff(15393,plain,
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[14544, 15191])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15394, 41, 33])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[15397, 2, 32])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[11740, 152, 332, 9403, 331])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[593, 15399])).
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% 3.05/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9330, 151, 328, 332])).
% 3.05/3.29 tff(15402,plain,
% 3.05/3.29 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15401])).
% 3.05/3.29 tff(15403,plain,
% 3.05/3.29 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15298, 151, 328, 152])).
% 3.05/3.29 tff(15404,plain,
% 3.05/3.29 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15403])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9459, 15404, 15402, 9403, 331])).
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% 3.05/3.29 tff(15407,plain,
% 3.05/3.29 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15406, 152, 331, 328, 9403, 332])).
% 3.05/3.29 tff(15408,plain,
% 3.05/3.29 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15407])).
% 3.05/3.29 tff(15409,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9411, 15408, 9403, 331, 15400])).
% 3.05/3.29 tff(15410,plain,
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15409])).
% 3.05/3.29 tff(15411,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[4967, 15408, 1185, 331, 15400])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3654, 15411])).
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% 3.05/3.29 tff(15415,plain,
% 3.05/3.29 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15414, 331, 332, 1185, 328, 9403])).
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% 3.05/3.29 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[176, 15415])).
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% 3.05/3.29 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[8483, 15416, 1185, 331])).
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% 3.05/3.29 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15417])).
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% 3.05/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9330, 15418, 328, 332])).
% 3.05/3.29 tff(15420,plain,
% 3.05/3.29 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[420, 15419])).
% 3.05/3.29 tff(15421,plain,
% 3.05/3.29 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[11851, 15418, 332, 1185, 15416, 15420])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[3654, 15421])).
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% 3.05/3.29 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9459, 15420, 9403, 331])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15423])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9431, 163, 328, 15418, 15424, 15422])).
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% 3.05/3.29 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[15426, 332, 328, 1185, 9403])).
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% 3.05/3.29 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[31, 15427])).
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% 3.05/3.29 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[11759, 163, 332, 15428, 152])).
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% 3.05/3.29 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[374, 15429])).
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% 3.05/3.29 inference(unit_resolution,[status(thm)],[9330, 423, 328, 332])).
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% 3.05/3.29 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3613, 15431])).
% 3.05/3.29 tff(15433,plain,
% 3.05/3.29 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[9505, 423, 328, 332])).
% 3.05/3.29 tff(15434,plain,
% 3.05/3.29 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.05/3.29 inference(unit_resolution,[status(thm)],[3654, 15433])).
% 3.05/3.30 tff(15435,plain,
% 3.05/3.30 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[11769, 423, 33, 332])).
% 3.05/3.30 tff(15436,plain,
% 3.05/3.30 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[176, 15435])).
% 3.05/3.30 tff(15437,plain,
% 3.05/3.30 (~b(z, s(z))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[4953, 15436, 1185, 15434])).
% 3.05/3.30 tff(15438,plain,
% 3.05/3.30 (r(z, s(z))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[593, 15437])).
% 3.05/3.30 tff(15439,plain,
% 3.05/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.30 inference(rewrite,[status(thm)],[])).
% 3.05/3.30 tff(15440,plain,
% 3.05/3.30 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.30 inference(rewrite,[status(thm)],[])).
% 3.05/3.30 tff(15441,plain,
% 3.05/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.05/3.30 inference(monotonicity,[status(thm)],[15440])).
% 3.05/3.30 tff(15442,plain,
% 3.05/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.05/3.30 inference(transitivity,[status(thm)],[15441, 15439])).
% 3.05/3.30 tff(15443,plain,
% 3.05/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 3.05/3.30 inference(quant_inst,[status(thm)],[])).
% 3.05/3.30 tff(15444,plain,
% 3.05/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 3.05/3.30 inference(modus_ponens,[status(thm)],[15443, 15442])).
% 3.05/3.30 tff(15445,plain,
% 3.05/3.30 ($false),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[15444, 163, 406, 328, 3450, 332])).
% 3.05/3.30 tff(15446,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.30 tff(15447,plain,
% 3.05/3.30 (~r(s(s(z)), s(z))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[15446, 15438, 328, 332])).
% 3.05/3.30 tff(15448,plain,
% 3.05/3.30 (b(s(s(z)), s(z))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[487, 15447])).
% 3.05/3.30 tff(15449,plain,
% 3.05/3.30 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[3626, 15448, 15434, 15432])).
% 3.05/3.30 tff(15450,plain,
% 3.05/3.30 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[374, 15449])).
% 3.05/3.30 tff(15451,plain,
% 3.05/3.30 ($false),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[12134, 163, 15450, 332, 33, 423])).
% 3.05/3.30 tff(15452,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.30 tff(15453,plain,
% 3.05/3.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[15452, 332, 15428, 328, 1185])).
% 3.05/3.30 tff(15454,plain,
% 3.05/3.30 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[420, 15453])).
% 3.05/3.30 tff(15455,plain,
% 3.05/3.30 (~b(s(s(s(s(s(z))))), z)),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[8803, 559, 1185, 595])).
% 3.05/3.30 tff(15456,plain,
% 3.05/3.30 (r(s(s(s(s(s(z))))), z)),
% 3.05/3.30 inference(unit_resolution,[status(thm)],[3841, 15455])).
% 3.05/3.30 tff(15457,plain,
% 3.05/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15458,plain,
% 3.15/3.30 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15459,plain,
% 3.15/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.30 inference(monotonicity,[status(thm)],[15458])).
% 3.15/3.30 tff(15460,plain,
% 3.15/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(transitivity,[status(thm)],[15459, 15457])).
% 3.15/3.30 tff(15461,plain,
% 3.15/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.15/3.30 inference(quant_inst,[status(thm)],[])).
% 3.15/3.30 tff(15462,plain,
% 3.15/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.30 inference(modus_ponens,[status(thm)],[15461, 15460])).
% 3.15/3.30 tff(15463,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15462, 198, 1185, 595, 3615, 2, 559])).
% 3.15/3.30 tff(15464,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3098, 15463])).
% 3.15/3.30 tff(15465,plain,
% 3.15/3.30 ($false),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[13007, 163, 15464, 33, 152, 15456])).
% 3.15/3.30 tff(15466,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.30 tff(15467,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15466, 2, 152, 1185, 595, 3615, 33])).
% 3.15/3.30 tff(15468,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[469, 15467])).
% 3.15/3.30 tff(15469,plain,
% 3.15/3.30 (~b(s(s(z)), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3626, 2, 348, 3615])).
% 3.15/3.30 tff(15470,plain,
% 3.15/3.30 (r(s(s(z)), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[487, 15469])).
% 3.15/3.30 tff(15471,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[2720, 163, 328, 15470, 422])).
% 3.15/3.30 tff(15472,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[9576, 15471])).
% 3.15/3.30 tff(15473,plain,
% 3.15/3.30 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[2711, 163, 328, 15470, 422])).
% 3.15/3.30 tff(15474,plain,
% 3.15/3.30 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[2715, 26, 507, 15473])).
% 3.15/3.30 tff(15475,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[4057, 15472, 3745, 3615, 348, 2])).
% 3.15/3.30 tff(15476,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3098, 15475])).
% 3.15/3.30 tff(15477,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[13007, 163, 15476, 33, 152])).
% 3.15/3.30 tff(15478,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3841, 15477])).
% 3.15/3.30 tff(15479,plain,
% 3.15/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15480,plain,
% 3.15/3.30 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15481,plain,
% 3.15/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.15/3.30 inference(monotonicity,[status(thm)],[15480])).
% 3.15/3.30 tff(15482,plain,
% 3.15/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(transitivity,[status(thm)],[15481, 15479])).
% 3.15/3.30 tff(15483,plain,
% 3.15/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(quant_inst,[status(thm)],[])).
% 3.15/3.30 tff(15484,plain,
% 3.15/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.15/3.30 inference(modus_ponens,[status(thm)],[15483, 15482])).
% 3.15/3.30 tff(15485,plain,
% 3.15/3.30 ($false),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15484, 198, 9403, 5428, 15478, 15474, 15472])).
% 3.15/3.30 tff(15486,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.30 tff(15487,plain,
% 3.15/3.30 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15486, 15468, 9403, 33, 152, 3745, 3615, 348, 2, 328])).
% 3.15/3.30 tff(15488,plain,
% 3.15/3.30 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[4110, 15487])).
% 3.15/3.30 tff(15489,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[2720, 163, 328, 15470, 15468])).
% 3.15/3.30 tff(15490,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[9576, 15489])).
% 3.15/3.30 tff(15491,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[4057, 15490, 3745, 3615, 348, 2])).
% 3.15/3.30 tff(15492,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3098, 15491])).
% 3.15/3.30 tff(15493,plain,
% 3.15/3.30 ($false),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[5347, 163, 15492, 33, 152, 15488])).
% 3.15/3.30 tff(15494,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.30 tff(15495,plain,
% 3.15/3.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15494, 595, 152, 15454, 3615, 15430, 328, 9403, 1185, 15428])).
% 3.15/3.30 tff(15496,plain,
% 3.15/3.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3654, 15495])).
% 3.15/3.30 tff(15497,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15498,plain,
% 3.15/3.30 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15499,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 3.15/3.30 inference(monotonicity,[status(thm)],[15498])).
% 3.15/3.30 tff(15500,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.30 inference(transitivity,[status(thm)],[15499, 15497])).
% 3.15/3.30 tff(15501,plain,
% 3.15/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 3.15/3.30 inference(quant_inst,[status(thm)],[])).
% 3.15/3.30 tff(15502,plain,
% 3.15/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.15/3.30 inference(modus_ponens,[status(thm)],[15501, 15500])).
% 3.15/3.30 tff(15503,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15502, 163, 328, 332, 9580])).
% 3.15/3.30 tff(15504,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[469, 15503])).
% 3.15/3.30 tff(15505,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[8803, 15504, 1185, 595])).
% 3.15/3.30 tff(15506,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3841, 15505])).
% 3.15/3.30 tff(15507,plain,
% 3.15/3.30 ($false),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[11947, 163, 332, 33, 9580, 15506])).
% 3.15/3.30 tff(15508,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.30 tff(15509,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15508, 595, 15428, 1185, 332, 328])).
% 3.15/3.30 tff(15510,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[9576, 15509])).
% 3.15/3.30 tff(15511,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[5672, 198, 15430, 15454, 15510])).
% 3.15/3.30 tff(15512,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3098, 15511])).
% 3.15/3.30 tff(15513,plain,
% 3.15/3.30 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[10392, 163, 15512, 15428, 15496])).
% 3.15/3.30 tff(15514,plain,
% 3.15/3.30 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3841, 15513])).
% 3.15/3.30 tff(15515,plain,
% 3.15/3.30 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[8803, 15514, 1185, 595])).
% 3.15/3.30 tff(15516,plain,
% 3.15/3.30 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[469, 15515])).
% 3.15/3.30 tff(15517,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15518,plain,
% 3.15/3.30 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15519,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.30 inference(monotonicity,[status(thm)],[15518])).
% 3.15/3.30 tff(15520,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(transitivity,[status(thm)],[15519, 15517])).
% 3.15/3.30 tff(15521,plain,
% 3.15/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(quant_inst,[status(thm)],[])).
% 3.15/3.30 tff(15522,plain,
% 3.15/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.30 inference(modus_ponens,[status(thm)],[15521, 15520])).
% 3.15/3.30 tff(15523,plain,
% 3.15/3.30 ($false),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15522, 163, 328, 15512, 15496, 15516])).
% 3.15/3.30 tff(15524,plain,((~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.30 tff(15525,plain,
% 3.15/3.30 (~b(z, s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15524, 3615, 1185, 332, 152, 328, 9403])).
% 3.15/3.30 tff(15526,plain,
% 3.15/3.30 (r(z, s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[593, 15525])).
% 3.15/3.30 tff(15527,plain,
% 3.15/3.30 (~r(s(s(z)), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[15446, 15526, 328, 332])).
% 3.15/3.30 tff(15528,plain,
% 3.15/3.30 (b(s(s(z)), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[487, 15527])).
% 3.15/3.30 tff(15529,plain,
% 3.15/3.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3626, 15528, 15430, 3615])).
% 3.15/3.30 tff(15530,plain,
% 3.15/3.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.30 inference(unit_resolution,[status(thm)],[3654, 15529])).
% 3.15/3.30 tff(15531,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15532,plain,
% 3.15/3.30 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.30 inference(rewrite,[status(thm)],[])).
% 3.15/3.30 tff(15533,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.30 inference(monotonicity,[status(thm)],[15532])).
% 3.15/3.30 tff(15534,plain,
% 3.15/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(transitivity,[status(thm)],[15533, 15531])).
% 3.15/3.31 tff(15535,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15536,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15535, 15534])).
% 3.15/3.31 tff(15537,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15536, 163, 15526, 328, 15428, 15530])).
% 3.15/3.31 tff(15538,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15539,plain,
% 3.15/3.31 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15538, 152, 332, 1185, 328, 9403])).
% 3.15/3.31 tff(15540,plain,
% 3.15/3.31 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3613, 15539])).
% 3.15/3.31 tff(15541,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15542,plain,
% 3.15/3.31 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15543,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.31 inference(monotonicity,[status(thm)],[15542])).
% 3.15/3.31 tff(15544,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(transitivity,[status(thm)],[15543, 15541])).
% 3.15/3.31 tff(15545,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15546,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15545, 15544])).
% 3.15/3.31 tff(15547,plain,
% 3.15/3.31 (~r(z, s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15546, 163, 15540, 15428, 152])).
% 3.15/3.31 tff(15548,plain,
% 3.15/3.31 (b(z, s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[593, 15547])).
% 3.15/3.31 tff(15549,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15508, 15548, 15428, 1185, 332, 328])).
% 3.15/3.31 tff(15550,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9576, 15549])).
% 3.15/3.31 tff(15551,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[11807, 15430, 15454, 15550, 15428, 152])).
% 3.15/3.31 tff(15552,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3841, 15551])).
% 3.15/3.31 tff(15553,plain,
% 3.15/3.31 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[8803, 15552, 1185, 15548])).
% 3.15/3.31 tff(15554,plain,
% 3.15/3.31 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[469, 15553])).
% 3.15/3.31 tff(15555,plain,
% 3.15/3.31 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[5672, 198, 15430, 15454, 15550])).
% 3.15/3.31 tff(15556,plain,
% 3.15/3.31 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3098, 15555])).
% 3.15/3.31 tff(15557,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[5680, 163, 15556, 15540, 152, 15554])).
% 3.15/3.31 tff(15558,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15559,plain,
% 3.15/3.31 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15558, 332, 1185, 328, 9403])).
% 3.15/3.31 tff(15560,plain,
% 3.15/3.31 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[176, 15559])).
% 3.15/3.31 tff(15561,plain,
% 3.15/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15452, 332, 33, 328, 1185])).
% 3.15/3.31 tff(15562,plain,
% 3.15/3.31 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[420, 15561])).
% 3.15/3.31 tff(15563,plain,
% 3.15/3.31 (~r(s(s(z)), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15446, 406, 328, 332])).
% 3.15/3.31 tff(15564,plain,
% 3.15/3.31 (b(s(s(z)), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[487, 15563])).
% 3.15/3.31 tff(15565,plain,
% 3.15/3.31 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[5769, 15564, 1185, 15562, 330])).
% 3.15/3.31 tff(15566,plain,
% 3.15/3.31 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3654, 15565])).
% 3.15/3.31 tff(15567,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15536, 163, 406, 328, 33, 15566])).
% 3.15/3.31 tff(15568,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15569,plain,
% 3.15/3.31 (~r(z, s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15568, 15428, 328, 1185, 15560, 332])).
% 3.15/3.31 tff(15570,plain,
% 3.15/3.31 (b(z, s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[593, 15569])).
% 3.15/3.31 tff(15571,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15508, 15570, 15428, 1185, 332, 328])).
% 3.15/3.31 tff(15572,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9576, 15571])).
% 3.15/3.31 tff(15573,plain,
% 3.15/3.31 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[4953, 15570, 1185, 15560])).
% 3.15/3.31 tff(15574,plain,
% 3.15/3.31 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3654, 15573])).
% 3.15/3.31 tff(15575,plain,
% 3.15/3.31 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[10086, 332, 15428, 15574])).
% 3.15/3.31 tff(15576,plain,
% 3.15/3.31 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[374, 15575])).
% 3.15/3.31 tff(15577,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15578,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15579,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15578, 15577])).
% 3.15/3.31 tff(15580,plain,
% 3.15/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15579, 163, 328, 3639, 422])).
% 3.15/3.31 tff(15581,plain,
% 3.15/3.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9643, 15580])).
% 3.15/3.31 tff(15582,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15522, 163, 328, 3639, 422])).
% 3.15/3.31 tff(15583,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3098, 15582])).
% 3.15/3.31 tff(15584,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[11544, 198, 15583, 348, 3745, 15581, 4049])).
% 3.15/3.31 tff(15585,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15586,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15585, 15576, 15454, 15574, 328, 15572])).
% 3.15/3.31 tff(15587,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[469, 15586])).
% 3.15/3.31 tff(15588,plain,
% 3.15/3.31 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[8803, 15587, 1185, 15570])).
% 3.15/3.31 tff(15589,plain,
% 3.15/3.31 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3841, 15588])).
% 3.15/3.31 tff(15590,plain,
% 3.15/3.31 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[12069, 163, 332, 15428, 15589])).
% 3.15/3.31 tff(15591,plain,
% 3.15/3.31 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[2715, 26, 507, 15590])).
% 3.15/3.31 tff(15592,plain,
% 3.15/3.31 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9515, 15591, 9403, 15570, 15587])).
% 3.15/3.31 tff(15593,plain,
% 3.15/3.31 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[4110, 15592])).
% 3.15/3.31 tff(15594,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[11987, 15593, 15428, 15574])).
% 3.15/3.31 tff(15595,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3098, 15594])).
% 3.15/3.31 tff(15596,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[5672, 198, 15595, 15576, 15454, 15572])).
% 3.15/3.31 tff(15597,plain,((~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15598,plain,
% 3.15/3.31 ((~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15597, 15191])).
% 3.15/3.31 tff(15599,plain,
% 3.15/3.31 (~r(s(s(z)), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15598, 15398, 9363])).
% 3.15/3.31 tff(15600,plain,
% 3.15/3.31 (b(s(s(z)), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[345, 15599])).
% 3.15/3.31 tff(15601,plain,
% 3.15/3.31 (b(s(z), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15383, 3450, 2, 33])).
% 3.15/3.31 tff(15602,plain,
% 3.15/3.31 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[12762, 163, 3066, 33, 423])).
% 3.15/3.31 tff(15603,plain,
% 3.15/3.31 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3841, 15602])).
% 3.15/3.31 tff(15604,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15605,plain,
% 3.15/3.31 (((~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(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15606,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.31 inference(monotonicity,[status(thm)],[15605])).
% 3.15/3.31 tff(15607,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(transitivity,[status(thm)],[15606, 15604])).
% 3.15/3.31 tff(15608,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15609,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15608, 15607])).
% 3.15/3.31 tff(15610,plain,
% 3.15/3.31 (~r(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15609, 163, 3066, 33, 423])).
% 3.15/3.31 tff(15611,plain,
% 3.15/3.31 (b(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[4110, 15610])).
% 3.15/3.31 tff(15612,plain,
% 3.15/3.31 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9948, 15611, 347, 15603])).
% 3.15/3.31 tff(15613,plain,
% 3.15/3.31 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9885, 15612])).
% 3.15/3.31 tff(15614,plain,
% 3.15/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[11233, 9472, 423, 3066])).
% 3.15/3.31 tff(15615,plain,
% 3.15/3.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9643, 15614])).
% 3.15/3.31 tff(15616,plain,
% 3.15/3.31 (~b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15237, 15615, 2, 559])).
% 3.15/3.31 tff(15617,plain,
% 3.15/3.31 (r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[3301, 15616])).
% 3.15/3.31 tff(15618,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15619,plain,
% 3.15/3.31 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15620,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.31 inference(monotonicity,[status(thm)],[15619])).
% 3.15/3.31 tff(15621,plain,
% 3.15/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.31 inference(transitivity,[status(thm)],[15620, 15618])).
% 3.15/3.31 tff(15622,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15623,plain,
% 3.15/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15622, 15621])).
% 3.15/3.31 tff(15624,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15623, 163, 328, 3066, 15617, 9472])).
% 3.15/3.31 tff(15625,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15626,plain,
% 3.15/3.31 ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15625, 15191])).
% 3.15/3.31 tff(15627,plain,
% 3.15/3.31 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15626, 15613, 2, 3066, 423])).
% 3.15/3.31 tff(15628,plain,
% 3.15/3.31 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[469, 15627])).
% 3.15/3.31 tff(15629,plain,
% 3.15/3.31 ($false),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[2711, 163, 15191, 3450, 15628, 15613])).
% 3.15/3.31 tff(15630,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.31 tff(15631,plain,
% 3.15/3.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15630, 3450, 2, 3066, 347, 33])).
% 3.15/3.31 tff(15632,plain,
% 3.15/3.31 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[420, 15631])).
% 3.15/3.31 tff(15633,plain,
% 3.15/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15634,plain,
% 3.15/3.31 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), z)) | (~b(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))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15635,plain,
% 3.15/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.15/3.31 inference(monotonicity,[status(thm)],[15634])).
% 3.15/3.31 tff(15636,plain,
% 3.15/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.31 inference(transitivity,[status(thm)],[15635, 15633])).
% 3.15/3.31 tff(15637,plain,
% 3.15/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.31 inference(quant_inst,[status(thm)],[])).
% 3.15/3.31 tff(15638,plain,
% 3.15/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.15/3.31 inference(modus_ponens,[status(thm)],[15637, 15636])).
% 3.15/3.31 tff(15639,plain,
% 3.15/3.31 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[15638, 198, 1185, 15632, 2, 9363])).
% 3.15/3.31 tff(15640,plain,
% 3.15/3.31 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[176, 15639])).
% 3.15/3.31 tff(15641,plain,
% 3.15/3.31 (~r(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[5347, 163, 3066, 33, 15640])).
% 3.15/3.31 tff(15642,plain,
% 3.15/3.31 (b(z, s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[4110, 15641])).
% 3.15/3.31 tff(15643,plain,
% 3.15/3.31 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9948, 15642, 347, 4167])).
% 3.15/3.31 tff(15644,plain,
% 3.15/3.31 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.31 inference(unit_resolution,[status(thm)],[9885, 15643])).
% 3.15/3.31 tff(15645,plain,
% 3.15/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 3.15/3.31 inference(rewrite,[status(thm)],[])).
% 3.15/3.31 tff(15646,plain,
% 3.15/3.31 (((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15647,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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)))))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15646])).
% 3.15/3.32 tff(15648,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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))))))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15647, 15645])).
% 3.15/3.32 tff(15649,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(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(z, s(s(z)))) | (~b(s(z), z)))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15650,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15649, 15648])).
% 3.15/3.32 tff(15651,plain,
% 3.15/3.32 (~b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15650, 198, 1185, 347, 9363, 15642, 4167])).
% 3.15/3.32 tff(15652,plain,
% 3.15/3.32 (r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3301, 15651])).
% 3.15/3.32 tff(15653,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[12976, 163, 3066, 3450, 15652, 15644])).
% 3.15/3.32 tff(15654,plain,((~b(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15655,plain,
% 3.15/3.32 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15654, 15601, 3450, 347, 3066, 33, 2])).
% 3.15/3.32 tff(15656,plain,
% 3.15/3.32 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3841, 15655])).
% 3.15/3.32 tff(15657,plain,
% 3.15/3.32 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15379, 15632, 347, 9363])).
% 3.15/3.32 tff(15658,plain,
% 3.15/3.32 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[176, 15657])).
% 3.15/3.32 tff(15659,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[13007, 163, 3066, 33, 15658, 15656])).
% 3.15/3.32 tff(15660,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15661,plain,
% 3.15/3.32 (~r(s(s(z)), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15660, 3066, 33, 347, 2])).
% 3.15/3.32 tff(15662,plain,
% 3.15/3.32 (b(s(s(z)), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[487, 15661])).
% 3.15/3.32 tff(15663,plain,
% 3.15/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[11233, 15613, 3066, 423])).
% 3.15/3.32 tff(15664,plain,
% 3.15/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[9643, 15663])).
% 3.15/3.32 tff(15665,plain,
% 3.15/3.32 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[9634, 15664, 15603, 15611])).
% 3.15/3.32 tff(15666,plain,
% 3.15/3.32 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[176, 15665])).
% 3.15/3.32 tff(15667,plain,
% 3.15/3.32 (~r(z, s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[9972, 15666, 15613, 423])).
% 3.15/3.32 tff(15668,plain,
% 3.15/3.32 (b(s(z), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15372, 15667])).
% 3.15/3.32 tff(15669,plain,
% 3.15/3.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[5691, 15668, 347, 2, 15662])).
% 3.15/3.32 tff(15670,plain,
% 3.15/3.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[374, 15669])).
% 3.15/3.32 tff(15671,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[13034, 163, 3066, 15670, 15666, 15613])).
% 3.15/3.32 tff(15672,plain,((~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))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15673,plain,
% 3.15/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15672, 3066, 347, 2, 33])).
% 3.15/3.32 tff(15674,plain,
% 3.15/3.32 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[420, 15673])).
% 3.15/3.32 tff(15675,plain,
% 3.15/3.32 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15379, 15674, 347, 9363])).
% 3.15/3.32 tff(15676,plain,
% 3.15/3.32 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[176, 15675])).
% 3.15/3.32 tff(15677,plain,
% 3.15/3.32 (b(s(z), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15375, 15676, 2, 33])).
% 3.15/3.32 tff(15678,plain,
% 3.15/3.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[5691, 15677, 347, 2, 15662])).
% 3.15/3.32 tff(15679,plain,
% 3.15/3.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[374, 15678])).
% 3.15/3.32 tff(15680,plain,
% 3.15/3.32 (~r(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[13052, 15679, 9363, 3066, 15676])).
% 3.15/3.32 tff(15681,plain,
% 3.15/3.32 (b(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[593, 15680])).
% 3.15/3.32 tff(15682,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[10425, 198, 15677, 15681, 15662, 347])).
% 3.15/3.32 tff(15683,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15684,plain,
% 3.15/3.32 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15683, 15600, 2, 32])).
% 3.15/3.32 tff(15685,plain,
% 3.15/3.32 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3098, 15684])).
% 3.15/3.32 tff(15686,plain,
% 3.15/3.32 (~r(s(s(z)), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15597, 1185, 9403, 328])).
% 3.15/3.32 tff(15687,plain,
% 3.15/3.32 (b(s(s(z)), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[345, 15686])).
% 3.15/3.32 tff(15688,plain,
% 3.15/3.32 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[14050, 198, 15687, 330, 9403])).
% 3.15/3.32 tff(15689,plain,
% 3.15/3.32 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[420, 15688])).
% 3.15/3.32 tff(15690,plain,
% 3.15/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15341, 163, 328, 3272, 423])).
% 3.15/3.32 tff(15691,plain,
% 3.15/3.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3654, 15690])).
% 3.15/3.32 tff(15692,plain,
% 3.15/3.32 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15213, 3272, 423, 328])).
% 3.15/3.32 tff(15693,plain,
% 3.15/3.32 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3613, 15692])).
% 3.15/3.32 tff(15694,plain,
% 3.15/3.32 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[356, 330, 347, 331])).
% 3.15/3.32 tff(15695,plain,
% 3.15/3.32 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[374, 15694])).
% 3.15/3.32 tff(15696,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15213, 15695, 10638, 423, 328])).
% 3.15/3.32 tff(15697,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15698,plain,
% 3.15/3.32 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15697, 423, 328, 15687, 331, 1185])).
% 3.15/3.32 tff(15699,plain,
% 3.15/3.32 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[176, 15698])).
% 3.15/3.32 tff(15700,plain,
% 3.15/3.32 (~b(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[4967, 15691, 1185, 331, 15693])).
% 3.15/3.32 tff(15701,plain,
% 3.15/3.32 (r(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[593, 15700])).
% 3.15/3.32 tff(15702,plain,
% 3.15/3.32 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[13052, 15701, 15699, 9403, 3272])).
% 3.15/3.32 tff(15703,plain,
% 3.15/3.32 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3098, 15702])).
% 3.15/3.32 tff(15704,plain,
% 3.15/3.32 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3825, 198, 15703, 15693, 15691])).
% 3.15/3.32 tff(15705,plain,
% 3.15/3.32 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[469, 15704])).
% 3.15/3.32 tff(15706,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15707,plain,
% 3.15/3.32 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15708,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15707])).
% 3.15/3.32 tff(15709,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15708, 15706])).
% 3.15/3.32 tff(15710,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15711,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15710, 15709])).
% 3.15/3.32 tff(15712,plain,
% 3.15/3.32 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15711, 163, 15701, 328, 15705])).
% 3.15/3.32 tff(15713,plain,
% 3.15/3.32 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3841, 15712])).
% 3.15/3.32 tff(15714,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15715,plain,
% 3.15/3.32 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15716,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15715])).
% 3.15/3.32 tff(15717,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15716, 15714])).
% 3.15/3.32 tff(15718,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15719,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15718, 15717])).
% 3.15/3.32 tff(15720,plain,
% 3.15/3.32 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15719, 198, 15703, 15687, 331])).
% 3.15/3.32 tff(15721,plain,
% 3.15/3.32 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15720, 15713])).
% 3.15/3.32 tff(15722,plain,
% 3.15/3.32 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[9576, 15721])).
% 3.15/3.32 tff(15723,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[12996, 163, 328, 3272, 15705, 15722])).
% 3.15/3.32 tff(15724,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(15725,plain,
% 3.15/3.32 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15724, 423, 331, 9403, 1185, 328])).
% 3.15/3.32 tff(15726,plain,
% 3.15/3.32 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[374, 15725])).
% 3.15/3.32 tff(15727,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15728,plain,
% 3.15/3.32 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15729,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15728])).
% 3.15/3.32 tff(15730,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15729, 15727])).
% 3.15/3.32 tff(15731,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15732,plain,
% 3.15/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15731, 15730])).
% 3.15/3.32 tff(15733,plain,
% 3.15/3.32 (~b(s(s(z)), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15732, 198, 1185, 15726, 15687, 331])).
% 3.15/3.32 tff(15734,plain,
% 3.15/3.32 (r(s(s(z)), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[487, 15733])).
% 3.15/3.32 tff(15735,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15736,plain,
% 3.15/3.32 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15737,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15736])).
% 3.15/3.32 tff(15738,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15737, 15735])).
% 3.15/3.32 tff(15739,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15740,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15739, 15738])).
% 3.15/3.32 tff(15741,plain,
% 3.15/3.32 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15740, 163, 328, 15734, 423])).
% 3.15/3.32 tff(15742,plain,
% 3.15/3.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3654, 15741])).
% 3.15/3.32 tff(15743,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15744,plain,
% 3.15/3.32 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15745,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15744])).
% 3.15/3.32 tff(15746,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15745, 15743])).
% 3.15/3.32 tff(15747,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15748,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15747, 15746])).
% 3.15/3.32 tff(15749,plain,
% 3.15/3.32 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15748, 163, 328, 15734, 423])).
% 3.15/3.32 tff(15750,plain,
% 3.15/3.32 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3613, 15749])).
% 3.15/3.32 tff(15751,plain,
% 3.15/3.32 (~b(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[4967, 15742, 1185, 331, 15750])).
% 3.15/3.32 tff(15752,plain,
% 3.15/3.32 (r(z, s(z))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[593, 15751])).
% 3.15/3.32 tff(15753,plain,
% 3.15/3.32 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[2720, 163, 328, 3450, 3827])).
% 3.15/3.32 tff(15754,plain,
% 3.15/3.32 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[9576, 15753])).
% 3.15/3.32 tff(15755,plain,
% 3.15/3.32 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15711, 163, 406, 328, 3827])).
% 3.15/3.32 tff(15756,plain,
% 3.15/3.32 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[3841, 15755])).
% 3.15/3.32 tff(15757,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15758,plain,
% 3.15/3.32 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(15759,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 3.15/3.32 inference(monotonicity,[status(thm)],[15758])).
% 3.15/3.32 tff(15760,plain,
% 3.15/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[15759, 15757])).
% 3.15/3.32 tff(15761,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(15762,plain,
% 3.15/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[15761, 15760])).
% 3.15/3.32 tff(15763,plain,
% 3.15/3.32 (~r(z, s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[15762, 163, 406, 328, 3827])).
% 3.15/3.32 tff(15764,plain,
% 3.15/3.32 (b(z, s(s(s(s(s(z))))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[4110, 15763])).
% 3.15/3.32 tff(15765,plain,
% 3.15/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15766,plain,
% 3.15/3.33 (((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15767,plain,
% 3.15/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[15766])).
% 3.15/3.33 tff(15768,plain,
% 3.15/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[15767, 15765])).
% 3.15/3.33 tff(15769,plain,
% 3.15/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.15/3.33 inference(quant_inst,[status(thm)],[])).
% 3.15/3.33 tff(15770,plain,
% 3.15/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.15/3.33 inference(modus_ponens,[status(thm)],[15769, 15768])).
% 3.15/3.33 tff(15771,plain,
% 3.15/3.33 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15770, 198, 3819, 348, 9403])).
% 3.15/3.33 tff(15772,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15771, 15764, 15756, 15754])).
% 3.15/3.33 tff(15773,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15774,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15773, 15726, 9403, 15752, 328, 15734, 15750, 15742])).
% 3.15/3.33 tff(15775,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3098, 15774])).
% 3.15/3.33 tff(15776,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[12777, 163, 3066, 3450, 423, 9580])).
% 3.15/3.33 tff(15777,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15778,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15777, 15775, 15734, 423])).
% 3.15/3.33 tff(15779,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9576, 15778])).
% 3.15/3.33 tff(15780,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[13985, 15775, 15699, 15752])).
% 3.15/3.33 tff(15781,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3841, 15780])).
% 3.15/3.33 tff(15782,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[12165, 198, 15687, 9403, 15781, 15779])).
% 3.15/3.33 tff(15783,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15784,plain,
% 3.15/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15783, 331, 328, 1185, 9403])).
% 3.15/3.33 tff(15785,plain,
% 3.15/3.33 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[420, 15784])).
% 3.15/3.33 tff(15786,plain,
% 3.15/3.33 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[12109, 198, 15687, 15785, 9403])).
% 3.15/3.33 tff(15787,plain,
% 3.15/3.33 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[176, 15786])).
% 3.15/3.33 tff(15788,plain,
% 3.15/3.33 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9459, 15785, 9403, 331])).
% 3.15/3.33 tff(15789,plain,
% 3.15/3.33 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[374, 15788])).
% 3.15/3.33 tff(15790,plain,
% 3.15/3.33 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15298, 15787, 328, 15789])).
% 3.15/3.33 tff(15791,plain,
% 3.15/3.33 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3613, 15790])).
% 3.15/3.33 tff(15792,plain,
% 3.15/3.33 (~b(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9411, 15791, 9403, 331, 15785])).
% 3.15/3.33 tff(15793,plain,
% 3.15/3.33 (r(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[593, 15792])).
% 3.15/3.33 tff(15794,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[13052, 15793, 15789, 9403, 15787])).
% 3.15/3.33 tff(15795,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3098, 15794])).
% 3.15/3.33 tff(15796,plain,
% 3.15/3.33 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15168, 15795, 331, 9403, 15785])).
% 3.15/3.33 tff(15797,plain,
% 3.15/3.33 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[4110, 15796])).
% 3.15/3.33 tff(15798,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15799,plain,
% 3.15/3.33 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15800,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[15799])).
% 3.15/3.33 tff(15801,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[15800, 15798])).
% 3.15/3.33 tff(15802,plain,
% 3.15/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 3.15/3.33 inference(quant_inst,[status(thm)],[])).
% 3.15/3.33 tff(15803,plain,
% 3.15/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.15/3.33 inference(modus_ponens,[status(thm)],[15802, 15801])).
% 3.15/3.33 tff(15804,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15803, 163, 406, 328, 3639, 152])).
% 3.15/3.33 tff(15805,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15806,plain,
% 3.15/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15805, 15793, 328, 15787])).
% 3.15/3.33 tff(15807,plain,
% 3.15/3.33 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3654, 15806])).
% 3.15/3.33 tff(15808,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3825, 198, 15795, 15791, 15807])).
% 3.15/3.33 tff(15809,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[469, 15808])).
% 3.15/3.33 tff(15810,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15762, 163, 15793, 328, 15809, 15797])).
% 3.15/3.33 tff(15811,plain,((~b(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15812,plain,
% 3.15/3.33 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15811, 328, 9403, 1185])).
% 3.15/3.33 tff(15813,plain,
% 3.15/3.33 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[31, 15812])).
% 3.15/3.33 tff(15814,plain,
% 3.15/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15341, 163, 328, 3272, 15689])).
% 3.15/3.33 tff(15815,plain,
% 3.15/3.33 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3654, 15814])).
% 3.15/3.33 tff(15816,plain,
% 3.15/3.33 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15213, 3272, 15689, 328])).
% 3.15/3.33 tff(15817,plain,
% 3.15/3.33 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3613, 15816])).
% 3.15/3.33 tff(15818,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3825, 198, 3819, 15817, 15815])).
% 3.15/3.33 tff(15819,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[469, 15818])).
% 3.15/3.33 tff(15820,plain,
% 3.15/3.33 (~b(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[4953, 15815, 1185, 330])).
% 3.15/3.33 tff(15821,plain,
% 3.15/3.33 (r(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[593, 15820])).
% 3.15/3.33 tff(15822,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15711, 163, 15821, 328, 15819])).
% 3.15/3.33 tff(15823,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3841, 15822])).
% 3.15/3.33 tff(15824,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[12769, 198, 15687, 9403, 15823])).
% 3.15/3.33 tff(15825,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9576, 15824])).
% 3.15/3.33 tff(15826,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[12996, 163, 328, 3272, 15819, 15825])).
% 3.15/3.33 tff(15827,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15828,plain,
% 3.15/3.33 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15827, 330, 9403, 3819, 1185, 328])).
% 3.15/3.33 tff(15829,plain,
% 3.15/3.33 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[374, 15828])).
% 3.15/3.33 tff(15830,plain,
% 3.15/3.33 ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[10372, 198, 3819, 15687, 330])).
% 3.15/3.33 tff(15831,plain,
% 3.15/3.33 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15830, 15829])).
% 3.15/3.33 tff(15832,plain,
% 3.15/3.33 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9885, 15831])).
% 3.15/3.33 tff(15833,plain,
% 3.15/3.33 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9480, 15832, 328, 15689])).
% 3.15/3.33 tff(15834,plain,
% 3.15/3.33 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3654, 15833])).
% 3.15/3.33 tff(15835,plain,
% 3.15/3.33 (~b(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[4953, 15834, 1185, 330])).
% 3.15/3.33 tff(15836,plain,
% 3.15/3.33 (r(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[593, 15835])).
% 3.15/3.33 tff(15837,plain,
% 3.15/3.33 (~b(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[5691, 15834, 1185, 15687, 15829])).
% 3.15/3.33 tff(15838,plain,
% 3.15/3.33 (r(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[487, 15837])).
% 3.15/3.33 tff(15839,plain,
% 3.15/3.33 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15773, 15838, 9403, 3819, 328, 15829, 15836, 15834])).
% 3.15/3.33 tff(15840,plain,
% 3.15/3.33 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3613, 15839])).
% 3.15/3.33 tff(15841,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[10060, 163, 15836, 15840, 15813, 15689])).
% 3.15/3.33 tff(15842,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15843,plain,
% 3.15/3.33 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15842, 15191])).
% 3.15/3.33 tff(15844,plain,
% 3.15/3.33 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15843, 15685, 9363, 15398])).
% 3.15/3.33 tff(15845,plain,
% 3.15/3.33 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[176, 15844])).
% 3.15/3.33 tff(15846,plain,
% 3.15/3.33 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15843, 1185, 9363, 3819])).
% 3.15/3.33 tff(15847,plain,
% 3.15/3.33 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[176, 15846])).
% 3.15/3.33 tff(15848,plain,
% 3.15/3.33 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[5691, 560, 347, 2, 1185])).
% 3.15/3.33 tff(15849,plain,
% 3.15/3.33 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[374, 15848])).
% 3.15/3.33 tff(15850,plain,
% 3.15/3.33 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15298, 15191])).
% 3.15/3.33 tff(15851,plain,
% 3.15/3.33 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15850, 15849, 15847])).
% 3.15/3.33 tff(15852,plain,
% 3.15/3.33 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3613, 15851])).
% 3.15/3.33 tff(15853,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3825, 198, 3819, 15852, 2])).
% 3.15/3.33 tff(15854,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[469, 15853])).
% 3.15/3.33 tff(15855,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[10042, 198, 1185, 595, 560, 347])).
% 3.15/3.33 tff(15856,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15857,plain,
% 3.15/3.33 (~b(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15856, 560, 1185, 347])).
% 3.15/3.33 tff(15858,plain,
% 3.15/3.33 (r(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[593, 15857])).
% 3.15/3.33 tff(15859,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15711, 163, 406, 15191, 422, 3828])).
% 3.15/3.33 tff(15860,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15861,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15860, 15858, 15854])).
% 3.15/3.33 tff(15862,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3841, 15861])).
% 3.15/3.33 tff(15863,plain,
% 3.15/3.33 (~r(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15762, 163, 15858, 15191, 15854])).
% 3.15/3.33 tff(15864,plain,
% 3.15/3.33 (b(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[4110, 15863])).
% 3.15/3.33 tff(15865,plain,
% 3.15/3.33 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9948, 15864, 347, 15862])).
% 3.15/3.33 tff(15866,plain,
% 3.15/3.33 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9885, 15865])).
% 3.15/3.33 tff(15867,plain,
% 3.15/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15868,plain,
% 3.15/3.33 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15869,plain,
% 3.15/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[15868])).
% 3.15/3.33 tff(15870,plain,
% 3.15/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[15869, 15867])).
% 3.15/3.33 tff(15871,plain,
% 3.15/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 3.15/3.33 inference(quant_inst,[status(thm)],[])).
% 3.15/3.33 tff(15872,plain,
% 3.15/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.33 inference(modus_ponens,[status(thm)],[15871, 15870])).
% 3.15/3.33 tff(15873,plain,
% 3.15/3.33 (~b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15872, 198, 1185, 3819, 15852, 15864])).
% 3.15/3.33 tff(15874,plain,
% 3.15/3.33 (r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3301, 15873])).
% 3.15/3.33 tff(15875,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15876,plain,
% 3.15/3.33 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(15877,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[15876])).
% 3.15/3.33 tff(15878,plain,
% 3.15/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[15877, 15875])).
% 3.15/3.33 tff(15879,plain,
% 3.15/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 3.15/3.33 inference(quant_inst,[status(thm)],[])).
% 3.15/3.33 tff(15880,plain,
% 3.15/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.15/3.33 inference(modus_ponens,[status(thm)],[15879, 15878])).
% 3.15/3.33 tff(15881,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15880, 163, 15191, 15874, 15854, 15866])).
% 3.15/3.33 tff(15882,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15883,plain,
% 3.15/3.33 (~b(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15882, 15685, 15398, 15600, 2])).
% 3.15/3.33 tff(15884,plain,
% 3.15/3.33 (r(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[487, 15883])).
% 3.15/3.33 tff(15885,plain,
% 3.15/3.33 (b(s(z), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15397, 2, 33])).
% 3.15/3.33 tff(15886,plain,
% 3.15/3.33 (~r(s(s(z)), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15598, 15885, 9363])).
% 3.15/3.33 tff(15887,plain,
% 3.15/3.33 (b(s(s(z)), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[345, 15886])).
% 3.15/3.33 tff(15888,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15683, 15887, 2, 33])).
% 3.15/3.33 tff(15889,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3098, 15888])).
% 3.15/3.33 tff(15890,plain,
% 3.15/3.33 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15843, 15889, 9363, 15885])).
% 3.15/3.33 tff(15891,plain,
% 3.15/3.33 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[176, 15890])).
% 3.15/3.33 tff(15892,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15546, 163, 406, 151, 33, 152])).
% 3.15/3.33 tff(15893,plain,((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15894,plain,
% 3.15/3.33 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15893, 406, 33, 15891])).
% 3.15/3.33 tff(15895,plain,
% 3.15/3.33 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3613, 15894])).
% 3.15/3.33 tff(15896,plain,
% 3.15/3.33 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3825, 198, 15889, 15895, 2])).
% 3.15/3.33 tff(15897,plain,
% 3.15/3.33 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[469, 15896])).
% 3.15/3.33 tff(15898,plain,
% 3.15/3.33 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15860, 15897, 406])).
% 3.15/3.33 tff(15899,plain,
% 3.15/3.33 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[3841, 15898])).
% 3.15/3.33 tff(15900,plain,
% 3.15/3.33 (~r(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15762, 163, 406, 15191, 15897])).
% 3.15/3.33 tff(15901,plain,
% 3.15/3.33 (b(z, s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[4110, 15900])).
% 3.15/3.33 tff(15902,plain,
% 3.15/3.33 (~b(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15882, 15889, 15885, 15887, 2])).
% 3.15/3.33 tff(15903,plain,
% 3.15/3.33 (r(s(s(z)), s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[487, 15902])).
% 3.15/3.33 tff(15904,plain,
% 3.15/3.33 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[2711, 163, 15191, 15903, 15897])).
% 3.15/3.33 tff(15905,plain,
% 3.15/3.33 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9885, 15904])).
% 3.15/3.33 tff(15906,plain,
% 3.15/3.33 ($false),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[9948, 15905, 15901, 15887, 15899])).
% 3.15/3.33 tff(15907,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.33 tff(15908,plain,
% 3.15/3.33 (~r(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[15907, 2, 33])).
% 3.15/3.33 tff(15909,plain,
% 3.15/3.33 (b(z, s(z))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[593, 15908])).
% 3.15/3.34 tff(15910,plain,
% 3.15/3.34 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15466, 559, 2, 15885, 15891, 15909, 33])).
% 3.15/3.34 tff(15911,plain,
% 3.15/3.34 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3613, 15910])).
% 3.15/3.34 tff(15912,plain,
% 3.15/3.34 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15850, 15911, 15891])).
% 3.15/3.34 tff(15913,plain,
% 3.15/3.34 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[374, 15912])).
% 3.15/3.34 tff(15914,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15915,plain,
% 3.15/3.34 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15916,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15915])).
% 3.15/3.34 tff(15917,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(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))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15916, 15914])).
% 3.15/3.34 tff(15918,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15919,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15918, 15917])).
% 3.15/3.34 tff(15920,plain,
% 3.15/3.34 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15919, 198, 15909, 15889, 15913, 15887, 2, 559])).
% 3.15/3.34 tff(15921,plain,
% 3.15/3.34 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9576, 15920])).
% 3.15/3.34 tff(15922,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[2720, 163, 328, 3450, 422, 9580])).
% 3.15/3.34 tff(15923,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.34 tff(15924,plain,
% 3.15/3.34 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15923, 15191])).
% 3.15/3.34 tff(15925,plain,
% 3.15/3.34 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15924, 10342, 3450])).
% 3.15/3.34 tff(15926,plain,
% 3.15/3.34 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9576, 15925])).
% 3.15/3.34 tff(15927,plain,
% 3.15/3.34 (~r(s(s(z)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15598, 1185, 9403])).
% 3.15/3.34 tff(15928,plain,
% 3.15/3.34 (b(s(s(z)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[345, 15927])).
% 3.15/3.34 tff(15929,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[12165, 198, 15928, 9403, 4167, 15926])).
% 3.15/3.34 tff(15930,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.34 tff(15931,plain,
% 3.15/3.34 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15930, 9363, 15903, 15909, 15885])).
% 3.15/3.34 tff(15932,plain,
% 3.15/3.34 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3841, 15931])).
% 3.15/3.34 tff(15933,plain,
% 3.15/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[11795, 163, 33, 15891, 15932])).
% 3.15/3.34 tff(15934,plain,
% 3.15/3.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9643, 15933])).
% 3.15/3.34 tff(15935,plain,
% 3.15/3.34 (~b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15237, 559, 2, 15934])).
% 3.15/3.34 tff(15936,plain,
% 3.15/3.34 (r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3301, 15935])).
% 3.15/3.34 tff(15937,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15938,plain,
% 3.15/3.34 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15939,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15938])).
% 3.15/3.34 tff(15940,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15939, 15937])).
% 3.15/3.34 tff(15941,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15942,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15941, 15940])).
% 3.15/3.34 tff(15943,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15942, 163, 15191, 15903, 15936, 15921])).
% 3.15/3.34 tff(15944,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.34 tff(15945,plain,
% 3.15/3.34 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15944, 2, 32])).
% 3.15/3.34 tff(15946,plain,
% 3.15/3.34 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[469, 15945])).
% 3.15/3.34 tff(15947,plain,
% 3.15/3.34 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15924, 15946, 15884])).
% 3.15/3.34 tff(15948,plain,
% 3.15/3.34 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9576, 15947])).
% 3.15/3.34 tff(15949,plain,
% 3.15/3.34 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[2711, 163, 15191, 15884, 15946])).
% 3.15/3.34 tff(15950,plain,
% 3.15/3.34 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9885, 15949])).
% 3.15/3.34 tff(15951,plain,
% 3.15/3.34 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[12188, 198, 9363, 15950, 15948])).
% 3.15/3.34 tff(15952,plain,
% 3.15/3.34 (~r(z, s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15907, 2, 32])).
% 3.15/3.34 tff(15953,plain,
% 3.15/3.34 (b(z, s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[593, 15952])).
% 3.15/3.34 tff(15954,plain,
% 3.15/3.34 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15930, 9363, 15884, 15953, 15398])).
% 3.15/3.34 tff(15955,plain,
% 3.15/3.34 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3841, 15954])).
% 3.15/3.34 tff(15956,plain,
% 3.15/3.34 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[11795, 163, 32, 15845, 15955])).
% 3.15/3.34 tff(15957,plain,
% 3.15/3.34 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[9643, 15956])).
% 3.15/3.34 tff(15958,plain,
% 3.15/3.34 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[10508, 198, 15950, 15957, 15948])).
% 3.15/3.34 tff(15959,plain,
% 3.15/3.34 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[420, 15958])).
% 3.15/3.34 tff(15960,plain,
% 3.15/3.34 (~r(z, s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[4981, 15959, 15884, 15845])).
% 3.15/3.34 tff(15961,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15962,plain,
% 3.15/3.34 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15963,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15962])).
% 3.15/3.34 tff(15964,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15963, 15961])).
% 3.15/3.34 tff(15965,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15966,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15965, 15964])).
% 3.15/3.34 tff(15967,plain,
% 3.15/3.34 (~b(s(s(elem!1)), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15966, 198, 723, 1185, 595, 347, 9403])).
% 3.15/3.34 tff(15968,plain,
% 3.15/3.34 (r(s(s(elem!1)), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3497, 26, 10705, 15967])).
% 3.15/3.34 tff(15969,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15970,plain,
% 3.15/3.34 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15971,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15970])).
% 3.15/3.34 tff(15972,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15971, 15969])).
% 3.15/3.34 tff(15973,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15974,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15973, 15972])).
% 3.15/3.34 tff(15975,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15974, 163, 15191, 9275, 3450, 15968])).
% 3.15/3.34 tff(15976,plain,((~b(s(s(elem!1)), z)) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.34 tff(15977,plain,
% 3.15/3.34 (~b(s(s(elem!1)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15976, 14243, 15884, 15398, 15953, 15600, 9363])).
% 3.15/3.34 tff(15978,plain,
% 3.15/3.34 (r(s(s(elem!1)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[801, 15977])).
% 3.15/3.34 tff(15979,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15980,plain,
% 3.15/3.34 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15981,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15980])).
% 3.15/3.34 tff(15982,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15981, 15979])).
% 3.15/3.34 tff(15983,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15984,plain,
% 3.15/3.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15983, 15982])).
% 3.15/3.34 tff(15985,plain,
% 3.15/3.34 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15984, 163, 15978, 32, 15955])).
% 3.15/3.34 tff(15986,plain,
% 3.15/3.34 (b(s(z), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15371, 328, 49])).
% 3.15/3.34 tff(15987,plain,
% 3.15/3.34 (~b(elem!1, s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[1444, 198, 271, 15986, 595])).
% 3.15/3.34 tff(15988,plain,
% 3.15/3.34 (~b(s(s(z)), elem!1)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[2404, 198, 95, 271, 15687])).
% 3.15/3.34 tff(15989,plain,
% 3.15/3.34 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[10743, 95, 4105])).
% 3.15/3.34 tff(15990,plain,
% 3.15/3.34 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[10750, 15989])).
% 3.15/3.34 tff(15991,plain,
% 3.15/3.34 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15842, 3819, 9403, 328, 1185])).
% 3.15/3.34 tff(15992,plain,
% 3.15/3.34 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[176, 15991])).
% 3.15/3.34 tff(15993,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15994,plain,
% 3.15/3.34 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(15995,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.15/3.34 inference(monotonicity,[status(thm)],[15994])).
% 3.15/3.34 tff(15996,plain,
% 3.15/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[15995, 15993])).
% 3.15/3.34 tff(15997,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(15998,plain,
% 3.15/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[15997, 15996])).
% 3.15/3.34 tff(15999,plain,
% 3.15/3.34 (~b(s(s(elem!1)), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15998, 198, 95, 271, 723, 15687, 9403])).
% 3.15/3.34 tff(16000,plain,
% 3.15/3.34 (r(s(s(elem!1)), s(s(z)))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[3497, 26, 10705, 15999])).
% 3.15/3.34 tff(16001,plain,
% 3.15/3.34 (~b(s(s(z)), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[10042, 198, 1185, 595, 15687])).
% 3.15/3.34 tff(16002,plain,
% 3.15/3.34 (r(s(s(z)), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[487, 16001])).
% 3.15/3.34 tff(16003,plain,
% 3.15/3.34 (~b(s(s(elem!1)), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[5249, 723, 1185, 95, 595, 271])).
% 3.15/3.34 tff(16004,plain,
% 3.15/3.34 (r(s(s(elem!1)), s(z))),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[626, 16003])).
% 3.15/3.34 tff(16005,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[15974, 163, 328, 16004, 16002, 16000])).
% 3.15/3.34 tff(16006,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.34 tff(16007,plain,
% 3.15/3.34 (~b(s(s(elem!1)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[16006, 95, 10705, 328, 271, 9403, 1185, 595])).
% 3.15/3.34 tff(16008,plain,
% 3.15/3.34 (r(s(s(elem!1)), z)),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[801, 16007])).
% 3.15/3.34 tff(16009,plain,
% 3.15/3.34 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.34 inference(rewrite,[status(thm)],[])).
% 3.15/3.34 tff(16010,plain,
% 3.15/3.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16009])).
% 3.15/3.35 tff(16011,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16010, 5278])).
% 3.15/3.35 tff(16012,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16013,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16012, 16011])).
% 3.15/3.35 tff(16014,plain,
% 3.15/3.35 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16013, 163, 16008, 15813, 15992])).
% 3.15/3.35 tff(16015,plain,
% 3.15/3.35 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[934, 26, 16014, 15990])).
% 3.15/3.35 tff(16016,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(z))))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16017,plain,
% 3.15/3.35 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(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(s(s(z))))))), 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(s(z))))))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16018,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(z)))))))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16017])).
% 3.15/3.35 tff(16019,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(z))))))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16018, 16016])).
% 3.15/3.35 tff(16020,plain,
% 3.15/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16021,plain,
% 3.15/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), 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(s(z)))))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16020, 16019])).
% 3.15/3.35 tff(16022,plain,
% 3.15/3.35 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16021, 198, 3819, 16015, 3404])).
% 3.15/3.35 tff(16023,plain,
% 3.15/3.35 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[3400, 16022, 3398])).
% 3.15/3.35 tff(16024,plain,
% 3.15/3.35 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16023])).
% 3.15/3.35 tff(16025,plain,
% 3.15/3.35 (s(elem!1) = s(s(s(s(z))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[135, 16024, 288])).
% 3.15/3.35 tff(16026,plain,
% 3.15/3.35 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16025])).
% 3.15/3.35 tff(16027,plain,
% 3.15/3.35 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.15/3.35 inference(symmetry,[status(thm)],[16026])).
% 3.15/3.35 tff(16028,plain,
% 3.15/3.35 (s(s(s(z))) = elem!1),
% 3.15/3.35 inference(transitivity,[status(thm)],[294, 16027, 129])).
% 3.15/3.35 tff(16029,plain,
% 3.15/3.35 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16028])).
% 3.15/3.35 tff(16030,plain,
% 3.15/3.35 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16029])).
% 3.15/3.35 tff(16031,plain,
% 3.15/3.35 (~(s(z) = elem!1)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[10804, 16030])).
% 3.15/3.35 tff(16032,plain,
% 3.15/3.35 (~(s(s(z)) = elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[9862, 16031, 16023])).
% 3.15/3.35 tff(16033,plain,
% 3.15/3.35 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(z))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16029, 1241])).
% 3.15/3.35 tff(16034,plain,
% 3.15/3.35 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(z)))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16033])).
% 3.15/3.35 tff(16035,plain,
% 3.15/3.35 (~(elem!1 = s(z))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[10804, 16034])).
% 3.15/3.35 tff(16036,plain,
% 3.15/3.35 (r(elem!1, s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[242, 237, 238])).
% 3.15/3.35 tff(16037,plain,
% 3.15/3.35 (~(s(z) = elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[2914, 237])).
% 3.15/3.35 tff(16038,plain,
% 3.15/3.35 (r(s(z), elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[217, 16037, 149])).
% 3.15/3.35 tff(16039,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16040,plain,
% 3.15/3.35 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16041,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16040])).
% 3.15/3.35 tff(16042,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16041, 16039])).
% 3.15/3.35 tff(16043,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16044,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16043, 16042])).
% 3.15/3.35 tff(16045,plain,
% 3.15/3.35 ($false),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16044, 163, 16038, 16036, 2113, 3450])).
% 3.15/3.35 tff(16046,plain,((elem!1 = s(z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.35 tff(16047,plain,
% 3.15/3.35 (~r(s(s(z)), elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16046, 16035, 16002, 9215, 2407])).
% 3.15/3.35 tff(16048,plain,
% 3.15/3.35 ($false),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[2139, 16047, 16032, 15988])).
% 3.15/3.35 tff(16049,plain,((~b(z, elem!1)) | r(s(s(elem!1)), 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(s(s(z))))))), s(s(s(s(s(z))))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.35 tff(16050,plain,
% 3.15/3.35 (~b(z, elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16049, 271, 3819, 3404, 14243, 328, 3398, 15192, 15986, 595, 4105])).
% 3.15/3.35 tff(16051,plain,
% 3.15/3.35 (r(z, elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[102, 16050, 3])).
% 3.15/3.35 tff(16052,plain,
% 3.15/3.35 (~(s(s(z)) = elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[13224, 16051, 49])).
% 3.15/3.35 tff(16053,plain,
% 3.15/3.35 (~(elem!1 = s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[8661, 16052])).
% 3.15/3.35 tff(16054,plain,
% 3.15/3.35 (~r(s(s(z)), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15597, 15986, 15192, 328])).
% 3.15/3.35 tff(16055,plain,
% 3.15/3.35 (b(s(s(z)), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[345, 16054])).
% 3.15/3.35 tff(16056,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16057,plain,
% 3.15/3.35 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16058,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16057])).
% 3.15/3.35 tff(16059,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16058, 16056])).
% 3.15/3.35 tff(16060,plain,
% 3.15/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16061,plain,
% 3.15/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16060, 16059])).
% 3.15/3.35 tff(16062,plain,
% 3.15/3.35 (~b(elem!1, s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16061, 198, 271, 15986, 595, 16055, 15192])).
% 3.15/3.35 tff(16063,plain,
% 3.15/3.35 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[5572, 26, 16062])).
% 3.15/3.35 tff(16064,plain,
% 3.15/3.35 (r(elem!1, s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16063, 16053])).
% 3.15/3.35 tff(16065,plain,
% 3.15/3.35 (~b(s(s(z)), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[10042, 198, 15986, 595, 16055])).
% 3.15/3.35 tff(16066,plain,
% 3.15/3.35 (r(s(s(z)), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[487, 16065])).
% 3.15/3.35 tff(16067,plain,
% 3.15/3.35 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16068,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16067])).
% 3.15/3.35 tff(16069,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16068, 6598])).
% 3.15/3.35 tff(16070,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16071,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16070, 16069])).
% 3.15/3.35 tff(16072,plain,
% 3.15/3.35 (~r(elem!1, s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16071, 163, 328, 16066, 16064])).
% 3.15/3.35 tff(16073,plain,
% 3.15/3.35 (elem!1 = s(z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[242, 16072, 15987])).
% 3.15/3.35 tff(16074,plain,
% 3.15/3.35 (b(z, elem!1) <=> b(z, s(z))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16073])).
% 3.15/3.35 tff(16075,plain,
% 3.15/3.35 (b(z, s(z)) <=> b(z, elem!1)),
% 3.15/3.35 inference(symmetry,[status(thm)],[16074])).
% 3.15/3.35 tff(16076,plain,
% 3.15/3.35 (b(z, elem!1)),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[595, 16075])).
% 3.15/3.35 tff(16077,plain,
% 3.15/3.35 ($false),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16050, 16076])).
% 3.15/3.35 tff(16078,plain,((~b(elem!1, z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | r(z, s(s(z))) | (z = elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.35 tff(16079,plain,
% 3.15/3.35 ((~b(elem!1, z)) | (~b(z, s(z))) | r(z, s(s(z))) | (z = elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16078, 15191])).
% 3.15/3.35 tff(16080,plain,
% 3.15/3.35 (~b(elem!1, z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16079, 15985, 15685, 15960, 15953, 15957, 3, 15951])).
% 3.15/3.35 tff(16081,plain,
% 3.15/3.35 (r(elem!1, z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[187, 16080, 3617])).
% 3.15/3.35 tff(16082,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16083,plain,
% 3.15/3.35 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.15/3.35 inference(rewrite,[status(thm)],[])).
% 3.15/3.35 tff(16084,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 3.15/3.35 inference(monotonicity,[status(thm)],[16083])).
% 3.15/3.35 tff(16085,plain,
% 3.15/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.15/3.35 inference(transitivity,[status(thm)],[16084, 16082])).
% 3.15/3.35 tff(16086,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 3.15/3.35 inference(quant_inst,[status(thm)],[])).
% 3.15/3.35 tff(16087,plain,
% 3.15/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.15/3.35 inference(modus_ponens,[status(thm)],[16086, 16085])).
% 3.15/3.35 tff(16088,plain,
% 3.15/3.35 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[16087, 163, 16081, 32, 15845])).
% 3.15/3.35 tff(16089,plain,
% 3.15/3.35 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15683, 347, 2, 32])).
% 3.15/3.35 tff(16090,plain,
% 3.15/3.35 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[3098, 16089])).
% 3.15/3.35 tff(16091,plain,
% 3.15/3.35 (b(s(z), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15392, 347, 2, 32])).
% 3.15/3.35 tff(16092,plain,
% 3.15/3.35 (~b(s(s(z)), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15882, 16091, 16090, 347, 2])).
% 3.15/3.35 tff(16093,plain,
% 3.15/3.35 (r(s(s(z)), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[487, 16092])).
% 3.15/3.35 tff(16094,plain,
% 3.15/3.35 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15748, 163, 15191, 16093, 423])).
% 3.15/3.35 tff(16095,plain,
% 3.15/3.35 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[3613, 16094])).
% 3.15/3.35 tff(16096,plain,
% 3.15/3.35 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[3825, 198, 16090, 16095, 2])).
% 3.15/3.35 tff(16097,plain,
% 3.15/3.35 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[469, 16096])).
% 3.15/3.35 tff(16098,plain,
% 3.15/3.35 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15924, 16097, 16093])).
% 3.15/3.35 tff(16099,plain,
% 3.15/3.35 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[9576, 16098])).
% 3.15/3.35 tff(16100,plain,
% 3.15/3.35 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15843, 16091, 9363, 16090])).
% 3.15/3.35 tff(16101,plain,
% 3.15/3.35 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[176, 16100])).
% 3.15/3.35 tff(16102,plain,
% 3.15/3.35 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[11795, 163, 32, 16101, 3828])).
% 3.15/3.35 tff(16103,plain,
% 3.15/3.35 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[9643, 16102])).
% 3.15/3.35 tff(16104,plain,
% 3.15/3.35 (~r(z, s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15860, 3828, 16097])).
% 3.15/3.35 tff(16105,plain,
% 3.15/3.35 (b(z, s(z))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[593, 16104])).
% 3.15/3.35 tff(16106,plain,
% 3.15/3.35 (~b(s(s(elem!1)), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15976, 14243, 16093, 16091, 16105, 347, 9363])).
% 3.15/3.35 tff(16107,plain,
% 3.15/3.35 (r(s(s(elem!1)), z)),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[801, 16106])).
% 3.15/3.35 tff(16108,plain,
% 3.15/3.35 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[15984, 163, 16107, 32, 3828])).
% 3.15/3.35 tff(16109,plain,
% 3.15/3.35 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[3400, 16108, 3396])).
% 3.15/3.35 tff(16110,plain,
% 3.15/3.35 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[2711, 163, 15191, 16093, 16097])).
% 3.15/3.35 tff(16111,plain,
% 3.15/3.35 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.35 inference(unit_resolution,[status(thm)],[9885, 16110])).
% 3.15/3.35 tff(16112,plain,
% 3.15/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16113,plain,
% 3.15/3.36 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), 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(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16114,plain,
% 3.15/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16113])).
% 3.15/3.36 tff(16115,plain,
% 3.15/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[16114, 16112])).
% 3.15/3.36 tff(16116,plain,
% 3.15/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(16117,plain,
% 3.15/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16116, 16115])).
% 3.15/3.36 tff(16118,plain,
% 3.15/3.36 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16117, 198, 16090, 16111, 16109, 16103, 16099])).
% 3.15/3.36 tff(16119,plain,
% 3.15/3.36 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16013, 163, 16107, 32, 16101])).
% 3.15/3.36 tff(16120,plain,
% 3.15/3.36 ((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))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[934, 26, 16119])).
% 3.15/3.36 tff(16121,plain,
% 3.15/3.36 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16120, 16118])).
% 3.15/3.36 tff(16122,plain,
% 3.15/3.36 (s(s(s(s(s(z))))) = elem!1),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[10750, 16121])).
% 3.15/3.36 tff(16123,plain,
% 3.15/3.36 (elem!1 = s(s(s(s(s(z)))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16122, 4740])).
% 3.15/3.36 tff(16124,plain,
% 3.15/3.36 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[12034, 198, 16090, 16111, 16103])).
% 3.15/3.36 tff(16125,plain,
% 3.15/3.36 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[374, 16124])).
% 3.15/3.36 tff(16126,plain,
% 3.15/3.36 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[13042, 198, 347, 9363, 16111, 16099])).
% 3.15/3.36 tff(16127,plain,
% 3.15/3.36 (~r(z, s(s(z)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[4981, 423, 16093, 16101])).
% 3.15/3.36 tff(16128,plain,
% 3.15/3.36 (~b(elem!1, z)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16079, 16108, 16090, 16127, 16105, 16103, 3, 16126])).
% 3.15/3.36 tff(16129,plain,
% 3.15/3.36 (r(elem!1, z)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[187, 16128, 3617])).
% 3.15/3.36 tff(16130,plain,
% 3.15/3.36 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16087, 163, 16129, 32, 16101])).
% 3.15/3.36 tff(16131,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16132,plain,
% 3.15/3.36 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16133,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16132])).
% 3.15/3.36 tff(16134,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[16133, 16131])).
% 3.15/3.36 tff(16135,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(16136,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16135, 16134])).
% 3.15/3.36 tff(16137,plain,
% 3.15/3.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16136, 163, 16129, 32, 16101])).
% 3.15/3.36 tff(16138,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16139,plain,
% 3.15/3.36 (((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16140,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16139])).
% 3.15/3.36 tff(16141,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.15/3.36 inference(transitivity,[status(thm)],[16140, 16138])).
% 3.15/3.36 tff(16142,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(16143,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16142, 16141])).
% 3.15/3.36 tff(16144,plain,
% 3.15/3.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16143, 163, 16129, 32, 3828])).
% 3.15/3.36 tff(16145,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 3.15/3.36 tff(16146,plain,
% 3.15/3.36 (b(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[528, 15989, 16145])).
% 3.15/3.36 tff(16147,plain,
% 3.15/3.36 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[3468, 95, 1])).
% 3.15/3.36 tff(16148,plain,
% 3.15/3.36 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[256, 16147, 9233])).
% 3.15/3.36 tff(16149,plain,
% 3.15/3.36 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[3792, 16147])).
% 3.15/3.36 tff(16150,plain,
% 3.15/3.36 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[703, 16149, 7797])).
% 3.15/3.36 tff(16151,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[3221, 198, 3819, 16150, 16148, 16146])).
% 3.15/3.36 tff(16152,plain,((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(z))))), elem!1) | b(z, s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16153,plain,
% 3.15/3.36 (~b(z, elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16152, 16144, 1, 16090, 16126, 16137, 16130])).
% 3.15/3.36 tff(16154,plain,
% 3.15/3.36 (r(z, elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[102, 16153, 3])).
% 3.15/3.36 tff(16155,plain,
% 3.15/3.36 (~(elem!1 = s(z))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[10935, 16154, 16104])).
% 3.15/3.36 tff(16156,plain,
% 3.15/3.36 (~(s(z) = elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[2914, 16155])).
% 3.15/3.36 tff(16157,plain,
% 3.15/3.36 (~(s(s(z)) = s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[227, 16156])).
% 3.15/3.36 tff(16158,plain,
% 3.15/3.36 (~(elem!1 = s(s(s(s(s(z))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[13824, 16157, 16101, 16125, 423, 32, 3618, 16090, 16095, 2, 16103, 347])).
% 3.15/3.36 tff(16159,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16158, 16123])).
% 3.15/3.36 tff(16160,plain,((z = elem!1) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | b(z, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z)) | (s(s(elem!1)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16161,plain,
% 3.15/3.36 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16160, 3, 2, 15600, 1, 15955, 15959])).
% 3.15/3.36 tff(16162,plain,
% 3.15/3.36 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16136, 163, 16081, 32, 15845])).
% 3.15/3.36 tff(16163,plain,
% 3.15/3.36 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[3792, 14196])).
% 3.15/3.36 tff(16164,plain,
% 3.15/3.36 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[703, 16163, 7797])).
% 3.15/3.36 tff(16165,plain,
% 3.15/3.36 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[256, 14196, 9233])).
% 3.15/3.36 tff(16166,plain,
% 3.15/3.36 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[8726, 16165, 1475, 790, 598, 116, 152, 833, 16164])).
% 3.15/3.36 tff(16167,plain,
% 3.15/3.36 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[3381, 16166])).
% 3.15/3.36 tff(16168,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[314, 16167])).
% 3.15/3.36 tff(16169,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16170,plain,
% 3.15/3.36 (elem!1 = s(s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16169, 3380, 790, 1475, 152, 833, 7797, 9233])).
% 3.15/3.36 tff(16171,plain,
% 3.15/3.36 (s(s(elem!1)) = elem!1),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[676, 16170])).
% 3.15/3.36 tff(16172,plain,
% 3.15/3.36 (s(s(s(elem!1))) = s(elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[2064, 16171])).
% 3.15/3.36 tff(16173,plain,
% 3.15/3.36 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 3.15/3.36 inference(transitivity,[status(thm)],[9254, 16172])).
% 3.15/3.36 tff(16174,plain,
% 3.15/3.36 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16173])).
% 3.15/3.36 tff(16175,plain,
% 3.15/3.36 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(symmetry,[status(thm)],[16174])).
% 3.15/3.36 tff(16176,plain,
% 3.15/3.36 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[3381, 16175])).
% 3.15/3.36 tff(16177,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[314, 16176])).
% 3.15/3.36 tff(16178,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(elem!1, z)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(s(z))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16179,plain,
% 3.15/3.36 (~r(z, elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16178, 16162, 15845, 16161, 15978, 16081, 16088])).
% 3.15/3.36 tff(16180,plain,
% 3.15/3.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16143, 163, 16081, 32, 15955])).
% 3.15/3.36 tff(16181,plain,
% 3.15/3.36 (~b(z, elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16152, 16180, 1, 15685, 15951, 16162, 16088])).
% 3.15/3.36 tff(16182,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[102, 16181, 16179, 3])).
% 3.15/3.36 tff(16183,plain,((z = elem!1) | b(z, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16184,plain,
% 3.15/3.36 (z = elem!1),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16183, 2, 1])).
% 3.15/3.36 tff(16185,plain,
% 3.15/3.36 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16184])).
% 3.15/3.36 tff(16186,plain,
% 3.15/3.36 (r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[15955, 16185])).
% 3.15/3.36 tff(16187,plain,
% 3.15/3.36 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16184])).
% 3.15/3.36 tff(16188,plain,
% 3.15/3.36 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[32, 16187])).
% 3.15/3.36 tff(16189,plain,
% 3.15/3.36 (s(z) = s(elem!1)),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16184])).
% 3.15/3.36 tff(16190,plain,
% 3.15/3.36 (s(s(z)) = s(s(elem!1))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16189])).
% 3.15/3.36 tff(16191,plain,
% 3.15/3.36 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16190])).
% 3.15/3.36 tff(16192,plain,
% 3.15/3.36 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16184])).
% 3.15/3.36 tff(16193,plain,
% 3.15/3.36 (b(s(s(z)), elem!1)),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[15600, 16192])).
% 3.15/3.36 tff(16194,plain,
% 3.15/3.36 (b(s(s(elem!1)), elem!1)),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16193, 16191])).
% 3.15/3.36 tff(16195,plain,
% 3.15/3.36 (elem!1 = z),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[78, 16184])).
% 3.15/3.36 tff(16196,plain,
% 3.15/3.36 (~r(z, s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[12249, 16195, 15960])).
% 3.15/3.36 tff(16197,plain,
% 3.15/3.36 (b(z, s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1096, 16196])).
% 3.15/3.36 tff(16198,plain,
% 3.15/3.36 (b(elem!1, s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[87, 16197, 16195])).
% 3.15/3.36 tff(16199,plain,
% 3.15/3.36 (s(elem!1) = s(z)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1646, 16195])).
% 3.15/3.36 tff(16200,plain,
% 3.15/3.36 (~r(z, s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[3240, 16199, 15952])).
% 3.15/3.36 tff(16201,plain,
% 3.15/3.36 (b(z, s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1791, 16200])).
% 3.15/3.36 tff(16202,plain,
% 3.15/3.36 (b(s(elem!1), z)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1209, 16184, 15398])).
% 3.15/3.36 tff(16203,plain,
% 3.15/3.36 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16190])).
% 3.15/3.36 tff(16204,plain,
% 3.15/3.36 (b(s(z), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[4923, 16184, 15398])).
% 3.15/3.36 tff(16205,plain,
% 3.15/3.36 (~(elem!1 = s(z))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[6595, 16204])).
% 3.15/3.36 tff(16206,plain,
% 3.15/3.36 (~(s(z) = elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[2914, 16205])).
% 3.15/3.36 tff(16207,plain,
% 3.15/3.36 (~(s(s(z)) = s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[227, 16206])).
% 3.15/3.36 tff(16208,plain,
% 3.15/3.36 (~b(s(s(z)), s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[6776, 16201, 15600, 16202])).
% 3.15/3.36 tff(16209,plain,
% 3.15/3.36 (r(s(s(z)), s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[2378, 16208, 16207])).
% 3.15/3.36 tff(16210,plain,
% 3.15/3.36 (r(s(s(elem!1)), s(elem!1))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16209, 16203])).
% 3.15/3.36 tff(16211,plain,
% 3.15/3.36 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[58])).
% 3.15/3.36 tff(16212,plain,
% 3.15/3.36 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16211])).
% 3.15/3.36 tff(16213,plain,
% 3.15/3.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[1282, 16212])).
% 3.15/3.36 tff(16214,plain,
% 3.15/3.36 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1263, 16213])).
% 3.15/3.36 tff(16215,plain,
% 3.15/3.36 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1270, 16214])).
% 3.15/3.36 tff(16216,plain,
% 3.15/3.36 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1874, 11093, 68, 1128])).
% 3.15/3.36 tff(16217,plain,
% 3.15/3.36 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1326, 16216, 16215])).
% 3.15/3.36 tff(16218,plain,
% 3.15/3.36 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 3.15/3.36 inference(symmetry,[status(thm)],[6032])).
% 3.15/3.36 tff(16219,plain,
% 3.15/3.36 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(elem!1), s(s(z))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16218])).
% 3.15/3.36 tff(16220,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 3.15/3.36 tff(16221,plain,
% 3.15/3.36 (~r(s(elem!1), s(s(z)))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16220, 16219])).
% 3.15/3.36 tff(16222,plain,
% 3.15/3.36 (r(s(elem!1), s(s(z)))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[15191, 6033])).
% 3.15/3.36 tff(16223,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16222, 16221])).
% 3.15/3.36 tff(16224,plain,((~(z = elem!1)) | r(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16225,plain,
% 3.15/3.36 (r(s(elem!1), s(s(elem!1)))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16224, 57])).
% 3.15/3.36 tff(16226,plain,
% 3.15/3.36 (r(s(s(s(elem!1))), s(elem!1))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[1339, 11104, 16213])).
% 3.15/3.36 tff(16227,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16228,plain,
% 3.15/3.36 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16229,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16228])).
% 3.15/3.36 tff(16230,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[16229, 16227])).
% 3.15/3.36 tff(16231,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(16232,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16231, 16230])).
% 3.15/3.36 tff(16233,plain,
% 3.15/3.36 ($false),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16232, 163, 16226, 1773, 16225, 16217])).
% 3.15/3.36 tff(16234,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.36 tff(16235,plain,
% 3.15/3.36 (r(s(s(s(elem!1))), elem!1)),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16234, 16210, 16202, 16201, 16198, 16194, 16184])).
% 3.15/3.36 tff(16236,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16237,plain,
% 3.15/3.36 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16238,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16237])).
% 3.15/3.36 tff(16239,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(transitivity,[status(thm)],[16238, 16236])).
% 3.15/3.36 tff(16240,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.36 inference(quant_inst,[status(thm)],[])).
% 3.15/3.36 tff(16241,plain,
% 3.15/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16240, 16239])).
% 3.15/3.36 tff(16242,plain,
% 3.15/3.36 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[16241, 163, 16235, 16188, 16186])).
% 3.15/3.36 tff(16243,plain,
% 3.15/3.36 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16190])).
% 3.15/3.36 tff(16244,plain,
% 3.15/3.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16243])).
% 3.15/3.36 tff(16245,plain,
% 3.15/3.36 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16244])).
% 3.15/3.36 tff(16246,plain,
% 3.15/3.36 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[10622, 16195])).
% 3.15/3.36 tff(16247,plain,
% 3.15/3.36 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[16246, 16245])).
% 3.15/3.36 tff(16248,plain,
% 3.15/3.36 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.15/3.36 inference(unit_resolution,[status(thm)],[4903, 26, 16247, 16242])).
% 3.15/3.36 tff(16249,plain,
% 3.15/3.36 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.36 inference(monotonicity,[status(thm)],[16184])).
% 3.15/3.36 tff(16250,plain,
% 3.15/3.36 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.36 inference(modus_ponens,[status(thm)],[15845, 16249])).
% 3.15/3.36 tff(16251,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16252,plain,
% 3.15/3.36 (((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 3.15/3.36 inference(rewrite,[status(thm)],[])).
% 3.15/3.36 tff(16253,plain,
% 3.15/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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)))))))))))),
% 3.15/3.37 inference(monotonicity,[status(thm)],[16252])).
% 3.15/3.37 tff(16254,plain,
% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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))))))))))),
% 3.15/3.37 inference(transitivity,[status(thm)],[16253, 16251])).
% 3.15/3.37 tff(16255,plain,
% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.37 inference(quant_inst,[status(thm)],[])).
% 3.15/3.37 tff(16256,plain,
% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~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)))))))))),
% 3.15/3.37 inference(modus_ponens,[status(thm)],[16255, 16254])).
% 3.15/3.37 tff(16257,plain,
% 3.15/3.37 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[16256, 163, 16235, 16188, 16250])).
% 3.15/3.37 tff(16258,plain,
% 3.15/3.37 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[4845, 16184])).
% 3.15/3.37 tff(16259,plain,
% 3.15/3.37 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[4849, 26, 16258, 16257])).
% 3.15/3.37 tff(16260,plain,
% 3.15/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(rewrite,[status(thm)],[])).
% 3.15/3.37 tff(16261,plain,
% 3.15/3.37 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(rewrite,[status(thm)],[])).
% 3.15/3.37 tff(16262,plain,
% 3.15/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.15/3.37 inference(monotonicity,[status(thm)],[16261])).
% 3.15/3.37 tff(16263,plain,
% 3.15/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(transitivity,[status(thm)],[16262, 16260])).
% 3.15/3.37 tff(16264,plain,
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% 3.15/3.37 inference(quant_inst,[status(thm)],[])).
% 3.15/3.37 tff(16265,plain,
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% 3.15/3.37 inference(modus_ponens,[status(thm)],[16264, 16263])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16265, 198, 15685, 15957, 16259, 16248])).
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% 3.15/3.37 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[3654, 16268])).
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% 3.15/3.37 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[10086, 332, 3639, 33])).
% 3.15/3.37 tff(16273,plain,
% 3.15/3.37 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 3.15/3.37 tff(16274,plain,
% 3.15/3.37 ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[9505, 15191])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16274, 332, 3639])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[15508, 15191])).
% 3.15/3.37 tff(16280,plain,
% 3.15/3.37 (~r(s(s(s(s(s(z))))), s(s(z)))),
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% 3.15/3.37 tff(16281,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[9576, 16280])).
% 3.15/3.37 tff(16282,plain,
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% 3.15/3.37 tff(16287,plain,
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% 3.15/3.37 tff(16291,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[593, 16291])).
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% 3.15/3.37 ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[15805, 15191])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16293, 16292, 3639])).
% 3.15/3.37 tff(16295,plain,
% 3.15/3.37 ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[15568, 15191])).
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% 3.15/3.37 tff(16298,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.37 tff(16299,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[15343, 15191])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[9576, 16321])).
% 3.15/3.37 tff(16323,plain,
% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(rewrite,[status(thm)],[])).
% 3.15/3.37 tff(16324,plain,
% 3.15/3.37 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(rewrite,[status(thm)],[])).
% 3.15/3.37 tff(16325,plain,
% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 3.15/3.37 inference(monotonicity,[status(thm)],[16324])).
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% 3.15/3.37 tff(16329,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16328, 163, 15373, 16322, 16316, 16320])).
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% 3.15/3.37 tff(16331,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16330, 16269, 32])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16298, 32, 16269])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[15536, 163, 406, 15191, 33, 3639])).
% 3.15/3.37 tff(16335,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.37 tff(16336,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16335, 32, 16269])).
% 3.15/3.37 tff(16337,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[593, 16336])).
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% 3.15/3.37 tff(16339,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[487, 16338])).
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% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
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% 3.15/3.37 tff(16341,plain,
% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.37 inference(quant_inst,[status(thm)],[])).
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% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 3.15/3.37 inference(modus_ponens,[status(thm)],[16341, 16340])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16342, 163, 15191, 16339, 16269])).
% 3.15/3.37 tff(16344,plain,
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% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
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% 3.15/3.37 tff(16346,plain,
% 3.15/3.37 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.37 inference(rewrite,[status(thm)],[])).
% 3.15/3.37 tff(16347,plain,
% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.37 inference(monotonicity,[status(thm)],[16346])).
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% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
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% 3.15/3.37 inference(modus_ponens,[status(thm)],[16349, 16348])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16350, 163, 15191, 16339, 16269])).
% 3.15/3.37 tff(16352,plain,
% 3.15/3.37 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
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% 3.15/3.37 tff(16353,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16335, 33, 3639])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[593, 16353])).
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[16330, 3639, 33])).
% 3.15/3.37 tff(16356,plain,
% 3.15/3.37 (~r(s(s(s(s(s(z))))), z)),
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% 3.15/3.37 tff(16357,plain,
% 3.15/3.37 (b(s(s(s(s(s(z))))), z)),
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% 3.15/3.37 tff(16358,plain,
% 3.15/3.37 (~b(s(s(s(s(s(z))))), s(z))),
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% 3.15/3.37 tff(16359,plain,
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% 3.15/3.37 tff(16360,plain,
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% 3.15/3.37 tff(16362,plain,
% 3.15/3.37 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[420, 16361])).
% 3.15/3.37 tff(16363,plain,
% 3.15/3.37 (~r(s(s(z)), s(s(s(s(s(z))))))),
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% 3.15/3.37 tff(16364,plain,
% 3.15/3.37 (b(s(s(z)), s(s(s(s(s(z))))))),
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% 3.15/3.37 tff(16365,plain,
% 3.15/3.37 (~b(z, s(s(s(s(s(z))))))),
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% 3.15/3.37 tff(16366,plain,
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% 3.15/3.37 tff(16367,plain,
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% 3.15/3.37 tff(16368,plain,
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% 3.15/3.37 inference(unit_resolution,[status(thm)],[9576, 16367])).
% 3.15/3.37 tff(16369,plain,
% 3.15/3.37 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
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% 3.15/3.37 tff(16370,plain,
% 3.15/3.37 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
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% 3.15/3.37 tff(16371,plain,
% 3.15/3.37 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
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% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.37 inference(monotonicity,[status(thm)],[16371])).
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% 3.15/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.37 inference(transitivity,[status(thm)],[16372, 12200])).
% 3.15/3.37 tff(16374,plain,
% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(quant_inst,[status(thm)],[])).
% 3.15/3.37 tff(16375,plain,
% 3.15/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.37 inference(modus_ponens,[status(thm)],[16374, 16373])).
% 3.15/3.37 tff(16376,plain,
% 3.15/3.37 ($false),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[16375, 163, 3066, 33, 16370, 16366])).
% 3.15/3.37 tff(16377,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.37 tff(16378,plain,
% 3.15/3.37 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[16377, 16357, 33, 16360, 16300, 16362, 3066])).
% 3.15/3.37 tff(16379,plain,
% 3.15/3.37 ($false),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[469, 16378, 16358])).
% 3.15/3.37 tff(16380,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.37 tff(16381,plain,
% 3.15/3.37 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[16380, 32, 16269])).
% 3.15/3.37 tff(16382,plain,
% 3.15/3.37 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[3098, 16381])).
% 3.15/3.37 tff(16383,plain,
% 3.15/3.37 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[4991, 198, 16382, 16352, 16344])).
% 3.15/3.37 tff(16384,plain,
% 3.15/3.37 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[9576, 16383])).
% 3.15/3.37 tff(16385,plain,
% 3.15/3.37 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[15924, 16384, 16339])).
% 3.15/3.37 tff(16386,plain,
% 3.15/3.37 (b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[469, 16385])).
% 3.15/3.37 tff(16387,plain,
% 3.15/3.37 (~r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[15942, 163, 15191, 16339, 16384])).
% 3.15/3.37 tff(16388,plain,
% 3.15/3.37 (b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[3301, 16387])).
% 3.15/3.37 tff(16389,plain,
% 3.15/3.37 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[11269, 16388, 16386, 16337])).
% 3.15/3.37 tff(16390,plain,
% 3.15/3.37 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[4110, 16389])).
% 3.15/3.37 tff(16391,plain,
% 3.15/3.37 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[11833, 16390, 32, 16384])).
% 3.15/3.37 tff(16392,plain,
% 3.15/3.37 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[9643, 16391])).
% 3.15/3.37 tff(16393,plain,
% 3.15/3.37 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[11330, 198, 16382, 16352, 16392])).
% 3.15/3.37 tff(16394,plain,
% 3.15/3.37 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[9885, 16393])).
% 3.15/3.37 tff(16395,plain,
% 3.15/3.37 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[8803, 16386, 16331, 16337])).
% 3.15/3.37 tff(16396,plain,
% 3.15/3.37 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.37 inference(unit_resolution,[status(thm)],[3841, 16395])).
% 3.15/3.38 tff(16397,plain,
% 3.15/3.38 (~b(s(s(z)), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15856, 595, 347, 1185])).
% 3.15/3.38 tff(16398,plain,
% 3.15/3.38 (r(s(s(z)), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[487, 16397])).
% 3.15/3.38 tff(16399,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16342, 163, 15191, 16398, 3639])).
% 3.15/3.38 tff(16400,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[420, 16399])).
% 3.15/3.38 tff(16401,plain,
% 3.15/3.38 (~b(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15379, 330, 347, 16400])).
% 3.15/3.38 tff(16402,plain,
% 3.15/3.38 (r(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[54, 16401])).
% 3.15/3.38 tff(16403,plain,
% 3.15/3.38 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[10396, 16402, 3639, 347, 595, 330, 16398])).
% 3.15/3.38 tff(16404,plain,
% 3.15/3.38 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3613, 16403])).
% 3.15/3.38 tff(16405,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16350, 163, 15191, 16398, 3639])).
% 3.15/3.38 tff(16406,plain,
% 3.15/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[374, 16405])).
% 3.15/3.38 tff(16407,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4991, 198, 3819, 16406, 16400])).
% 3.15/3.38 tff(16408,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9576, 16407])).
% 3.15/3.38 tff(16409,plain,
% 3.15/3.38 (~r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15942, 163, 15191, 16398, 16408])).
% 3.15/3.38 tff(16410,plain,
% 3.15/3.38 (b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3301, 16409])).
% 3.15/3.38 tff(16411,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16412,plain,
% 3.15/3.38 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16413,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16412])).
% 3.15/3.38 tff(16414,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.38 inference(transitivity,[status(thm)],[16413, 16411])).
% 3.15/3.38 tff(16415,plain,
% 3.15/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(quant_inst,[status(thm)],[])).
% 3.15/3.38 tff(16416,plain,
% 3.15/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16415, 16414])).
% 3.15/3.38 tff(16417,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16416, 198, 1185, 3819, 16410, 16404, 330])).
% 3.15/3.38 tff(16418,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16419,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16418, 16331, 16382, 16269, 16333, 16337])).
% 3.15/3.38 tff(16420,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[176, 16419])).
% 3.15/3.38 tff(16421,plain,
% 3.15/3.38 (~r(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[5001, 16420, 16339, 16352, 16396])).
% 3.15/3.38 tff(16422,plain,
% 3.15/3.38 (b(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[54, 16421])).
% 3.15/3.38 tff(16423,plain,
% 3.15/3.38 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14275, 14243, 16384, 16333, 16422, 16390, 16394])).
% 3.15/3.38 tff(16424,plain,
% 3.15/3.38 (~b(elem!1, z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16079, 16423, 16382, 16421, 16337, 16392, 3, 16389])).
% 3.15/3.38 tff(16425,plain,
% 3.15/3.38 (r(elem!1, z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[187, 16424, 3617])).
% 3.15/3.38 tff(16426,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16087, 163, 16425, 32, 16420])).
% 3.15/3.38 tff(16427,plain,
% 3.15/3.38 (~b(s(s(elem!1)), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15976, 14243, 16339, 16331, 16337, 16333, 16422])).
% 3.15/3.38 tff(16428,plain,
% 3.15/3.38 (r(s(s(elem!1)), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[801, 16427])).
% 3.15/3.38 tff(16429,plain,
% 3.15/3.38 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16136, 163, 16425, 32, 16420])).
% 3.15/3.38 tff(16430,plain,
% 3.15/3.38 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16143, 163, 16425, 32, 16396])).
% 3.15/3.38 tff(16431,plain,
% 3.15/3.38 (~b(z, elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16152, 16430, 1, 16382, 16389, 16429, 16426])).
% 3.15/3.38 tff(16432,plain,
% 3.15/3.38 (r(z, elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[102, 16431, 3])).
% 3.15/3.38 tff(16433,plain,
% 3.15/3.38 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16178, 16432, 16420, 16429, 16428, 16425, 16426])).
% 3.15/3.38 tff(16434,plain,
% 3.15/3.38 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3400, 16433, 16423])).
% 3.15/3.38 tff(16435,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16436,plain,
% 3.15/3.38 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16437,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16436])).
% 3.15/3.38 tff(16438,plain,
% 3.15/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(transitivity,[status(thm)],[16437, 16435])).
% 3.15/3.38 tff(16439,plain,
% 3.15/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(quant_inst,[status(thm)],[])).
% 3.15/3.38 tff(16440,plain,
% 3.15/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16439, 16438])).
% 3.15/3.38 tff(16441,plain,
% 3.15/3.38 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16440, 198, 16382, 16388, 16386, 16434, 16392])).
% 3.15/3.38 tff(16442,plain,
% 3.15/3.38 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16013, 163, 16428, 32, 16420])).
% 3.15/3.38 tff(16443,plain,
% 3.15/3.38 ((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))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[934, 26, 16442])).
% 3.15/3.38 tff(16444,plain,
% 3.15/3.38 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16443, 16441])).
% 3.15/3.38 tff(16445,plain,
% 3.15/3.38 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16444])).
% 3.15/3.38 tff(16446,plain,
% 3.15/3.38 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 3.15/3.38 inference(symmetry,[status(thm)],[16445])).
% 3.15/3.38 tff(16447,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(s(z)))))))), z) <=> b(s(s(s(elem!1))), z)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16446])).
% 3.15/3.38 tff(16448,plain,
% 3.15/3.38 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.15/3.38 inference(symmetry,[status(thm)],[16447])).
% 3.15/3.38 tff(16449,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(s(z)))))))), z) <=> r(s(s(s(elem!1))), z)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16446])).
% 3.15/3.38 tff(16450,plain,
% 3.15/3.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16449])).
% 3.15/3.38 tff(16451,plain,
% 3.15/3.38 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16445])).
% 3.15/3.38 tff(16452,plain,
% 3.15/3.38 (~(s(s(z)) = elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[13224, 16432, 16421])).
% 3.15/3.38 tff(16453,plain,
% 3.15/3.38 (~(s(s(s(elem!1))) = elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[11360, 16444, 16452])).
% 3.15/3.38 tff(16454,plain,
% 3.15/3.38 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16444])).
% 3.15/3.38 tff(16455,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.15/3.38 inference(symmetry,[status(thm)],[16454])).
% 3.15/3.38 tff(16456,plain,
% 3.15/3.38 (s(s(s(s(s(z))))) = elem!1),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[10750, 16444])).
% 3.15/3.38 tff(16457,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16456])).
% 3.15/3.38 tff(16458,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), elem!1)),
% 3.15/3.38 inference(transitivity,[status(thm)],[16457, 16455])).
% 3.15/3.38 tff(16459,plain,
% 3.15/3.38 (b(s(s(elem!1)), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16392, 16458])).
% 3.15/3.38 tff(16460,plain,
% 3.15/3.38 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16444])).
% 3.15/3.38 tff(16461,plain,
% 3.15/3.38 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.15/3.38 inference(symmetry,[status(thm)],[16460])).
% 3.15/3.38 tff(16462,plain,
% 3.15/3.38 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16456])).
% 3.15/3.38 tff(16463,plain,
% 3.15/3.38 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.15/3.38 inference(transitivity,[status(thm)],[16462, 16461])).
% 3.15/3.38 tff(16464,plain,
% 3.15/3.38 (b(elem!1, s(s(elem!1)))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16382, 16463])).
% 3.15/3.38 tff(16465,plain,
% 3.15/3.38 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16444])).
% 3.15/3.38 tff(16466,plain,
% 3.15/3.38 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(elem!1)))),
% 3.15/3.38 inference(symmetry,[status(thm)],[16465])).
% 3.15/3.38 tff(16467,plain,
% 3.15/3.38 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14077, 198, 16382, 16388, 16392])).
% 3.15/3.38 tff(16468,plain,
% 3.15/3.38 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3613, 16467])).
% 3.15/3.38 tff(16469,plain,
% 3.15/3.38 (r(s(z), s(s(elem!1)))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16468, 16466])).
% 3.15/3.38 tff(16470,plain,
% 3.15/3.38 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16456])).
% 3.15/3.38 tff(16471,plain,
% 3.15/3.38 (b(elem!1, s(z))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16386, 16470])).
% 3.15/3.38 tff(16472,plain,
% 3.15/3.38 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16456])).
% 3.15/3.38 tff(16473,plain,
% 3.15/3.38 (b(s(z), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16388, 16472])).
% 3.15/3.38 tff(16474,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[11338])).
% 3.15/3.38 tff(16475,plain,
% 3.15/3.38 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.15/3.38 inference(symmetry,[status(thm)],[16474])).
% 3.15/3.38 tff(16476,plain,
% 3.15/3.38 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16475])).
% 3.15/3.38 tff(16477,plain,
% 3.15/3.38 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[2840])).
% 3.15/3.38 tff(16478,plain,
% 3.15/3.38 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(transitivity,[status(thm)],[16477, 663])).
% 3.15/3.38 tff(16479,plain,
% 3.15/3.38 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 3.15/3.38 inference(symmetry,[status(thm)],[16478])).
% 3.15/3.38 tff(16480,plain,
% 3.15/3.38 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[11341])).
% 3.15/3.38 tff(16481,plain,
% 3.15/3.38 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 3.15/3.38 inference(transitivity,[status(thm)],[16480, 16479])).
% 3.15/3.38 tff(16482,plain,
% 3.15/3.38 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16481])).
% 3.15/3.38 tff(16483,plain,
% 3.15/3.38 (~(s(s(elem!1)) = elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[314, 16482])).
% 3.15/3.38 tff(16484,plain,
% 3.15/3.38 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1250, 16483])).
% 3.15/3.38 tff(16485,plain,
% 3.15/3.38 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1263, 16484])).
% 3.15/3.38 tff(16486,plain,
% 3.15/3.38 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1270, 16485])).
% 3.15/3.38 tff(16487,plain,
% 3.15/3.38 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1326, 14310, 16486])).
% 3.15/3.38 tff(16488,plain,
% 3.15/3.38 (~r(s(s(s(elem!1))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[2801, 16487, 790, 682])).
% 3.15/3.38 tff(16489,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16488, 16476])).
% 3.15/3.38 tff(16490,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[11403, 26, 14336, 14331, 16489])).
% 3.15/3.38 tff(16491,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16492,plain,
% 3.15/3.38 (~b(s(s(s(elem!1))), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16491, 16473, 16471, 16444, 16428, 16469, 16464, 16459])).
% 3.15/3.38 tff(16493,plain,
% 3.15/3.38 (r(s(s(s(elem!1))), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1308, 16492, 16453])).
% 3.15/3.38 tff(16494,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16493, 16451])).
% 3.15/3.38 tff(16495,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14348, 163, 16432, 16425, 16494])).
% 3.15/3.38 tff(16496,plain,
% 3.15/3.38 (~r(s(s(s(elem!1))), z)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16495, 16450])).
% 3.15/3.38 tff(16497,plain,
% 3.15/3.38 (b(s(s(s(elem!1))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1295, 16496])).
% 3.15/3.38 tff(16498,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16497, 16448])).
% 3.15/3.38 tff(16499,plain,
% 3.15/3.38 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16456])).
% 3.15/3.38 tff(16500,plain,
% 3.15/3.38 (r(s(s(z)), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16394, 16499])).
% 3.15/3.38 tff(16501,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14360, 163, 16425, 16500, 16494])).
% 3.15/3.38 tff(16502,plain,
% 3.15/3.38 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14364, 26, 11379, 16501])).
% 3.15/3.38 tff(16503,plain,
% 3.15/3.38 (r(z, s(s(s(s(s(s(s(s(z))))))))) <=> r(z, s(s(s(elem!1))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16446])).
% 3.15/3.38 tff(16504,plain,
% 3.15/3.38 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(symmetry,[status(thm)],[16503])).
% 3.15/3.38 tff(16505,plain,
% 3.15/3.38 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16504])).
% 3.15/3.38 tff(16506,plain,
% 3.15/3.38 (~r(z, s(s(s(elem!1))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[8223, 16493, 16425, 16432])).
% 3.15/3.38 tff(16507,plain,
% 3.15/3.38 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16506, 16505])).
% 3.15/3.38 tff(16508,plain,
% 3.15/3.38 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14380, 14376, 16507])).
% 3.15/3.38 tff(16509,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(s(z)))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[14387, 198, 16333, 16508, 16502])).
% 3.15/3.38 tff(16510,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16509, 16498])).
% 3.15/3.38 tff(16511,plain,((z = elem!1) | b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16512,plain,
% 3.15/3.38 (z = elem!1),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16511, 1])).
% 3.15/3.38 tff(16513,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16512])).
% 3.15/3.38 tff(16514,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16396, 16513])).
% 3.15/3.38 tff(16515,plain,
% 3.15/3.38 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16512])).
% 3.15/3.38 tff(16516,plain,
% 3.15/3.38 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[32, 16515])).
% 3.15/3.38 tff(16517,plain,
% 3.15/3.38 (s(z) = s(elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16512])).
% 3.15/3.38 tff(16518,plain,
% 3.15/3.38 (s(s(z)) = s(s(elem!1))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16517])).
% 3.15/3.38 tff(16519,plain,
% 3.15/3.38 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16518])).
% 3.15/3.38 tff(16520,plain,
% 3.15/3.38 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16512])).
% 3.15/3.38 tff(16521,plain,
% 3.15/3.38 (b(s(s(z)), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16333, 16520])).
% 3.15/3.38 tff(16522,plain,
% 3.15/3.38 (b(s(s(elem!1)), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16521, 16519])).
% 3.15/3.38 tff(16523,plain,
% 3.15/3.38 (elem!1 = z),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[78, 16512])).
% 3.15/3.38 tff(16524,plain,
% 3.15/3.38 (~r(z, s(s(elem!1)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[12249, 16523, 16421])).
% 3.15/3.38 tff(16525,plain,
% 3.15/3.38 (b(z, s(s(elem!1)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1096, 16524])).
% 3.15/3.38 tff(16526,plain,
% 3.15/3.38 (b(elem!1, s(s(elem!1)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[87, 16525, 16523])).
% 3.15/3.38 tff(16527,plain,
% 3.15/3.38 (s(elem!1) = s(z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1646, 16523])).
% 3.15/3.38 tff(16528,plain,
% 3.15/3.38 (~r(z, s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3240, 16527, 16336])).
% 3.15/3.38 tff(16529,plain,
% 3.15/3.38 (b(z, s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1791, 16528])).
% 3.15/3.38 tff(16530,plain,
% 3.15/3.38 (b(s(elem!1), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[1209, 16512, 16331])).
% 3.15/3.38 tff(16531,plain,
% 3.15/3.38 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16518])).
% 3.15/3.38 tff(16532,plain,
% 3.15/3.38 (b(s(z), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4923, 16512, 16331])).
% 3.15/3.38 tff(16533,plain,
% 3.15/3.38 (~(elem!1 = s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[6595, 16532])).
% 3.15/3.38 tff(16534,plain,
% 3.15/3.38 (~(s(z) = elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[2914, 16533])).
% 3.15/3.38 tff(16535,plain,
% 3.15/3.38 (~(s(s(z)) = s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[227, 16534])).
% 3.15/3.38 tff(16536,plain,
% 3.15/3.38 (~b(s(s(z)), s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[6776, 16529, 16333, 16530])).
% 3.15/3.38 tff(16537,plain,
% 3.15/3.38 (r(s(s(z)), s(elem!1))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[2378, 16536, 16535])).
% 3.15/3.38 tff(16538,plain,
% 3.15/3.38 (r(s(s(elem!1)), s(elem!1))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16537, 16531])).
% 3.15/3.38 tff(16539,plain,
% 3.15/3.38 (r(s(s(s(elem!1))), elem!1)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16234, 16538, 16530, 16529, 16526, 16522, 16512])).
% 3.15/3.38 tff(16540,plain,
% 3.15/3.38 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16241, 163, 16539, 16516, 16514])).
% 3.15/3.38 tff(16541,plain,
% 3.15/3.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16518])).
% 3.15/3.38 tff(16542,plain,
% 3.15/3.38 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16541])).
% 3.15/3.38 tff(16543,plain,
% 3.15/3.38 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16542])).
% 3.15/3.38 tff(16544,plain,
% 3.15/3.38 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[10622, 16523])).
% 3.15/3.38 tff(16545,plain,
% 3.15/3.38 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16544, 16543])).
% 3.15/3.38 tff(16546,plain,
% 3.15/3.38 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4903, 26, 16545, 16540])).
% 3.15/3.38 tff(16547,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16512])).
% 3.15/3.38 tff(16548,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16420, 16547])).
% 3.15/3.38 tff(16549,plain,
% 3.15/3.38 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16256, 163, 16539, 16516, 16548])).
% 3.15/3.38 tff(16550,plain,
% 3.15/3.38 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4845, 16512])).
% 3.15/3.38 tff(16551,plain,
% 3.15/3.38 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4849, 26, 16550, 16549])).
% 3.15/3.38 tff(16552,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16265, 198, 16382, 16392, 16551, 16546])).
% 3.15/3.38 tff(16553,plain,(b(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16554,plain,
% 3.15/3.38 ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[340, 15191])).
% 3.15/3.38 tff(16555,plain,
% 3.15/3.38 (~r(s(s(z)), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16554, 15373, 41])).
% 3.15/3.38 tff(16556,plain,
% 3.15/3.38 (b(s(s(z)), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[345, 16555])).
% 3.15/3.38 tff(16557,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[356, 16556, 16553, 15388])).
% 3.15/3.38 tff(16558,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[176, 16557])).
% 3.15/3.38 tff(16559,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9533, 16558, 41])).
% 3.15/3.38 tff(16560,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[7283, 16558, 16553, 41, 15373])).
% 3.15/3.38 tff(16561,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3654, 16560, 16559])).
% 3.15/3.38 tff(16562,plain,(b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16563,plain,
% 3.15/3.38 ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(z)))) | (~b(s(z), z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15811, 15191])).
% 3.15/3.38 tff(16564,plain,
% 3.15/3.38 (~b(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16563, 16562, 16553])).
% 3.15/3.38 tff(16565,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9362, 16564])).
% 3.15/3.38 tff(16566,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3654, 16565])).
% 3.15/3.38 tff(16567,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16293, 406, 16566])).
% 3.15/3.38 tff(16568,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[176, 16567])).
% 3.15/3.38 tff(16569,plain,
% 3.15/3.38 (r(z, s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[54, 16564])).
% 3.15/3.38 tff(16570,plain,
% 3.15/3.38 ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[8860, 15191])).
% 3.15/3.38 tff(16571,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16570, 406, 16569])).
% 3.15/3.38 tff(16572,plain,
% 3.15/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[374, 16571])).
% 3.15/3.38 tff(16573,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[356, 16572, 16568, 16553, 347])).
% 3.15/3.38 tff(16574,plain,((~r(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16575,plain,
% 3.15/3.38 (~r(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16574, 347])).
% 3.15/3.38 tff(16576,plain,
% 3.15/3.38 (b(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[593, 16575])).
% 3.15/3.38 tff(16577,plain,
% 3.15/3.38 (~b(s(s(z)), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15856, 16576, 347, 16562])).
% 3.15/3.38 tff(16578,plain,
% 3.15/3.38 (r(s(s(z)), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[487, 16577])).
% 3.15/3.38 tff(16579,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16350, 163, 15191, 16578, 16566])).
% 3.15/3.38 tff(16580,plain,
% 3.15/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[374, 16579])).
% 3.15/3.38 tff(16581,plain,
% 3.15/3.38 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[356, 16580, 16553, 347])).
% 3.15/3.38 tff(16582,plain,
% 3.15/3.38 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[176, 16581])).
% 3.15/3.38 tff(16583,plain,
% 3.15/3.38 (~r(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[5001, 16582, 16569, 16578, 16580])).
% 3.15/3.38 tff(16584,plain,
% 3.15/3.38 (b(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3841, 16583])).
% 3.15/3.38 tff(16585,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[8803, 16584, 16562, 16576])).
% 3.15/3.38 tff(16586,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[469, 16585])).
% 3.15/3.38 tff(16587,plain,
% 3.15/3.38 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[15924, 16586, 16578])).
% 3.15/3.38 tff(16588,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16342, 163, 15191, 16578, 16566])).
% 3.15/3.38 tff(16589,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[420, 16588])).
% 3.15/3.38 tff(16590,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16288, 16586, 16566, 16589, 16580])).
% 3.15/3.38 tff(16591,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9576, 16590, 16587])).
% 3.15/3.38 tff(16592,plain,(~b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16593,plain,
% 3.15/3.38 (r(s(s(z)), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[345, 16592])).
% 3.15/3.38 tff(16594,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[5727, 163, 406, 15191, 16569, 332])).
% 3.15/3.38 tff(16595,plain,((~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16596,plain,
% 3.15/3.38 (~r(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16595, 9544])).
% 3.15/3.38 tff(16597,plain,
% 3.15/3.38 (b(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[593, 16596])).
% 3.15/3.38 tff(16598,plain,
% 3.15/3.38 (~r(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16595, 332])).
% 3.15/3.38 tff(16599,plain,
% 3.15/3.38 (b(z, s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[593, 16598])).
% 3.15/3.38 tff(16600,plain,
% 3.15/3.38 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[8483, 330, 16553, 16562])).
% 3.15/3.38 tff(16601,plain,
% 3.15/3.38 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3613, 16600])).
% 3.15/3.38 tff(16602,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9431, 163, 15191, 151, 3272, 16566])).
% 3.15/3.38 tff(16603,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16604,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16603, 16601])).
% 3.15/3.38 tff(16605,plain,
% 3.15/3.38 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[374, 16604])).
% 3.15/3.38 tff(16606,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4174, 3819, 16553, 330])).
% 3.15/3.38 tff(16607,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3841, 16606])).
% 3.15/3.38 tff(16608,plain,
% 3.15/3.38 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16274, 332, 16566])).
% 3.15/3.38 tff(16609,plain,
% 3.15/3.38 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[420, 16608])).
% 3.15/3.38 tff(16610,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4991, 198, 3819, 16605, 16609])).
% 3.15/3.38 tff(16611,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9576, 16610])).
% 3.15/3.38 tff(16612,plain,
% 3.15/3.38 ($false),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[568, 163, 16569, 332, 16611, 16607])).
% 3.15/3.38 tff(16613,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.38 tff(16614,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[16613, 330, 332])).
% 3.15/3.38 tff(16615,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3098, 16614])).
% 3.15/3.38 tff(16616,plain,
% 3.15/3.38 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[11684, 3066, 16566, 151])).
% 3.15/3.38 tff(16617,plain,
% 3.15/3.38 (b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[469, 16616])).
% 3.15/3.38 tff(16618,plain,
% 3.15/3.38 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[8803, 16617, 16562, 16599])).
% 3.15/3.38 tff(16619,plain,
% 3.15/3.38 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3841, 16618])).
% 3.15/3.38 tff(16620,plain,
% 3.15/3.38 (~r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[9612, 163, 3066, 151, 16566])).
% 3.15/3.38 tff(16621,plain,
% 3.15/3.38 (b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[3301, 16620])).
% 3.15/3.38 tff(16622,plain,
% 3.15/3.38 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[11269, 16621, 16617, 16599])).
% 3.15/3.38 tff(16623,plain,
% 3.15/3.38 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.38 inference(unit_resolution,[status(thm)],[4110, 16622])).
% 3.15/3.38 tff(16624,plain,
% 3.15/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16625,plain,
% 3.15/3.38 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(rewrite,[status(thm)],[])).
% 3.15/3.38 tff(16626,plain,
% 3.15/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 3.15/3.38 inference(monotonicity,[status(thm)],[16625])).
% 3.15/3.38 tff(16627,plain,
% 3.15/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(transitivity,[status(thm)],[16626, 16624])).
% 3.15/3.38 tff(16628,plain,
% 3.15/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.15/3.38 inference(quant_inst,[status(thm)],[])).
% 3.15/3.38 tff(16629,plain,
% 3.15/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 3.15/3.38 inference(modus_ponens,[status(thm)],[16628, 16627])).
% 3.15/3.38 tff(16630,plain,
% 3.15/3.38 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16629, 163, 332, 16623, 16619])).
% 3.15/3.39 tff(16631,plain,
% 3.15/3.39 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9885, 16630])).
% 3.15/3.39 tff(16632,plain,
% 3.15/3.39 ($false),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[12879, 198, 560, 16621, 16617, 16631])).
% 3.15/3.39 tff(16633,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.39 tff(16634,plain,
% 3.15/3.39 (~b(s(s(z)), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16633, 16615, 332, 16601])).
% 3.15/3.39 tff(16635,plain,
% 3.15/3.39 (r(s(s(z)), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[487, 16634])).
% 3.15/3.39 tff(16636,plain,
% 3.15/3.39 (~r(s(s(s(s(s(z))))), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[11684, 16615, 16566, 16601])).
% 3.15/3.39 tff(16637,plain,
% 3.15/3.39 (b(s(s(s(s(s(z))))), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[469, 16636])).
% 3.15/3.39 tff(16638,plain,
% 3.15/3.39 (~r(s(z), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9612, 163, 16615, 16601, 16566])).
% 3.15/3.39 tff(16639,plain,
% 3.15/3.39 (b(s(z), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[3301, 16638])).
% 3.15/3.39 tff(16640,plain,
% 3.15/3.39 (~b(s(s(s(s(s(z))))), z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[8803, 16637, 16562, 16599])).
% 3.15/3.39 tff(16641,plain,
% 3.15/3.39 (r(s(s(s(s(s(z))))), z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[3841, 16640])).
% 3.15/3.39 tff(16642,plain,
% 3.15/3.39 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10685, 198, 723, 16562, 595, 16553, 330])).
% 3.15/3.39 tff(16643,plain,
% 3.15/3.39 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[934, 26, 16642, 930])).
% 3.15/3.39 tff(16644,plain,
% 3.15/3.39 (~b(s(s(elem!1)), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[1191, 198, 723, 16562, 595])).
% 3.15/3.39 tff(16645,plain,
% 3.15/3.39 (r(s(s(elem!1)), s(z))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[626, 16644])).
% 3.15/3.39 tff(16646,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16647,plain,
% 3.15/3.39 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16648,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16647])).
% 3.15/3.39 tff(16649,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[16648, 16646])).
% 3.15/3.39 tff(16650,plain,
% 3.15/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.39 inference(quant_inst,[status(thm)],[])).
% 3.15/3.39 tff(16651,plain,
% 3.15/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16650, 16649])).
% 3.15/3.39 tff(16652,plain,
% 3.15/3.39 ($false),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16651, 163, 15191, 16645, 16566, 16643])).
% 3.15/3.39 tff(16653,plain,((~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.39 tff(16654,plain,
% 3.15/3.39 (~b(s(s(elem!1)), z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16653, 930, 16599, 330])).
% 3.15/3.39 tff(16655,plain,
% 3.15/3.39 (r(s(s(elem!1)), z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[801, 16654])).
% 3.15/3.39 tff(16656,plain,
% 3.15/3.39 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10703, 163, 16655, 16569, 16641])).
% 3.15/3.39 tff(16657,plain,
% 3.15/3.39 (~r(s(s(elem!1)), s(s(z)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10711, 163, 16655, 16569, 332])).
% 3.15/3.39 tff(16658,plain,
% 3.15/3.39 (b(s(s(elem!1)), s(s(z)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[3497, 26, 16657, 14243])).
% 3.15/3.39 tff(16659,plain,
% 3.15/3.39 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10400, 163, 16569, 332, 16641])).
% 3.15/3.39 tff(16660,plain,
% 3.15/3.39 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9576, 16659])).
% 3.15/3.39 tff(16661,plain,
% 3.15/3.39 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10408, 163, 16569, 332, 16641])).
% 3.15/3.39 tff(16662,plain,
% 3.15/3.39 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9885, 16661])).
% 3.15/3.39 tff(16663,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16664,plain,
% 3.15/3.39 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16665,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16664])).
% 3.15/3.39 tff(16666,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[16665, 16663])).
% 3.15/3.39 tff(16667,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.39 inference(quant_inst,[status(thm)],[])).
% 3.15/3.39 tff(16668,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16667, 16666])).
% 3.15/3.39 tff(16669,plain,
% 3.15/3.39 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16668, 198, 16605, 16609, 16662, 16660, 16658])).
% 3.15/3.39 tff(16670,plain,
% 3.15/3.39 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[3400, 16669, 16656])).
% 3.15/3.39 tff(16671,plain,
% 3.15/3.39 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16670])).
% 3.15/3.39 tff(16672,plain,
% 3.15/3.39 (s(elem!1) = s(s(s(s(z))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[135, 16671, 288])).
% 3.15/3.39 tff(16673,plain,
% 3.15/3.39 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16672])).
% 3.15/3.39 tff(16674,plain,
% 3.15/3.39 (elem!1 = s(s(s(z)))),
% 3.15/3.39 inference(transitivity,[status(thm)],[4242, 16673, 293])).
% 3.15/3.39 tff(16675,plain,
% 3.15/3.39 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16674])).
% 3.15/3.39 tff(16676,plain,
% 3.15/3.39 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.15/3.39 inference(symmetry,[status(thm)],[16675])).
% 3.15/3.39 tff(16677,plain,
% 3.15/3.39 ((~r(s(s(s(z))), z)) <=> (~r(elem!1, z))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16676])).
% 3.15/3.39 tff(16678,plain,
% 3.15/3.39 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.15/3.39 inference(symmetry,[status(thm)],[16673])).
% 3.15/3.39 tff(16679,plain,
% 3.15/3.39 (s(s(s(z))) = elem!1),
% 3.15/3.39 inference(transitivity,[status(thm)],[294, 16678, 129])).
% 3.15/3.39 tff(16680,plain,
% 3.15/3.39 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16679])).
% 3.15/3.39 tff(16681,plain,
% 3.15/3.39 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16680])).
% 3.15/3.39 tff(16682,plain,
% 3.15/3.39 (~(s(z) = elem!1)),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[10804, 16681])).
% 3.15/3.39 tff(16683,plain,
% 3.15/3.39 (~(s(s(z)) = elem!1)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9862, 16682, 16670])).
% 3.15/3.39 tff(16684,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16685,plain,
% 3.15/3.39 (((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16686,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16685])).
% 3.15/3.39 tff(16687,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[16686, 16684])).
% 3.15/3.39 tff(16688,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.15/3.39 inference(quant_inst,[status(thm)],[])).
% 3.15/3.39 tff(16689,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16688, 16687])).
% 3.15/3.39 tff(16690,plain,
% 3.15/3.39 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16689, 198, 16605, 16609, 16658])).
% 3.15/3.39 tff(16691,plain,
% 3.15/3.39 (~r(s(s(z)), s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10767, 163, 16655, 16569, 332])).
% 3.15/3.39 tff(16692,plain,
% 3.15/3.39 (b(s(s(z)), s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[2161, 26, 16691, 5276])).
% 3.15/3.39 tff(16693,plain,
% 3.15/3.39 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(elem!1)))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16694,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16693])).
% 3.15/3.39 tff(16695,plain,
% 3.15/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[16694, 11455])).
% 3.15/3.39 tff(16696,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 3.15/3.39 inference(quant_inst,[status(thm)],[])).
% 3.15/3.39 tff(16697,plain,
% 3.15/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16696, 16695])).
% 3.15/3.39 tff(16698,plain,
% 3.15/3.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[16697, 198, 16609, 16692, 16658])).
% 3.15/3.39 tff(16699,plain,
% 3.15/3.39 (~r(s(z), s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[945, 16698, 16601, 930, 16690])).
% 3.15/3.39 tff(16700,plain,
% 3.15/3.39 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16670])).
% 3.15/3.39 tff(16701,plain,
% 3.15/3.39 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16700])).
% 3.15/3.39 tff(16702,plain,
% 3.15/3.39 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16701])).
% 3.15/3.39 tff(16703,plain,
% 3.15/3.39 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 3.15/3.39 inference(symmetry,[status(thm)],[16702])).
% 3.15/3.39 tff(16704,plain,
% 3.15/3.39 (r(s(z), s(s(s(s(elem!1)))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16601, 16703])).
% 3.15/3.39 tff(16705,plain,
% 3.15/3.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[14125, 16704, 16699])).
% 3.15/3.39 tff(16706,plain,
% 3.15/3.39 (~(s(s(elem!1)) = elem!1)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[2064, 16705])).
% 3.15/3.39 tff(16707,plain,
% 3.15/3.39 (~(elem!1 = s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[676, 16706])).
% 3.15/3.39 tff(16708,plain,
% 3.15/3.39 (~r(s(s(s(z))), z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[10859, 16707, 16569, 16641, 16670, 16683, 332])).
% 3.15/3.39 tff(16709,plain,
% 3.15/3.39 (~r(elem!1, z)),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16708, 16677])).
% 3.15/3.39 tff(16710,plain,
% 3.15/3.39 (b(elem!1, z)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[187, 16709, 3617])).
% 3.15/3.39 tff(16711,plain,
% 3.15/3.39 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9265, 16670])).
% 3.15/3.39 tff(16712,plain,
% 3.15/3.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16679])).
% 3.15/3.39 tff(16713,plain,
% 3.15/3.39 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16712])).
% 3.15/3.39 tff(16714,plain,
% 3.15/3.39 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16679])).
% 3.15/3.39 tff(16715,plain,
% 3.15/3.39 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(symmetry,[status(thm)],[16714])).
% 3.15/3.39 tff(16716,plain,
% 3.15/3.39 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16670])).
% 3.15/3.39 tff(16717,plain,
% 3.15/3.39 (r(elem!1, s(s(elem!1)))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[147, 16707, 85])).
% 3.15/3.39 tff(16718,plain,
% 3.15/3.39 (r(elem!1, s(s(s(s(s(z))))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16717, 16716])).
% 3.15/3.39 tff(16719,plain,
% 3.15/3.39 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(modus_ponens,[status(thm)],[16718, 16715])).
% 3.15/3.39 tff(16720,plain,
% 3.15/3.39 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[5369, 198, 16609, 16662, 16660])).
% 3.15/3.39 tff(16721,plain,
% 3.15/3.39 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.15/3.39 inference(unit_resolution,[status(thm)],[9643, 16720])).
% 3.15/3.39 tff(16722,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16723,plain,
% 3.15/3.39 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(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))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.15/3.39 inference(rewrite,[status(thm)],[])).
% 3.15/3.39 tff(16724,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 3.15/3.39 inference(monotonicity,[status(thm)],[16723])).
% 3.15/3.39 tff(16725,plain,
% 3.15/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.15/3.39 inference(transitivity,[status(thm)],[16724, 16722])).
% 3.15/3.39 tff(16726,plain,
% 3.15/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 3.15/3.39 inference(quant_inst,[status(thm)],[])).
% 3.15/3.39 tff(16727,plain,
% 3.15/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.15/3.40 inference(modus_ponens,[status(thm)],[16726, 16725])).
% 3.15/3.40 tff(16728,plain,
% 3.15/3.40 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[16727, 163, 16615, 16721])).
% 3.15/3.40 tff(16729,plain,
% 3.15/3.40 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[16728, 16719])).
% 3.15/3.40 tff(16730,plain,
% 3.15/3.40 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.40 inference(modus_ponens,[status(thm)],[16729, 16713])).
% 3.15/3.40 tff(16731,plain,
% 3.15/3.40 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[256, 16730, 16711])).
% 3.15/3.40 tff(16732,plain,
% 3.15/3.40 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 3.15/3.40 inference(monotonicity,[status(thm)],[16674])).
% 3.15/3.40 tff(16733,plain,
% 3.15/3.40 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 3.15/3.40 inference(symmetry,[status(thm)],[16732])).
% 3.15/3.40 tff(16734,plain,
% 3.15/3.40 ((~r(z, s(s(s(z))))) <=> (~r(z, elem!1))),
% 3.15/3.40 inference(monotonicity,[status(thm)],[16733])).
% 3.15/3.40 tff(16735,plain,
% 3.15/3.40 (~b(z, s(s(s(s(s(z))))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[11269, 16639, 16637, 16599])).
% 3.15/3.40 tff(16736,plain,
% 3.15/3.40 (r(z, s(s(s(s(s(z))))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[4110, 16735])).
% 3.15/3.40 tff(16737,plain,
% 3.15/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.40 inference(rewrite,[status(thm)],[])).
% 3.15/3.40 tff(16738,plain,
% 3.15/3.40 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(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))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.40 inference(rewrite,[status(thm)],[])).
% 3.15/3.40 tff(16739,plain,
% 3.15/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.15/3.40 inference(monotonicity,[status(thm)],[16738])).
% 3.15/3.40 tff(16740,plain,
% 3.15/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 3.15/3.40 inference(transitivity,[status(thm)],[16739, 16737])).
% 3.15/3.40 tff(16741,plain,
% 3.15/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.15/3.40 inference(quant_inst,[status(thm)],[])).
% 3.15/3.40 tff(16742,plain,
% 3.15/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 3.15/3.40 inference(modus_ponens,[status(thm)],[16741, 16740])).
% 3.15/3.40 tff(16743,plain,
% 3.15/3.40 ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[16742, 163, 16615, 16736])).
% 3.15/3.40 tff(16744,plain,
% 3.15/3.40 (~r(z, s(s(s(z))))),
% 3.15/3.40 inference(unit_resolution,[status(thm)],[16743, 16719])).
% 3.25/3.40 tff(16745,plain,
% 3.25/3.40 (~r(z, elem!1)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16744, 16734])).
% 3.25/3.40 tff(16746,plain,
% 3.25/3.40 (b(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[102, 16745, 3])).
% 3.25/3.40 tff(16747,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9622, 16746, 16731, 330, 16710])).
% 3.25/3.40 tff(16748,plain,((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (z = elem!1) | (~r(s(s(z)), z)) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16749,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16748, 85, 3, 332, 330])).
% 3.25/3.40 tff(16750,plain,
% 3.25/3.40 (s(s(s(s(s(z))))) = elem!1),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10750, 16749])).
% 3.25/3.40 tff(16751,plain,
% 3.25/3.40 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16750])).
% 3.25/3.40 tff(16752,plain,
% 3.25/3.40 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16751])).
% 3.25/3.40 tff(16753,plain,
% 3.25/3.40 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16749])).
% 3.25/3.40 tff(16754,plain,
% 3.25/3.40 (~b(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10743, 11341, 4105])).
% 3.25/3.40 tff(16755,plain,
% 3.25/3.40 (r(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[102, 16754, 3])).
% 3.25/3.40 tff(16756,plain,
% 3.25/3.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[7261, 16755, 7255])).
% 3.25/3.40 tff(16757,plain,
% 3.25/3.40 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[256, 16756, 9233])).
% 3.25/3.40 tff(16758,plain,
% 3.25/3.40 (b(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16757, 11424])).
% 3.25/3.40 tff(16759,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[597, 16758])).
% 3.25/3.40 tff(16760,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1) | r(z, s(s(s(s(s(s(s(z)))))))) | (z = elem!1) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16761,plain,
% 3.25/3.40 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16760, 9233, 597, 7255, 3, 16735])).
% 3.25/3.40 tff(16762,plain,
% 3.25/3.40 (~b(s(s(elem!1)), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16653, 16761, 16599, 330])).
% 3.25/3.40 tff(16763,plain,
% 3.25/3.40 (r(s(s(elem!1)), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[801, 16762])).
% 3.25/3.40 tff(16764,plain,
% 3.25/3.40 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10703, 163, 16763, 16569, 16641])).
% 3.25/3.40 tff(16765,plain,
% 3.25/3.40 (~r(s(s(elem!1)), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10711, 163, 16763, 16569, 332])).
% 3.25/3.40 tff(16766,plain,
% 3.25/3.40 (b(s(s(elem!1)), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3497, 26, 16765, 14243])).
% 3.25/3.40 tff(16767,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16668, 198, 16605, 16609, 16662, 16660, 16766])).
% 3.25/3.40 tff(16768,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3400, 16767, 16764])).
% 3.25/3.40 tff(16769,plain,
% 3.25/3.40 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16768])).
% 3.25/3.40 tff(16770,plain,
% 3.25/3.40 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.40 inference(transitivity,[status(thm)],[135, 16769, 288])).
% 3.25/3.40 tff(16771,plain,
% 3.25/3.40 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16770])).
% 3.25/3.40 tff(16772,plain,
% 3.25/3.40 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16771])).
% 3.25/3.40 tff(16773,plain,
% 3.25/3.40 (s(s(s(z))) = elem!1),
% 3.25/3.40 inference(transitivity,[status(thm)],[294, 16772, 129])).
% 3.25/3.40 tff(16774,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16773])).
% 3.25/3.40 tff(16775,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16774])).
% 3.25/3.40 tff(16776,plain,
% 3.25/3.40 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10703, 163, 790, 16569, 3828])).
% 3.25/3.40 tff(16777,plain,
% 3.25/3.40 (~r(s(s(elem!1)), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10711, 163, 790, 16569, 332])).
% 3.25/3.40 tff(16778,plain,
% 3.25/3.40 (b(s(s(elem!1)), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3497, 26, 16777, 10705])).
% 3.25/3.40 tff(16779,plain,
% 3.25/3.40 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10400, 163, 16569, 332, 3828])).
% 3.25/3.40 tff(16780,plain,
% 3.25/3.40 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9576, 16779])).
% 3.25/3.40 tff(16781,plain,
% 3.25/3.40 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10408, 163, 16569, 332, 3828])).
% 3.25/3.40 tff(16782,plain,
% 3.25/3.40 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9885, 16781])).
% 3.25/3.40 tff(16783,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16668, 198, 348, 16609, 16782, 16780, 16778])).
% 3.25/3.40 tff(16784,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3400, 16783, 16776])).
% 3.25/3.40 tff(16785,plain,
% 3.25/3.40 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16784])).
% 3.25/3.40 tff(16786,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(symmetry,[status(thm)],[16785])).
% 3.25/3.40 tff(16787,plain,
% 3.25/3.40 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16786])).
% 3.25/3.40 tff(16788,plain,
% 3.25/3.40 (~r(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16145, 16787])).
% 3.25/3.40 tff(16789,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16689, 198, 348, 16609, 16778])).
% 3.25/3.40 tff(16790,plain,
% 3.25/3.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9265, 16784])).
% 3.25/3.40 tff(16791,plain,
% 3.25/3.40 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3792, 16790])).
% 3.25/3.40 tff(16792,plain,
% 3.25/3.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[703, 16791, 7797])).
% 3.25/3.40 tff(16793,plain,
% 3.25/3.40 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[711, 16792, 16789])).
% 3.25/3.40 tff(16794,plain,
% 3.25/3.40 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[118, 16793])).
% 3.25/3.40 tff(16795,plain,
% 3.25/3.40 (r(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[602, 16794, 597])).
% 3.25/3.40 tff(16796,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16795, 16788])).
% 3.25/3.40 tff(16797,plain,((~r(s(s(elem!1)), z)) | r(s(s(s(s(s(z))))), elem!1) | b(s(s(elem!1)), elem!1) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16798,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16797, 16763, 597, 7797, 16605, 14243, 16641, 332])).
% 3.25/3.40 tff(16799,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16798, 16775])).
% 3.25/3.40 tff(16800,plain,
% 3.25/3.40 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16773])).
% 3.25/3.40 tff(16801,plain,
% 3.25/3.40 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16800])).
% 3.25/3.40 tff(16802,plain,
% 3.25/3.40 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16768])).
% 3.25/3.40 tff(16803,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16689, 198, 16605, 16609, 16766])).
% 3.25/3.40 tff(16804,plain,
% 3.25/3.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9265, 16768])).
% 3.25/3.40 tff(16805,plain,
% 3.25/3.40 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3792, 16804])).
% 3.25/3.40 tff(16806,plain,
% 3.25/3.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[703, 16805, 7797])).
% 3.25/3.40 tff(16807,plain,
% 3.25/3.40 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[711, 16806, 16803])).
% 3.25/3.40 tff(16808,plain,
% 3.25/3.40 (r(elem!1, s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[147, 16807, 85])).
% 3.25/3.40 tff(16809,plain,
% 3.25/3.40 (r(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16808, 16802])).
% 3.25/3.40 tff(16810,plain,
% 3.25/3.40 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16809, 16801])).
% 3.25/3.40 tff(16811,plain,
% 3.25/3.40 (elem!1 = s(s(s(z)))),
% 3.25/3.40 inference(transitivity,[status(thm)],[4242, 16771, 293])).
% 3.25/3.40 tff(16812,plain,
% 3.25/3.40 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16811])).
% 3.25/3.40 tff(16813,plain,
% 3.25/3.40 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[256, 16804, 9233])).
% 3.25/3.40 tff(16814,plain,
% 3.25/3.40 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16811])).
% 3.25/3.40 tff(16815,plain,
% 3.25/3.40 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.25/3.40 inference(symmetry,[status(thm)],[16814])).
% 3.25/3.40 tff(16816,plain,
% 3.25/3.40 ((~r(s(s(s(z))), z)) <=> (~r(elem!1, z))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16815])).
% 3.25/3.40 tff(16817,plain,
% 3.25/3.40 (~(s(z) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9821, 16813, 16565])).
% 3.25/3.40 tff(16818,plain,
% 3.25/3.40 (~(s(s(z)) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9862, 16817, 16768])).
% 3.25/3.40 tff(16819,plain,
% 3.25/3.40 (~r(s(s(s(z))), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10859, 16818, 16569, 16641, 16768, 16807, 332])).
% 3.25/3.40 tff(16820,plain,
% 3.25/3.40 (~r(elem!1, z)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16819, 16816])).
% 3.25/3.40 tff(16821,plain,
% 3.25/3.40 (b(elem!1, z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[187, 16820, 3617])).
% 3.25/3.40 tff(16822,plain,
% 3.25/3.40 (~b(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9622, 16821, 330, 16813])).
% 3.25/3.40 tff(16823,plain,
% 3.25/3.40 (r(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[102, 16822, 3])).
% 3.25/3.40 tff(16824,plain,
% 3.25/3.40 (r(z, s(s(s(z))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16823, 16812])).
% 3.25/3.40 tff(16825,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16826,plain,
% 3.25/3.40 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16827,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16826])).
% 3.25/3.40 tff(16828,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(transitivity,[status(thm)],[16827, 16825])).
% 3.25/3.40 tff(16829,plain,
% 3.25/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(quant_inst,[status(thm)],[])).
% 3.25/3.40 tff(16830,plain,
% 3.25/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16829, 16828])).
% 3.25/3.40 tff(16831,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16830, 163, 16824, 16736, 16810, 16799])).
% 3.25/3.40 tff(16832,plain,(r(s(s(s(s(s(s(s(z))))))), elem!1) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), elem!1) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16833,plain,
% 3.25/3.40 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16832, 7797, 330, 332, 85, 3, 597, 7255])).
% 3.25/3.40 tff(16834,plain,
% 3.25/3.40 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10703, 163, 790, 16569, 16641])).
% 3.25/3.40 tff(16835,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16668, 198, 16605, 16609, 16662, 16660, 16778])).
% 3.25/3.40 tff(16836,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3400, 16835, 16834])).
% 3.25/3.40 tff(16837,plain,
% 3.25/3.40 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16836])).
% 3.25/3.40 tff(16838,plain,
% 3.25/3.40 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.40 inference(transitivity,[status(thm)],[135, 16837, 288])).
% 3.25/3.40 tff(16839,plain,
% 3.25/3.40 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16838])).
% 3.25/3.40 tff(16840,plain,
% 3.25/3.40 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16839])).
% 3.25/3.40 tff(16841,plain,
% 3.25/3.40 (s(s(s(z))) = elem!1),
% 3.25/3.40 inference(transitivity,[status(thm)],[294, 16840, 129])).
% 3.25/3.40 tff(16842,plain,
% 3.25/3.40 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16841])).
% 3.25/3.40 tff(16843,plain,
% 3.25/3.40 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16842])).
% 3.25/3.40 tff(16844,plain,
% 3.25/3.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9265, 16836])).
% 3.25/3.40 tff(16845,plain,
% 3.25/3.40 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3792, 16844])).
% 3.25/3.40 tff(16846,plain,
% 3.25/3.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[703, 16845, 7797])).
% 3.25/3.40 tff(16847,plain,
% 3.25/3.40 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16846, 16843])).
% 3.25/3.40 tff(16848,plain,
% 3.25/3.40 (elem!1 = s(s(s(z)))),
% 3.25/3.40 inference(transitivity,[status(thm)],[4242, 16839, 293])).
% 3.25/3.40 tff(16849,plain,
% 3.25/3.40 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16848])).
% 3.25/3.40 tff(16850,plain,
% 3.25/3.40 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16848])).
% 3.25/3.40 tff(16851,plain,
% 3.25/3.40 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 3.25/3.40 inference(symmetry,[status(thm)],[16850])).
% 3.25/3.40 tff(16852,plain,
% 3.25/3.40 ((~r(s(s(s(z))), z)) <=> (~r(elem!1, z))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16851])).
% 3.25/3.40 tff(16853,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16689, 198, 16605, 16609, 16778])).
% 3.25/3.40 tff(16854,plain,
% 3.25/3.40 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[711, 16846, 16853])).
% 3.25/3.40 tff(16855,plain,
% 3.25/3.40 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[118, 16854])).
% 3.25/3.40 tff(16856,plain,
% 3.25/3.40 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[1250, 16855])).
% 3.25/3.40 tff(16857,plain,
% 3.25/3.40 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[2619, 16856])).
% 3.25/3.40 tff(16858,plain,
% 3.25/3.40 (~(s(z) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9808, 16857, 16615, 258, 16835, 16853])).
% 3.25/3.40 tff(16859,plain,
% 3.25/3.40 (~(s(s(z)) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[9862, 16858, 16836])).
% 3.25/3.40 tff(16860,plain,
% 3.25/3.40 (~r(s(s(s(z))), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10859, 16859, 16569, 16641, 16836, 16854, 332])).
% 3.25/3.40 tff(16861,plain,
% 3.25/3.40 (~r(elem!1, z)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16860, 16852])).
% 3.25/3.40 tff(16862,plain,
% 3.25/3.40 (b(elem!1, z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[187, 16861, 76])).
% 3.25/3.40 tff(16863,plain,
% 3.25/3.40 (b(s(s(s(z))), z)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16862, 16849])).
% 3.25/3.40 tff(16864,plain,
% 3.25/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16865,plain,
% 3.25/3.40 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16866,plain,
% 3.25/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16865])).
% 3.25/3.40 tff(16867,plain,
% 3.25/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.40 inference(transitivity,[status(thm)],[16866, 16864])).
% 3.25/3.40 tff(16868,plain,
% 3.25/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 3.25/3.40 inference(quant_inst,[status(thm)],[])).
% 3.25/3.40 tff(16869,plain,
% 3.25/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16868, 16867])).
% 3.25/3.40 tff(16870,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16869, 198, 16562, 16599, 16863, 16553, 330, 16847])).
% 3.25/3.40 tff(16871,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (elem!1 = z) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | r(elem!1, s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16872,plain,
% 3.25/3.40 (~r(s(s(elem!1)), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16871, 16833, 3617, 332, 330, 7797, 14243])).
% 3.25/3.40 tff(16873,plain,
% 3.25/3.40 (b(s(s(elem!1)), z)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[801, 16872])).
% 3.25/3.40 tff(16874,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16653, 16873, 16599, 330])).
% 3.25/3.40 tff(16875,plain,
% 3.25/3.40 (s(s(s(s(s(z))))) = elem!1),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10750, 16874])).
% 3.25/3.40 tff(16876,plain,
% 3.25/3.40 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16875])).
% 3.25/3.40 tff(16877,plain,
% 3.25/3.40 (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))))))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16876])).
% 3.25/3.40 tff(16878,plain,
% 3.25/3.40 (~b(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[10743, 16875, 16735])).
% 3.25/3.40 tff(16879,plain,
% 3.25/3.40 (r(z, elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[102, 16878, 3])).
% 3.25/3.40 tff(16880,plain,
% 3.25/3.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[7261, 16879, 7255])).
% 3.25/3.40 tff(16881,plain,
% 3.25/3.40 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3792, 16880])).
% 3.25/3.40 tff(16882,plain,
% 3.25/3.40 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[703, 16881, 7797])).
% 3.25/3.40 tff(16883,plain,
% 3.25/3.40 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16882, 16877])).
% 3.25/3.40 tff(16884,plain,
% 3.25/3.40 ($false),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16614, 16883])).
% 3.25/3.40 tff(16885,plain,(r(elem!1, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))) | (z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | b(elem!1, s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.25/3.40 tff(16886,plain,
% 3.25/3.40 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16885, 597, 3, 330, 332, 85, 7255])).
% 3.25/3.40 tff(16887,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16888,plain,
% 3.25/3.40 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.25/3.40 inference(rewrite,[status(thm)],[])).
% 3.25/3.40 tff(16889,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16888])).
% 3.25/3.40 tff(16890,plain,
% 3.25/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.25/3.40 inference(transitivity,[status(thm)],[16889, 16887])).
% 3.25/3.40 tff(16891,plain,
% 3.25/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.25/3.40 inference(quant_inst,[status(thm)],[])).
% 3.25/3.40 tff(16892,plain,
% 3.25/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16891, 16890])).
% 3.25/3.40 tff(16893,plain,
% 3.25/3.40 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16892, 163, 16615, 16886, 16566])).
% 3.25/3.40 tff(16894,plain,
% 3.25/3.40 (b(s(s(elem!1)), s(s(z)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3497, 26, 16657, 3494])).
% 3.25/3.40 tff(16895,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16668, 198, 16605, 16609, 16662, 16660, 16894])).
% 3.25/3.40 tff(16896,plain,
% 3.25/3.40 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[3400, 16895, 16656])).
% 3.25/3.40 tff(16897,plain,
% 3.25/3.40 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16896])).
% 3.25/3.40 tff(16898,plain,
% 3.25/3.40 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(symmetry,[status(thm)],[16897])).
% 3.25/3.40 tff(16899,plain,
% 3.25/3.40 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16898])).
% 3.25/3.40 tff(16900,plain,
% 3.25/3.40 (~r(s(s(elem!1)), elem!1)),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16145, 16899])).
% 3.25/3.40 tff(16901,plain,
% 3.25/3.40 (s(s(elem!1)) = elem!1),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[602, 16900, 597])).
% 3.25/3.40 tff(16902,plain,
% 3.25/3.40 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16689, 198, 16605, 16609, 16894])).
% 3.25/3.40 tff(16903,plain,
% 3.25/3.40 (b(s(s(z)), s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[2161, 26, 16691, 2154])).
% 3.25/3.40 tff(16904,plain,
% 3.25/3.40 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[16697, 198, 16609, 16903, 16894])).
% 3.25/3.40 tff(16905,plain,
% 3.25/3.40 (~r(s(z), s(s(elem!1)))),
% 3.25/3.40 inference(unit_resolution,[status(thm)],[945, 16904, 16601, 930, 16902])).
% 3.25/3.40 tff(16906,plain,
% 3.25/3.40 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16896])).
% 3.25/3.40 tff(16907,plain,
% 3.25/3.40 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16906])).
% 3.25/3.40 tff(16908,plain,
% 3.25/3.40 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.40 inference(monotonicity,[status(thm)],[16907])).
% 3.25/3.40 tff(16909,plain,
% 3.25/3.40 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 3.25/3.40 inference(symmetry,[status(thm)],[16908])).
% 3.25/3.40 tff(16910,plain,
% 3.25/3.40 (r(s(z), s(s(s(s(elem!1)))))),
% 3.25/3.40 inference(modus_ponens,[status(thm)],[16601, 16909])).
% 3.25/3.41 tff(16911,plain,
% 3.25/3.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[14125, 16910, 16905])).
% 3.25/3.41 tff(16912,plain,
% 3.25/3.41 ($false),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[2064, 16911, 16901])).
% 3.25/3.41 tff(16913,plain,((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), elem!1) | r(s(s(s(s(s(z))))), elem!1) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.41 tff(16914,plain,
% 3.25/3.41 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16913, 597, 16893, 5276, 332, 330])).
% 3.25/3.41 tff(16915,plain,
% 3.25/3.41 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 3.25/3.41 inference(symmetry,[status(thm)],[16914])).
% 3.25/3.41 tff(16916,plain,
% 3.25/3.41 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16914])).
% 3.25/3.41 tff(16917,plain,
% 3.25/3.41 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 3.25/3.41 inference(symmetry,[status(thm)],[16916])).
% 3.25/3.41 tff(16918,plain,
% 3.25/3.41 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16917, 16915])).
% 3.25/3.41 tff(16919,plain,
% 3.25/3.41 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.41 inference(symmetry,[status(thm)],[16918])).
% 3.25/3.41 tff(16920,plain,
% 3.25/3.41 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16760, 16914, 597, 7255, 3, 16735])).
% 3.25/3.41 tff(16921,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16922,plain,
% 3.25/3.41 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16923,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16922])).
% 3.25/3.41 tff(16924,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(transitivity,[status(thm)],[16923, 16921])).
% 3.25/3.41 tff(16925,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16926,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16925, 16924])).
% 3.25/3.41 tff(16927,plain,
% 3.25/3.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16926, 163, 15191, 16566])).
% 3.25/3.41 tff(16928,plain,
% 3.25/3.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[4456, 16914, 16927])).
% 3.25/3.41 tff(16929,plain,
% 3.25/3.41 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[671, 16928, 16920])).
% 3.25/3.41 tff(16930,plain,
% 3.25/3.41 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[118, 16929])).
% 3.25/3.41 tff(16931,plain,
% 3.25/3.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1250, 16930])).
% 3.25/3.41 tff(16932,plain,
% 3.25/3.41 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1263, 16931])).
% 3.25/3.41 tff(16933,plain,
% 3.25/3.41 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1270, 16932])).
% 3.25/3.41 tff(16934,plain,
% 3.25/3.41 (r(s(s(elem!1)), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[602, 16930, 597])).
% 3.25/3.41 tff(16935,plain,
% 3.25/3.41 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16914])).
% 3.25/3.41 tff(16936,plain,
% 3.25/3.41 (b(s(s(s(s(s(s(s(z))))))), z) <=> b(s(s(elem!1)), z)),
% 3.25/3.41 inference(symmetry,[status(thm)],[16935])).
% 3.25/3.41 tff(16937,plain,
% 3.25/3.41 (b(s(s(elem!1)), z)),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[330, 16936])).
% 3.25/3.41 tff(16938,plain,
% 3.25/3.41 (s(s(s(s(s(z))))) = elem!1),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[10750, 16914])).
% 3.25/3.41 tff(16939,plain,
% 3.25/3.41 (~b(z, elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[10743, 16938, 16735])).
% 3.25/3.41 tff(16940,plain,
% 3.25/3.41 (r(z, elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[102, 16939, 3])).
% 3.25/3.41 tff(16941,plain,
% 3.25/3.41 (r(elem!1, s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[147, 16929, 85])).
% 3.25/3.41 tff(16942,plain,
% 3.25/3.41 (~(s(s(z)) = elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[8694, 16914])).
% 3.25/3.41 tff(16943,plain,
% 3.25/3.41 (~(s(s(s(elem!1))) = elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[11360, 16914, 16942])).
% 3.25/3.41 tff(16944,plain,
% 3.25/3.41 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16917])).
% 3.25/3.41 tff(16945,plain,
% 3.25/3.41 ((~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16944])).
% 3.25/3.41 tff(16946,plain,
% 3.25/3.41 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16938])).
% 3.25/3.41 tff(16947,plain,
% 3.25/3.41 (b(elem!1, s(s(z)))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16660, 16946])).
% 3.25/3.41 tff(16948,plain,
% 3.25/3.41 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), elem!1)),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16938])).
% 3.25/3.41 tff(16949,plain,
% 3.25/3.41 (b(s(s(z)), elem!1)),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16662, 16948])).
% 3.25/3.41 tff(16950,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16951,plain,
% 3.25/3.41 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16952,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16951])).
% 3.25/3.41 tff(16953,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(transitivity,[status(thm)],[16952, 16950])).
% 3.25/3.41 tff(16954,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(z))))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16955,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16954, 16953])).
% 3.25/3.41 tff(16956,plain,
% 3.25/3.41 (~r(elem!1, s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16955, 163, 16886, 16601, 16566])).
% 3.25/3.41 tff(16957,plain,
% 3.25/3.41 (~(s(z) = elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[7345, 16914])).
% 3.25/3.41 tff(16958,plain,
% 3.25/3.41 (~(s(s(z)) = s(elem!1))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[227, 16957])).
% 3.25/3.41 tff(16959,plain,
% 3.25/3.41 (~(elem!1 = s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[234, 16958])).
% 3.25/3.41 tff(16960,plain,
% 3.25/3.41 (b(elem!1, s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[242, 16959, 16956])).
% 3.25/3.41 tff(16961,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), 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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16962,plain,
% 3.25/3.41 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16963,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16962])).
% 3.25/3.41 tff(16964,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.41 inference(transitivity,[status(thm)],[16963, 16961])).
% 3.25/3.41 tff(16965,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), elem!1)))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16966,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16965, 16964])).
% 3.25/3.41 tff(16967,plain,
% 3.25/3.41 (~r(s(z), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16966, 163, 16886, 16601, 16566])).
% 3.25/3.41 tff(16968,plain,
% 3.25/3.41 (b(s(z), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[217, 16957, 16967])).
% 3.25/3.41 tff(16969,plain,
% 3.25/3.41 (~(s(s(s(s(s(s(s(s(z)))))))) = s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[14335, 16914])).
% 3.25/3.41 tff(16970,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), elem!1)), introduced(assumption)).
% 3.25/3.41 tff(16971,plain,
% 3.25/3.41 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[14330, 16970])).
% 3.25/3.41 tff(16972,assumption,(~(s(s(s(s(s(s(s(s(z)))))))) = s(z))), introduced(assumption)).
% 3.25/3.41 tff(16973,plain,
% 3.25/3.41 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[11403, 26, 16972, 16971])).
% 3.25/3.41 tff(16974,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16975,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16976,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16975, 16974])).
% 3.25/3.41 tff(16977,plain,
% 3.25/3.41 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16976, 163, 15191, 3450, 16973])).
% 3.25/3.41 tff(16978,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 3.25/3.41 tff(16979,plain,
% 3.25/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16980,plain,
% 3.25/3.41 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16981,plain,
% 3.25/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16980])).
% 3.25/3.41 tff(16982,plain,
% 3.25/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.25/3.41 inference(transitivity,[status(thm)],[16981, 16979])).
% 3.25/3.41 tff(16983,plain,
% 3.25/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16984,plain,
% 3.25/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16983, 16982])).
% 3.25/3.41 tff(16985,plain,
% 3.25/3.41 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16984, 198, 5927, 320, 2682, 16978])).
% 3.25/3.41 tff(16986,plain,
% 3.25/3.41 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16985, 16970])).
% 3.25/3.41 tff(16987,plain,
% 3.25/3.41 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[11389, 26, 16986])).
% 3.25/3.41 tff(16988,plain,
% 3.25/3.41 ($false),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16987, 16977, 11380])).
% 3.25/3.41 tff(16989,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(z)), s(z))) | (s(s(s(s(s(s(s(s(z)))))))) = s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.41 tff(16990,plain,
% 3.25/3.41 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16989, 16969, 16635, 16968, 16960, 16949, 16947])).
% 3.25/3.41 tff(16991,plain,
% 3.25/3.41 (~b(s(s(s(elem!1))), elem!1)),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16990, 16945])).
% 3.25/3.41 tff(16992,plain,
% 3.25/3.41 (r(s(s(s(elem!1))), elem!1)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1308, 16991, 16943])).
% 3.25/3.41 tff(16993,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16994,plain,
% 3.25/3.41 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(16995,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[16994])).
% 3.25/3.41 tff(16996,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.25/3.41 inference(transitivity,[status(thm)],[16995, 16993])).
% 3.25/3.41 tff(16997,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(16998,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[16997, 16996])).
% 3.25/3.41 tff(16999,plain,
% 3.25/3.41 (~r(z, s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[16998, 163, 1475, 1115, 405])).
% 3.25/3.41 tff(17000,plain,
% 3.25/3.41 (b(z, s(s(elem!1)))),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1094, 26, 16999, 1090])).
% 3.25/3.41 tff(17001,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 3.25/3.41 tff(17002,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(17003,plain,
% 3.25/3.41 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(17004,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 3.25/3.41 inference(monotonicity,[status(thm)],[17003])).
% 3.25/3.41 tff(17005,plain,
% 3.25/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.25/3.41 inference(transitivity,[status(thm)],[17004, 17002])).
% 3.25/3.41 tff(17006,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 3.25/3.41 inference(quant_inst,[status(thm)],[])).
% 3.25/3.41 tff(17007,plain,
% 3.25/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 3.25/3.41 inference(modus_ponens,[status(thm)],[17006, 17005])).
% 3.25/3.41 tff(17008,plain,
% 3.25/3.41 (~r(s(s(s(elem!1))), z)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[17007, 163, 1475, 1363, 405])).
% 3.25/3.41 tff(17009,plain,
% 3.25/3.41 (b(s(s(s(elem!1))), z)),
% 3.25/3.41 inference(unit_resolution,[status(thm)],[1295, 17008])).
% 3.25/3.41 tff(17010,plain,
% 3.25/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(17011,plain,
% 3.25/3.41 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.25/3.41 inference(rewrite,[status(thm)],[])).
% 3.25/3.41 tff(17012,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17011])).
% 3.25/3.42 tff(17013,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 3.25/3.42 inference(transitivity,[status(thm)],[17012, 17010])).
% 3.25/3.42 tff(17014,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 3.25/3.42 inference(quant_inst,[status(thm)],[])).
% 3.25/3.42 tff(17015,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17014, 17013])).
% 3.25/3.42 tff(17016,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17015, 198, 723, 17009, 17001, 17000])).
% 3.25/3.42 tff(17017,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.42 tff(17018,plain,
% 3.25/3.42 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17017, 16992, 16941, 16940, 16937, 16934])).
% 3.25/3.42 tff(17019,plain,
% 3.25/3.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1326, 17018, 16933])).
% 3.25/3.42 tff(17020,plain,
% 3.25/3.42 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17019, 16919])).
% 3.25/3.42 tff(17021,plain,
% 3.25/3.42 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[16916])).
% 3.25/3.42 tff(17022,plain,
% 3.25/3.42 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[16992, 17021])).
% 3.25/3.42 tff(17023,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), z) <=> r(elem!1, z)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[16938])).
% 3.25/3.42 tff(17024,plain,
% 3.25/3.42 (r(elem!1, z)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[16641, 17023])).
% 3.25/3.42 tff(17025,plain,
% 3.25/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17026,plain,
% 3.25/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.42 inference(quant_inst,[status(thm)],[])).
% 3.25/3.42 tff(17027,plain,
% 3.25/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17026, 17025])).
% 3.25/3.42 tff(17028,plain,
% 3.25/3.42 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17027, 163, 17024, 16920, 17022])).
% 3.25/3.42 tff(17029,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17028, 17020])).
% 3.25/3.42 tff(17030,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (z = elem!1) | b(elem!1, s(s(elem!1))) | r(z, s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.42 tff(17031,plain,
% 3.25/3.42 (b(s(s(elem!1)), elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17030, 85, 3, 330, 7255, 332])).
% 3.25/3.42 tff(17032,plain,
% 3.25/3.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17031, 16753])).
% 3.25/3.42 tff(17033,plain,
% 3.25/3.42 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17032, 16752])).
% 3.25/3.42 tff(17034,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[16720, 17033])).
% 3.25/3.42 tff(17035,plain,(b(elem!1, s(s(elem!1))) | (z = elem!1) | (~r(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.42 tff(17036,plain,
% 3.25/3.42 (b(elem!1, s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17035, 3, 332, 330, 7255])).
% 3.25/3.42 tff(17037,plain,
% 3.25/3.42 (~b(s(s(s(s(s(z))))), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[8803, 559, 16562, 16599])).
% 3.25/3.42 tff(17038,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3841, 17037])).
% 3.25/3.42 tff(17039,plain,
% 3.25/3.42 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10703, 163, 790, 16569, 17038])).
% 3.25/3.42 tff(17040,plain,
% 3.25/3.42 (b(s(s(elem!1)), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3497, 26, 16777, 3494])).
% 3.25/3.42 tff(17041,plain,
% 3.25/3.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10400, 163, 16569, 332, 17038])).
% 3.25/3.42 tff(17042,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9576, 17041])).
% 3.25/3.42 tff(17043,plain,
% 3.25/3.42 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10408, 163, 16569, 332, 17038])).
% 3.25/3.42 tff(17044,plain,
% 3.25/3.42 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9885, 17043])).
% 3.25/3.42 tff(17045,plain,
% 3.25/3.42 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[16668, 198, 348, 16609, 17044, 17042, 17040])).
% 3.25/3.42 tff(17046,plain,
% 3.25/3.42 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3400, 17045, 17039])).
% 3.25/3.42 tff(17047,plain,
% 3.25/3.42 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17046])).
% 3.25/3.42 tff(17048,plain,
% 3.25/3.42 (s(elem!1) = s(s(s(s(z))))),
% 3.25/3.42 inference(transitivity,[status(thm)],[135, 17047, 288])).
% 3.25/3.42 tff(17049,plain,
% 3.25/3.42 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17048])).
% 3.25/3.42 tff(17050,plain,
% 3.25/3.42 (elem!1 = s(s(s(z)))),
% 3.25/3.42 inference(transitivity,[status(thm)],[4242, 17049, 293])).
% 3.25/3.42 tff(17051,plain,
% 3.25/3.42 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17050])).
% 3.25/3.42 tff(17052,plain,
% 3.25/3.42 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17051])).
% 3.25/3.42 tff(17053,plain,
% 3.25/3.42 ((~r(s(s(s(z))), s(z))) <=> (~r(elem!1, s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17052])).
% 3.25/3.42 tff(17054,plain,
% 3.25/3.42 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17049])).
% 3.25/3.42 tff(17055,plain,
% 3.25/3.42 (s(s(s(z))) = elem!1),
% 3.25/3.42 inference(transitivity,[status(thm)],[294, 17054, 129])).
% 3.25/3.42 tff(17056,plain,
% 3.25/3.42 (b(s(s(s(z))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17055])).
% 3.25/3.42 tff(17057,plain,
% 3.25/3.42 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17056])).
% 3.25/3.42 tff(17058,plain,
% 3.25/3.42 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17057])).
% 3.25/3.42 tff(17059,plain,
% 3.25/3.42 (~r(s(s(z)), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10767, 163, 790, 16569, 332])).
% 3.25/3.42 tff(17060,plain,
% 3.25/3.42 (b(s(s(z)), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[2161, 26, 17059, 2154])).
% 3.25/3.42 tff(17061,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17062,plain,
% 3.25/3.42 (((~b(s(s(z)), s(s(elem!1)))) | (~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(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17063,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17062])).
% 3.25/3.42 tff(17064,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.25/3.42 inference(transitivity,[status(thm)],[17063, 17061])).
% 3.25/3.42 tff(17065,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))))),
% 3.25/3.42 inference(quant_inst,[status(thm)],[])).
% 3.25/3.42 tff(17066,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17065, 17064])).
% 3.25/3.42 tff(17067,plain,
% 3.25/3.42 (~b(elem!1, s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17066, 198, 68, 17060, 17040])).
% 3.25/3.42 tff(17068,plain,
% 3.25/3.42 (~b(s(s(s(z))), s(s(z)))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17067, 17058])).
% 3.25/3.42 tff(17069,plain,
% 3.25/3.42 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17055])).
% 3.25/3.42 tff(17070,plain,
% 3.25/3.42 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 3.25/3.42 inference(transitivity,[status(thm)],[17069, 6630])).
% 3.25/3.42 tff(17071,plain,
% 3.25/3.42 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17070])).
% 3.25/3.42 tff(17072,plain,
% 3.25/3.42 ((~(s(s(z)) = elem!1)) <=> (~(s(s(s(z))) = s(s(z))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17071])).
% 3.25/3.42 tff(17073,plain,
% 3.25/3.42 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17055])).
% 3.25/3.42 tff(17074,plain,
% 3.25/3.42 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17073])).
% 3.25/3.42 tff(17075,plain,
% 3.25/3.42 (~(s(z) = elem!1)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[10804, 17074])).
% 3.25/3.42 tff(17076,plain,
% 3.25/3.42 (~(s(s(z)) = elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9862, 17075, 17046])).
% 3.25/3.42 tff(17077,plain,
% 3.25/3.42 (~(s(s(s(z))) = s(s(z)))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17076, 17072])).
% 3.25/3.42 tff(17078,plain,
% 3.25/3.42 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10849, 26])).
% 3.25/3.42 tff(17079,plain,
% 3.25/3.42 (r(s(s(s(z))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17078, 17077, 17068])).
% 3.25/3.42 tff(17080,plain,
% 3.25/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17081,plain,
% 3.25/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.25/3.42 inference(quant_inst,[status(thm)],[])).
% 3.25/3.42 tff(17082,plain,
% 3.25/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17081, 17080])).
% 3.25/3.42 tff(17083,plain,
% 3.25/3.42 (~r(s(s(s(z))), s(z))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17082, 163, 15191, 17079, 3450])).
% 3.25/3.42 tff(17084,plain,
% 3.25/3.42 (~r(elem!1, s(z))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17083, 17053])).
% 3.25/3.42 tff(17085,plain,
% 3.25/3.42 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(z))),
% 3.25/3.42 inference(transitivity,[status(thm)],[17073, 1241])).
% 3.25/3.42 tff(17086,plain,
% 3.25/3.42 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17085])).
% 3.25/3.42 tff(17087,plain,
% 3.25/3.42 (~(elem!1 = s(z))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[10804, 17086])).
% 3.25/3.42 tff(17088,plain,
% 3.25/3.42 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17050])).
% 3.25/3.42 tff(17089,plain,
% 3.25/3.42 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17088])).
% 3.25/3.42 tff(17090,plain,
% 3.25/3.42 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17089])).
% 3.25/3.42 tff(17091,plain,
% 3.25/3.42 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17055])).
% 3.25/3.42 tff(17092,plain,
% 3.25/3.42 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17091])).
% 3.25/3.42 tff(17093,plain,
% 3.25/3.42 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17046])).
% 3.25/3.42 tff(17094,plain,
% 3.25/3.42 (b(elem!1, s(s(s(s(s(z))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[68, 17093])).
% 3.25/3.42 tff(17095,plain,
% 3.25/3.42 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17094, 17092])).
% 3.25/3.42 tff(17096,plain,
% 3.25/3.42 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[14210, 198, 6262, 559])).
% 3.25/3.42 tff(17097,plain,
% 3.25/3.42 (~b(s(s(s(z))), s(z))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17096, 17095])).
% 3.25/3.42 tff(17098,plain,
% 3.25/3.42 (~b(elem!1, s(z))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17097, 17090])).
% 3.25/3.42 tff(17099,plain,
% 3.25/3.42 (r(elem!1, s(z))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[242, 17098, 17087])).
% 3.25/3.42 tff(17100,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17099, 17084])).
% 3.25/3.42 tff(17101,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.42 tff(17102,plain,
% 3.25/3.42 (~r(s(s(elem!1)), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17101, 17036, 16639, 16637, 16635, 16605, 5276, 332])).
% 3.25/3.42 tff(17103,plain,
% 3.25/3.42 (b(s(s(elem!1)), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[801, 17102])).
% 3.25/3.42 tff(17104,plain,
% 3.25/3.42 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[16653, 17103, 16599, 330])).
% 3.25/3.42 tff(17105,plain,
% 3.25/3.42 (s(s(s(s(s(z))))) = elem!1),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10750, 17104])).
% 3.25/3.42 tff(17106,plain,
% 3.25/3.42 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17105])).
% 3.25/3.42 tff(17107,plain,
% 3.25/3.42 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17106])).
% 3.25/3.42 tff(17108,plain,
% 3.25/3.42 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17107])).
% 3.25/3.42 tff(17109,plain,
% 3.25/3.42 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17108])).
% 3.25/3.42 tff(17110,plain,
% 3.25/3.42 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(elem!1)))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17109])).
% 3.25/3.42 tff(17111,plain,
% 3.25/3.42 ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(elem!1))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17110])).
% 3.25/3.42 tff(17112,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17105])).
% 3.25/3.42 tff(17113,plain,
% 3.25/3.42 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) <=> (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17112])).
% 3.25/3.42 tff(17114,plain,
% 3.25/3.42 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[16614, 17113])).
% 3.25/3.42 tff(17115,plain,
% 3.25/3.42 (~b(elem!1, s(s(elem!1)))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17114, 17111])).
% 3.25/3.42 tff(17116,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17036, 17115])).
% 3.25/3.42 tff(17117,plain,((z = elem!1) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.42 tff(17118,plain,
% 3.25/3.42 (z = elem!1),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17117, 330, 9544, 7255])).
% 3.25/3.42 tff(17119,plain,
% 3.25/3.42 (s(z) = s(elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17118])).
% 3.25/3.42 tff(17120,plain,
% 3.25/3.42 (s(s(z)) = s(s(elem!1))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17119])).
% 3.25/3.42 tff(17121,plain,
% 3.25/3.42 (s(s(elem!1)) = s(s(z))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17120])).
% 3.25/3.42 tff(17122,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17121])).
% 3.25/3.42 tff(17123,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.25/3.42 inference(symmetry,[status(thm)],[17122])).
% 3.25/3.42 tff(17124,plain,
% 3.25/3.42 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[16613, 330, 9544])).
% 3.25/3.42 tff(17125,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3098, 17124])).
% 3.25/3.42 tff(17126,plain,
% 3.25/3.42 (~r(s(s(s(s(s(z))))), s(z))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[11684, 17125, 16566, 16601])).
% 3.25/3.42 tff(17127,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(z))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[469, 17126])).
% 3.25/3.42 tff(17128,plain,
% 3.25/3.42 (~b(s(s(s(s(s(z))))), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[8803, 17127, 16562, 16597])).
% 3.25/3.42 tff(17129,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3841, 17128])).
% 3.25/3.42 tff(17130,plain,
% 3.25/3.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10400, 163, 16569, 9544, 17129])).
% 3.25/3.42 tff(17131,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9576, 17130])).
% 3.25/3.42 tff(17132,plain,
% 3.25/3.42 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17131, 17123])).
% 3.25/3.42 tff(17133,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17118])).
% 3.25/3.42 tff(17134,plain,
% 3.25/3.42 (r(s(s(s(s(s(z))))), elem!1)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17129, 17133])).
% 3.25/3.42 tff(17135,plain,
% 3.25/3.42 (~b(elem!1, s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[71, 17118, 16564])).
% 3.25/3.42 tff(17136,plain,
% 3.25/3.42 (elem!1 = z),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[78, 17118])).
% 3.25/3.42 tff(17137,plain,
% 3.25/3.42 (~b(z, s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[87, 17136, 17135])).
% 3.25/3.42 tff(17138,plain,
% 3.25/3.42 (~r(z, elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[7300, 17118])).
% 3.25/3.42 tff(17139,plain,
% 3.25/3.42 (~(elem!1 = s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[110, 17138, 17137])).
% 3.25/3.42 tff(17140,plain,
% 3.25/3.42 (r(elem!1, s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[147, 17135, 17139])).
% 3.25/3.42 tff(17141,plain,
% 3.25/3.42 (s(elem!1) = s(z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1646, 17136])).
% 3.25/3.42 tff(17142,plain,
% 3.25/3.42 (~r(z, s(elem!1))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[3240, 17141, 16596])).
% 3.25/3.42 tff(17143,plain,
% 3.25/3.42 (b(z, s(elem!1))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1791, 17142])).
% 3.25/3.42 tff(17144,plain,
% 3.25/3.42 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17119])).
% 3.25/3.42 tff(17145,plain,
% 3.25/3.42 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[16566, 17144])).
% 3.25/3.42 tff(17146,plain,
% 3.25/3.42 (~(s(s(elem!1)) = elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[118, 17139])).
% 3.25/3.42 tff(17147,plain,
% 3.25/3.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1250, 17146])).
% 3.25/3.42 tff(17148,plain,
% 3.25/3.42 (b(s(elem!1), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1209, 17118, 16562])).
% 3.25/3.42 tff(17149,plain,
% 3.25/3.42 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[2942, 17118, 16601])).
% 3.25/3.42 tff(17150,plain,
% 3.25/3.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1032, 17136, 330])).
% 3.25/3.42 tff(17151,plain,
% 3.25/3.42 (b(z, s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17118])).
% 3.25/3.42 tff(17152,plain,
% 3.25/3.42 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[16553, 17151])).
% 3.25/3.42 tff(17153,plain,
% 3.25/3.42 (r(s(s(s(elem!1))), elem!1)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[11114, 17152, 17150, 17149, 17148, 17147, 17145, 17143, 17118])).
% 3.25/3.42 tff(17154,plain,
% 3.25/3.42 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[11121, 163, 17153, 17140, 17134])).
% 3.25/3.42 tff(17155,plain,
% 3.25/3.42 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[2619, 17147])).
% 3.25/3.42 tff(17156,plain,
% 3.25/3.42 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[4899, 17155, 17118])).
% 3.25/3.42 tff(17157,plain,
% 3.25/3.42 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[4903, 26, 17156, 17154])).
% 3.25/3.42 tff(17158,plain,
% 3.25/3.42 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17120])).
% 3.25/3.42 tff(17159,plain,
% 3.25/3.42 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[10408, 163, 16569, 9544, 17129])).
% 3.25/3.42 tff(17160,plain,
% 3.25/3.42 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9885, 17159])).
% 3.25/3.42 tff(17161,plain,
% 3.25/3.42 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17160, 17158])).
% 3.25/3.42 tff(17162,plain,
% 3.25/3.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1263, 17147])).
% 3.25/3.42 tff(17163,plain,
% 3.25/3.42 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1270, 17162])).
% 3.25/3.42 tff(17164,plain,
% 3.25/3.42 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17118])).
% 3.25/3.42 tff(17165,plain,
% 3.25/3.42 (~b(s(s(elem!1)), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[9564, 17136, 8234])).
% 3.25/3.42 tff(17166,plain,
% 3.25/3.42 (r(s(s(elem!1)), z)),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[801, 17165])).
% 3.25/3.42 tff(17167,plain,
% 3.25/3.42 (r(s(s(elem!1)), elem!1)),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17166, 17164])).
% 3.25/3.42 tff(17168,plain,
% 3.25/3.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[11133, 163, 17167, 17153, 17140])).
% 3.25/3.42 tff(17169,plain,
% 3.25/3.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1326, 17168, 17163])).
% 3.25/3.42 tff(17170,plain,
% 3.25/3.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1372, 17153, 17140, 17167])).
% 3.25/3.42 tff(17171,plain,
% 3.25/3.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[1377, 17170, 17162])).
% 3.25/3.42 tff(17172,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17173,plain,
% 3.25/3.42 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(rewrite,[status(thm)],[])).
% 3.25/3.42 tff(17174,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 3.25/3.42 inference(monotonicity,[status(thm)],[17173])).
% 3.25/3.42 tff(17175,plain,
% 3.25/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 3.25/3.42 inference(transitivity,[status(thm)],[17174, 17172])).
% 3.25/3.42 tff(17176,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.25/3.42 inference(quant_inst,[status(thm)],[])).
% 3.25/3.42 tff(17177,plain,
% 3.25/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 3.25/3.42 inference(modus_ponens,[status(thm)],[17176, 17175])).
% 3.25/3.42 tff(17178,plain,
% 3.25/3.42 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17177, 198, 17171, 17169, 17161, 17157])).
% 3.25/3.42 tff(17179,plain,
% 3.25/3.42 ($false),
% 3.25/3.42 inference(unit_resolution,[status(thm)],[17178, 17132])).
% 3.25/3.42 tff(17180,plain,((~b(s(s(s(s(s(s(s(z))))))), z)) | b(s(s(z)), z) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.43 tff(17181,plain,
% 3.25/3.43 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17180, 8234, 7255])).
% 3.25/3.43 tff(17182,plain,
% 3.25/3.43 (r(s(s(s(s(s(s(s(z))))))), z)),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[176, 17181])).
% 3.25/3.43 tff(17183,plain,
% 3.25/3.43 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[15579, 163, 15191, 16566, 422])).
% 3.25/3.43 tff(17184,plain,
% 3.25/3.43 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[9643, 17183])).
% 3.25/3.43 tff(17185,plain,
% 3.25/3.43 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[15522, 163, 15191, 16566, 422])).
% 3.25/3.43 tff(17186,plain,
% 3.25/3.43 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[3098, 17185])).
% 3.25/3.43 tff(17187,plain,
% 3.25/3.43 (~b(z, s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[10515, 198, 17186, 16553, 17184])).
% 3.25/3.43 tff(17188,plain,
% 3.25/3.43 (r(z, s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[4110, 17187])).
% 3.25/3.43 tff(17189,plain,
% 3.25/3.43 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[10000, 17188, 16569, 422])).
% 3.25/3.43 tff(17190,plain,
% 3.25/3.43 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[9885, 17189])).
% 3.25/3.43 tff(17191,plain,
% 3.25/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.43 inference(rewrite,[status(thm)],[])).
% 3.25/3.43 tff(17192,plain,
% 3.25/3.43 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.43 inference(rewrite,[status(thm)],[])).
% 3.25/3.43 tff(17193,plain,
% 3.25/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 3.25/3.43 inference(monotonicity,[status(thm)],[17192])).
% 3.25/3.43 tff(17194,plain,
% 3.25/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.43 inference(transitivity,[status(thm)],[17193, 17191])).
% 3.25/3.43 tff(17195,plain,
% 3.25/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 3.25/3.43 inference(quant_inst,[status(thm)],[])).
% 3.25/3.43 tff(17196,plain,
% 3.25/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 3.25/3.43 inference(modus_ponens,[status(thm)],[17195, 17194])).
% 3.25/3.43 tff(17197,plain,
% 3.25/3.43 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17196, 163, 332, 152, 17188])).
% 3.25/3.43 tff(17198,plain,
% 3.25/3.43 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[374, 17197])).
% 3.25/3.43 tff(17199,plain,
% 3.25/3.43 ($false),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[11330, 198, 17186, 17198, 17190, 17184])).
% 3.25/3.43 tff(17200,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.43 tff(17201,plain,
% 3.25/3.43 (~r(s(s(s(s(s(z))))), s(z))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17200, 9544, 17182])).
% 3.25/3.43 tff(17202,plain,
% 3.25/3.43 (b(s(s(s(s(s(z))))), s(z))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[469, 17201])).
% 3.25/3.43 tff(17203,plain,
% 3.25/3.43 (~b(s(s(s(s(s(z))))), z)),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[8803, 17202, 16562, 16597])).
% 3.25/3.43 tff(17204,plain,
% 3.25/3.43 (r(s(s(s(s(s(z))))), z)),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[3841, 17203])).
% 3.25/3.43 tff(17205,plain,
% 3.25/3.43 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[16274, 9544, 16566])).
% 3.25/3.43 tff(17206,plain,
% 3.25/3.43 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[420, 17205])).
% 3.25/3.43 tff(17207,plain,
% 3.25/3.43 (~r(s(s(s(s(s(z))))), s(z))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17200, 332, 152])).
% 3.25/3.43 tff(17208,plain,
% 3.25/3.43 (b(s(s(s(s(s(z))))), s(z))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[469, 17207])).
% 3.25/3.43 tff(17209,plain,
% 3.25/3.43 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[15850, 3272, 152])).
% 3.25/3.43 tff(17210,plain,
% 3.25/3.43 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[3613, 17209])).
% 3.25/3.43 tff(17211,plain,
% 3.25/3.43 (~b(z, s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[10469, 198, 16599, 17210, 16553, 17208])).
% 3.25/3.43 tff(17212,plain,
% 3.25/3.43 (r(z, s(s(s(s(s(z))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[4110, 17211])).
% 3.25/3.43 tff(17213,plain,
% 3.25/3.43 ($false),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17196, 163, 3272, 332, 152, 17212])).
% 3.25/3.43 tff(17214,plain,((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.43 tff(17215,plain,
% 3.25/3.43 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17214, 9544, 17182])).
% 3.25/3.43 tff(17216,plain,
% 3.25/3.43 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[374, 17215])).
% 3.25/3.43 tff(17217,plain,
% 3.25/3.43 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[3882, 17204, 16569, 17182])).
% 3.25/3.43 tff(17218,plain,
% 3.25/3.43 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[3098, 17217])).
% 3.25/3.43 tff(17219,plain,
% 3.25/3.43 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[4991, 198, 17218, 17216, 17206])).
% 3.25/3.43 tff(17220,plain,
% 3.25/3.43 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[9576, 17219])).
% 3.25/3.43 tff(17221,plain,
% 3.25/3.43 ($false),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[568, 163, 16569, 9544, 17220, 17204])).
% 3.25/3.43 tff(17222,plain,(b(s(s(z)), z) | r(z, s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 3.25/3.43 tff(17223,plain,
% 3.25/3.43 (r(z, s(s(s(s(s(s(s(z))))))))),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[17222, 16592])).
% 3.25/3.43 tff(17224,plain,
% 3.25/3.43 ($false),
% 3.25/3.43 inference(unit_resolution,[status(thm)],[16298, 17223, 16593, 16566])).
% 3.25/3.43 % SZS output end Proof
% 3.25/3.43 % E exiting
%------------------------------------------------------------------------------